Arabic_Origins_of_Cryptology4

Series on
Arabic Origins of Cryptology
Volume Four
ibn Dunaynir's Book:
Expositive Chapters on
Cryptanalysis
(Maq id al-Fu l al-Mutar ima an all at-Tar ama)
Series Editors
M. Mrayati, Ph.D.
Y. Meer Alam, Ph.D. M. H. at-Tayyan, Ph.D.
Published by
KFCRIS & KACST

Acknowledgments
The editors of this series greatly appreciate the encouragement they
had from Dr. Yahya Mahmoud Ben Jonayd, Secretary General of
King Faisal Center for Research and Islamic Studies, to publish this
Series. We are also in the debt to Dr. Saleh Athel, the president of
King Abdulaziz City for Science and Technology (KACST), for
supporting the project of translating this series to English.
Many thanks to Dr. Daham Ismail Alani, the Secretary General of the
Scientific Council of KACST, for all his efforts to make this
publication possible.
The typesetting of this bilingual version of the series was realized with
skill and dedication by Mr. Ousama Rajab; we offer hearty thanks to
him.
Finally, we would like to mention our recognition to the many who
had previously contributed to the Arabic version of this series, and
particularly to Dr. Wathek Shaheed, Dr. Shaker al-Faham, the late
Prof. Rateb an-Naffakh, and Dr. Fouad Sezgin.

Series on
Arabic Origins of Cryptology
Volume 4
Translated by
Said M. al-Asaad
Revised by
Mohammed I. al-Suwaiyel, Ph.D.
Ibrahim A. al-Kadi, Ph.D.
Marwan al-Bawab

Contents
List of Figures .…........................................................................... vii
List of Tables ......…….................................................................... viii
Transliterating Arabic words ....................................................... ix
Preface ............................................................................................ xi
Section 1: Analytical Study of ibn Dunayn r’s Book:
Expositive Chapters on Cryptanalysis ....................... 1
1.1. Biography of ibn Dunayn r ......................…........................... 3
1.2. Study and Analysis of ibn Dunayn r’s Book .......................... 5
1.2.1. ibn Dunayn r’s Sources .................................................... 5
1.2.2. ibn Dunayn r’s Cryptological Practice ............................. 8
1.3. Structure of the Book ............................................................. 10
1.3.1. Cryptanalysis of Prose Ciphers ...................................... 11
1.3.1.1. Principles and Tools of Cryptanalysis ...............… 11
1.3.1.2. Types of Encipherment .........................…............. 13
1.3.1.3. Algorithms of Cryptanalysis ….............................. 15
1.3.1.4. Composite Encipherment ....................................... 32
1.3.2. Cryptanalysis of Poetry Ciphers .................................... 47
1.3.2.1. Tools for Cryptanalysing Poetry Ciphers .............. 48
1.3.2.2. On Prosody (Metrics) ............................…............ 49
1.3.2.3. On Rhymes ....................….................................... 49
1.3.2.4. Insight into Writing Knack ...…............................. 50
1.3.2.5. Other Useful Observations .................................... 53
1.3.2.6. Practical Examples .................…........................... 54
1.3.2.7. Conclusion ............................................................. 56
1.4. Originality of ibn Dunayn r .................................................. 58
v

Section 2: ibn Dunayn r’s Edited Book:
Expositive Chapters on Cryptanalysis ...................... 60
2.1. Editing Methodology .............................................................62
2.2. Description of the Manuscript ............................................... 63
2.3. ibn Dunayn r’s Book (Original Arabic Text and English
Translation) ............................................................................ 67
PART ONE. Cryptanalysis of Prose Ciphers ........................... 70
� Principles and Tools of Cryptanalysis (Chapters 1-2) ..... 72
� Types of Encipherment
- Simple (Chapters 3-5) ............................................... 76
- Composite (Chapter 6) .............................................. 82
� Algorithms of Cryptanalysis (Chapters 7-35) ................ 84
PART TWO. Cryptanalysis of Poetry Ciphers ........................142
� Tools for Cryptanalysing Poetry Ciphers
(Chapters 36-37) ......................................................... 142
� On Prosody (Chapters 38-40) ........................................ 144
� On Rhymes (Chapter 41) ............................................... 148
� Writing Knack (Chapters 42-52) ................................... 154
� Other Useful Observations (Chapters 53-59) ................ 168
- Comment on an important cipher method from The
Two Essays (Chapter 60) ................................... 176
� Practical Examples (Chapters 61-62) ............................ 178
� Conclusion (Chapters 63-66) ......................................... 184
vi

List of Figures
1.1. ibn Dunayn r's types of encipherment ........................................ 14
1.2. Encipherment by numerical processing using ADWNA .......... . 40
2.1. A photocopy of the first sheet of ibn Dunayn r's book ............... 64
2.2. A photocopy of the second sheet of ibn Dunayn r's book ......... 65
2.3. A photocopy of the last sheet of ibn Dunayn r's book ........….. 66
vii

List of Tables
1.1. ibn Dunayn r's work on the orders of letter frequency
(statistical cryptanalysis) .......................................................... 18
1.2. Noncombinable letters (in texts) as observed by ibn Dunayn r
(without repetition) .................................................................. 22
1.3. Noncombinable letters (in texts) according to ibn Dunayn r,
arranged alphabetically (with repetition) ................................. 23
1.4. Noncombinable letters as demonstrated in our statistical
analysis of Arabic roots ........................................................... 24
1.5. Table of noncombinable letters as observed by al-Kind ......... 25
1.6. Numerical values of letters ....................................................... 36
1.7. Finger-spelling using ADWNA ................................................ 38
1.8. The first of ibn Dunayn r's two practical examples .................. 55
1.9. The second of ibn Dunayn r's two practical examples ............. 56
viii

Transliterating Arabic words
For transliterating Arabic words (names, titles, etc.) we have adopted the
International System for the Transliteration of Arabic characters, devised by the
International Standards Organization (ISO). The system constitutes ISO
Recommendation R233 (December 1961). Given below is this system, with some
additional explanations found to be necessary.
Vowels:
Short
Vowels
Long
Vowels
Arabic characters Transliteration Examples
(fat a) a as u in cup.
( amma) u
(kasra) i
ix
as o in rock,
and u in put.
as e in red,
and i in big.
As a in last.
ٚ (preceded by ) as oo in moon.
ٞ (preceded by ) as ee in sheet.
Consonants:
Arabic
characters
Transliteration Examples
' (e.g. 'amr, 'ibr h m, fu' d, kis ' , t ').
ة b as b in back.
د t as t in tea.
س as th in thin.
ط as g in logic.
ػ (e.g. tim).
ؿ (e.g. lid).
ك d as d in day.
م as th in then.
ه r as r in red.
as a in add (e.g. ' dam, qur' n).

ى z as z in zoo.
ً s as s in soon.
ُ as sh in show.
ص (e.g. mi r).
ض (e.g. ir r).
ط (e.g. riq).
ظ (e.g. fir).
ع (e.g. Abb s).
ؽ (e.g. lib).
ف f as f in few.
ق q (e.g. qur' n).
ن k as k in key.
ي l as l in led.
َ m as m in sum.
ْ n as n in sun.
ـ٘ h as h in hot.
ٚ w as w in wet (e.g. wahab, nawfal).
ٞ y as ie in orient (e.g. y q t, dunayn r).
Notes:
(t ' marb a): In the absolute state, ignored in transliteration (e.g. mad na); in
the construct state, rendered by (t) (mad nat annab ).
(suk n): Ignored in transliteration.
( adda): Rendered by doubling the consonant.
x

Preface
This is the fourth book of The Arabic Origins of Cryptology series,
which addresses the cryptological contributions of the Arabs, and
translates a number of treatises by Arab cryptologists.
An individual book is dedicated to each treatise. The first book was
devoted to the oldest ever found treatise on cryptanalysis, written by
the well-known Arab philosopher al-Kind about 1200 years ago. The
second book of the series tackles ibn Adl n's treatise al-mu'allaf lilmalik
al-'A raf (The manual written for King al-A raf). The third
book deals with ibn ad-Durayhim's treatise Mift al-Kun z f al-
Marm z (Key to treasures on clarifying ciphers), while the fourth
book (this one) covers ibn Dunayn r's work. For the time being, nine
books are envisaged, unless more manuscripts are discovered.
In Book One we have devoted a full chapter to study and analyse
the birth of cryptology by the Arab civilization. This would highlight
important aspects and prove useful for understanding the whole series.
* * *
This book is divided into two sections. Section 1 is an analytical
study of the edited book of ibn Dunayn r. It aims at introducing the
book and elucidating difficult or vague points, spotting particular
features and, more remarkably, highlighting aspects of originality and
innovation in ibn Dunayn r's book. This section is divided into four
sub-sections: one gives a brief biography of ibn Dunayn r, another
provides an account of his sources and cryptological practice, a third
details the structure of the book as regards cryptanalysis of both prose
and poetry ciphers, and a fourth sub-section summing up the
analytical study of the book, exposing ibn Dunayn r's cryptological
contributions and aspects of originality.
Section 2 comprises an English translation of the original Arabic
text of ibn Dunayn r's edited book. It opens with a statement outlining
the editing methodology adopted, which basically conforms to that
commonly used by the scientific community. The edited book is
xi

preceded by a brief description of the manuscript, followed by sample
photocopies of selected pages from the original.
The task of editing the manuscript text was a challenge indeed.
Special care has been taken to present the text in due form. The
English translation appears on the left-hand (even) pages, and the
original Arabic text on the right-hand (odd) pages. No effort has been
spared correcting the mistakes and clearing the ambiguities. For ease
of reference, individual chapters have been assigned numbers (by the
editors). Wherever appropriate, lead-in headings have been
introduced.
Damascus, May 2005
* * *
Dr. M. Mrayati
Dr. Y. Meer Alam Dr. M. H. Tayyan
xii

Section 1
Analytical Study of ibn Dunayn r's Book:
Expositive Chapters on Cryptanalysis
(Maq id al-Fu l al-Mutar ima an all at-Tar ama)

1.1. Biography of ibn Dunaynir
He is 'Ibr h m ibn Mu ammad ibn 'Ibr h m ibn Al ibn Hibat
All h ibn Y suf ibn Na r ibn 'A mad, alias ibn Dunayn r 1 al-La m ,
son of King Q b s ibn al-Mun ir ibn M ' as-Sam '. Born in Mosul in
AH 583/ AD 1187, he lived during the reign of King a - hir z ,
son of Sultan Saladin, and governor of Aleppo and its administrative
districts (d. AH 613/ AD 1216). He was in the employ of Prince Asad
ad-D n A mad ibn Abdull h al-Muhr n on whom he made
panegyrics. He was then reported to have worked for N ir ad-D n
Mu ammad ibn 'Ayy b, king of Egypt (d. AH 635/AD 1238).
ibn Dunayn r journeyed between Greater Syria and Egypt and
lauded a number of kings and notobilities there. His life ended at the
hands of King al- Az z U m n ibn al-Malik al- dil, who crucified
him in as-Subayta Fort near Banyas in the year AH 627/ AD 1229.
His works
According to his biographies, ibn Dunayn r wrote primarily in the
following two fields:
a) Poetry, in which he wrote two books, i.e. his own poetical
collection (divan), and al-K f ilm al-qaw f (Sufficiency in the
science of rhymes), which is still missing.
b) Cryptology, the science in which he excelled and was particularly
well-known. a - afad [a biographer and historian, d. AH 764/
AD 1363] has mentioned two books on cryptology by ibn
Dunayn r, i.e.
1. a - ih b an-n im f ilm wa at-tar im (The shooting star
in the science of making ciphers), also numbered among the
missing compilations. ibn Dunayn r, however, refers to it in
Maq id al-fu l. 2
1 Diminutive of dinar ـــa unit of currency.
2 See p.98.
3

2. Maq id al-fu l al-mutar ima an all at-tar ama
(Expositive chapters on cryptanalysis) ـــthe subject of this
volume of the series.
4

1.2. Study and Analysis of ibn Dunaynir's Book
This study involves a general review of ibn Dunayn r's Maq id
al-Fu l al-Mutar ima an all at-Tar ama, along the same lines as
in the previous treatises. Thus, the book is to be analysed according to
the order of topics that it covers. It has been found useful to add, in
square brackets, explicatory headings to the already numbered
chapters of the edited text. This would make life easier for the reader,
and mark the sequence of ideas. A full analysis of every chapter is
provided, along with illustrative examples where necessary, to rule out
any possibility of ambiguity that might be encountered especially by
nonprofessionals. It is only natural, on our part, to highlight ibn
Dunayn r's novel additions to the contributions of his predecessors,
and point out his refinements of already existing ideas. A brief
appraisal is also given for each of the chapters of his book, then to
conclude with a statement manifesting the aspects of ibn Dunayn r's
originality.
1.2.1. ibn Dunaynir's Sources
In his book, ibn Dunayn r has attained a high degree of excellence
as regards his extensive knowledge, precise methodology, and wellorganized
access to both cryptography and cryptanalysis. His sound
systematic approach is in fact an outcome of a broad personal
knowledge of the work of his predecessors in this art; he manages to
make full use of their efforts, to set straight their mistakes, to redress
their omissions, as well as to add his own new contributions. ibn
Dunayn r's scientific method is reflected in that he considers
cryptography and cryptanalysis as separate sciences, each having its
own set of principles and concepts. He demonstrates this distinction
particularly in the designation of two of his compilations, namely a -
ih b an-n im f ilm wa at-tar im, which is dedicated to
cryptography, and Maq id al-fu l al-mutar ima an all attar
ama, devoted to cryptanalysis ـــa fact revealing his insistence on
treating them as separate sciences. In this respect he precedes ibn ad-
Durayhim (d. AH 762/ AD 1361) who states in his treatise Mift alkun
z f ' al-marm z, describing the cryptologue's tools: "It is
5

necessary for one experiencing cryptanalysis to develop a thorough
knowledge…" 3
ibn Dunayn r seems keen to glean and marshal whatever earlier
manuscripts he has run down of this science. He does proclaim that he
quoted from al-Kind , and from "the Author of the Two Essays", as
well as from Ab al- asan ibn ab ab (d. AH 322/ AD 934). It is
also likely that he tapped the works of ibn Wahab al-K tib and the
author of the book Adab a - u ar ' (The art of poets), among other
great figures of this art who lived between the third and sixth centuries
of the Hegira (9 th - 12 th AD). This is so because ibn Dunayn r's
professional scientific life began in the early part of the seventh
century of the Hegira.
But his main source is really al-Kind 's treatise on cryptanalysis
(Volume One of this series). He leans heavily on it and quotes much
of its contents, yet he has been shrewd enough to adjust and modify
what he takes, bidding fair to succeed at times, and falling wide of the
mark at other times. He does well in explaining the points summed up
by al-Kind , while he misses the mark in overlooking some things that
al-Kind mentions. In this context, ibn Dunayn r's citations are not a
slavish indiscriminate repetition, but a leisurely premeditated practice
based on verification and experimentation. For example, he does not
only cite al-Kind 's computation of letter frequency of occurrence and
the resultant orders, but also emulates him in reckoning the letters of
texts that appear in some sheets, and setting the letters in order, as per
his own calculations, and in substantiation of al-Kind 's results. At the
beginning of Chapter 8 of his book, ibn Dunayn r says: "I have
considered the orders of letter frequencies according to the reckoning
of Ya q b al-Kind , peace be on his soul. He said he had turned to
seven parchments and counted all the orders of letter frequency of
occurrence in them … It so occurred to me to take up [other] written
sheets myself and count the letter frequency orders in them … So it
came home to me the validity of the statement of Ya q b ibn 'Is q,
peace be on his soul." 4
The fact that ibn Dunayn r adapts his quotations from al-Kind is
maintained by his own statement: "and I abridged that considerably
3 See his treatise, Volume Three of this series, p.52.
4 See his book, p.86.
6

such that my version should suffice instead of al-Kind 's treatise and
its long-winded prolixity." 5 This very account, however, remains a
moot point, since al-Kind 's treatise is, by rights, a typical example of
conciseness, concentration and richness ـــa fact which denies the
claim of any substitute that can do duty for it, and which refutes any
redundance in it, with the exception perhaps of some repetition
marking his treatment of letter non-combination.
ibn Dunayn r's enlargement on al-Kind 's text, and also his
acquaintance with the bulk of material written on the subject, are
evident in his discussion of composite encipherment. He says that
al-Kind did not in the least touch upon it, and that those who dealt
with it later fumbled and disarranged things. He adds: "But I
mentioned a good few of them [i.e. composite ciphers] to serve as a
guideline in deciding on unmentioned cases, if any. al-Kind never
attended to composite encipherment except incidentally [without
dwelling on details]. Whoever attempted to deal with it, other than
al-Kind , certainly raved and went astray on that score…". 6
By the same token, ibn Dunayn r proposes novel ideas overlooked
by his predecessors for some reason. For example his approach to
encipherment by utilizing the chessboard to communicate with
someone who is present, and his notion of the possibility of
developing it so as to convey a cipher message to an absent person. As
he puts it: "It [chessboard encipherment] may be employed to address
an absent person in a way I shall tell you without precedent." 7
Among those whom ibn Dunayn r proclaims to have drawn on and
quoted is the Author of the Two Essays. This is manifested in his own
words: "Towards the end of his Second Essay, the Author of the Two
Essays on cryptanalysis states that we are destined to follow an
intricate path." 8 This is the second of ibn Dunayn r's sources.
The third reference is Ab al- asan ibn ab ab 's Treatise on
Cryptanalysis. ibn Dunayn r writes: "I have [herein] adduced
something novel that none else had ever broached before, because
5 See his book, p.94.
6 Ibid., p.108.
7 Ibid., p.120.
8 Ibid., p.176.
7

al-Kind 's book [treatise] tackles prose simple encipherment only; and
Ab al- asan's book treats poetry encipherment. Both failed to
develop the topic exhaustively in either case." 9
This shows that ibn Dunayn r is keen to explicitly bring his own
new and original views to notice, insomuch that he asserts that none
had ever before him taken the lead in introducing them. His keenness
is all-often associated with observing the concepts that his
predecessors overlooked, or imperfectly handled, or those that eluded
their attention. It seems that he opts to cite some of his references
especially to point out any one of these implications. Upon comparing
ibn Dunayn r's work with that of the author of Adab a - u ar ' (in his
treatise on cryptanalysis of poetry), one realizes that the latter is not
only extensively quoted by ibn Dunayn r, but is sometimes literally
copied in many places.
1.2.2. ibn Dunaynir's Cryptological Practice
In addition to his mastery of cryptography and cryptanalysis, ibn
Dunayn r attained high practical expertise. This is evident in the
works he left and the nature of activity he pursued. He says, for
instance, concluding his discussion of the encipherment implemented
by adding insignificant letters (nulls): "I was asked to cryptanalyse a
ciphered message, but found it incompatible with any of the [simple
encipherment] divisions. I pondered on it, sorted out its characters…
and by the good assistance of the Almighty, I managed to solve it
straightway." 10 A similar picture of ibn Dunayn r's practical
knowledge lies in his statement, closing his argument about composite
encipherment: "And we have straightforward methods out of
composites… This method is within easy reach of the enlightened
people of this profession, who consider it carefully." 11 It goes without
saying that the last quotation above reflects ibn Dunayn r's conviction
of the fact that cryptography is an established science based on rules
9 His book, p.184.
10 Ibid., p.104.
11 Ibid., p.136.
8

and regulations, and exercised by qualified professionals, just like
other sciences.
ibn Dunayn r practiced encipherment and cryptanalysis by virtue of
his personal contacts with a number of Ayyubid kings and princes of
his time, and his approaches to gain their favour in Egypt and Greater
Syria. Considering, as stated earlier, that he was in the employ of King
N ir ad-D n Mu ammad ibn 'Ayy b of Egypt, and Prince Asad ad-
D n 'A amad ibn Abdull h al-Muhr n , it is all-probable that he has
written this treatise at the behest of one of the sovereigns of the time.
There are reasons to believe that, after the fashion of many
cryptologists, he may have made mention of the assignment in the
introduction, which was left out by the scribe for some reason. This is
testified right from the outset of the treatise: "He [ibn Dunayn r] said,
following the honorific opening statement in praise of God and the
introduction: This book is divided into two parts…". 12 We live in
hope of time to come and reveal the original of this copy so as to set
right our assumptions once and for all.
12 ibn Dunayn r's book, p.70.
9

1.3. Structure of the Book
ibn Dunayn r's book is characterized by its rich content and
inclusive coverage of the requisites for those engaged in cryptanalysis.
It covers quantitative and qualitative data and a variety of algorithms
for cryptanalysis, arranged in a way similar to the arrangement of the
compilations of cryptology today.
ibn Dunayn r divides his book into two broad parts: The first part
(1.3.1.) treats of cryptanalysis of prose ciphers, featuring the main
principles and tools thereof, and surveying, among other things, the
techniques utilized in cryptanalysing the various types of
encipherment, including what he calls "composite" encipherment. In
addition to his use of statistical techniques in cryptanalysis pioneered
earlier by al-Kind , ibn Dunayn r was the first to describe an
arithmetical cipher using the decimal numerical alphabet.
The other part (1.3.2.) addresses algorithms peculiar to the
cryptanalysis of poetical ciphers, considering the topics of prosody,
rhyme, meter, word-patterns, and principles regulating proper writing
skills. ibn Dunayn r also explores snags that can possibly hamper the
cryptologue's endeavour towards cryptanalysis. He winds up with a
couple of practical illustrative examples, followed by verses intended,
he says, for sustained mental exertion in pursuit of solution.
This is a bird's eye view of ibn Dunayn r's book in its totality. A
systematic analysis of the work follows; organized in conformity with
the order of chapters in the edited text, so as to help the reader
navigate and keep step, with a view to appreciate the author's ultimate
objectives. We shall augment our analysis with illustrative examples
as often as necessary, highlighting in the meanwhile the scientific
value of ibn Dunayn r's achievement in the light of the past from
which he has drawn, and the sophisticated present to which we
belong.
10

1.3.1. Cryptanalysis of Prose Ciphers
1.3.1.1. Principles and Tools of Cryptanalysis
ibn Dunayn r establishes, right from the beginning, the significant
fact that cryptanalysis is actually based on conjecture, or what is
known in today's terminology as "tentative assumption". This
conjecture is by no means arbitrary, but measured according to fixed
rules and principles "so that what is assumed by the cryptanalyst is an
outcome of reasoning and argument by analogy" 13 . ibn Dunayn r
limits the rules and principles in two aspects and one "instrument" 14 .
The first aspect is the conversancy with letter frequency count; the
other is the knowledge of variety contact of letters; and the instrument
is the familiarity with the methods of encipherment.
He then enumerates the personal attributes characteristic of the
person involved in this science, i.e. intelligence, observation, tenacity,
insightful delicacy (which helps comprehend underlying obscurity),
keen intuition, equanimity of mind, proper flair and apt conjecture.
Chapters 1 & 2
The Quantitative Methods
ibn Dunayn r expands on the two aspects of cryptanalysis, using
al-Kind 's term of quantitative and qualitative expedients.
By the quantitative expedients he means the utilization of letter
frequency of occurrence (or frequency count) in the cipher text, and
matching it against the order of letter frequency in the given language.
ibn Dunayn r indicates that vowel letters have the highest frequency of
occurrence in the Arabic language. In this respect, however, his
coverage probably falls short of al-Kind 's splendid
comprehensiveness and precision of treatment. First and foremost, he
fails to be on a level with al-Kind , who gives the exact meaning of
vowels as including the three long (or major) vowels [i.e. the letters: ا,
ٚ and ٞ], as well as the three short (or minor) ones [i.e. the diacritical
13 See ibn Dunayn r's book, p.70.
14 Ibid., p.72.
11

marks in Arabic: fat a, amma and kasra] 15 . This is an important
phonetic question of which former linguists were fully conscious.
Then came a time when it was neglected and remained under wraps,
so much so that it was unfortunately attributed to more recent
phoneticians rather than to its real originators.
ibn Dunayn r maintains that the most frequently occurring letters in
Arabic are the vowels; but adds the two consonant letters of ي (l) and
َ (m), so that the order of the highly-frequent letters, according to him,
is: ا (a), ي (l), َ (m), ٚ (w) and ٞ (y). Nevertheless, he considers the
vowels to "have the highest frequency among all letters in all
tongues" 16 . Other letters vary in their frequency from one language
to another. Here ibn Dunayn r reviews some of the languages
prevalent there and then, such as Latin, in which the letter ً (s) is
highly frequent 17 ; Seljuk Turkish and Mongol, in both of which the
letter ْ (n) has high frequency. But then one wonders why French is
not among these languages, although the Crusades were peaking up at
the time of ibn Dunayn r. Considering that ibn ad-Durayhim does
refer to French in the context of citing calligraphs and alphabet sizes 18 ,
one finds no good reason why it has slipped ibn Dunayn r's mind. In
fact this question remains to be answered.
The last lines of Chapter 2 indicate knowledge, on the part of the
author, of these different tongues, suggesting a certain degree of
cryptanalytical practice in them: "If we set out to describe the
algorithms of cryptanalysis in each tongue, the book would grow
larger…" 19 .
15
See al-Kind 's treatise, p.170.
16
See his book, p.74. This fact has been established by al-Kind before; see his
treatise (Volume One of this series), p.122.
17
This notion has also been mentioned earlier by al-Kind (see his treatise, p.122),
and confirmed by ibn ad-Durayhim later (see his treatise, p.52).
18
See ibn ad-Durayhim's treatise, p.19 and p.54.
19 See ibn Dunayn r's book, p.74.
12

1.3.1.2. Types of Encipherment
ibn Dunayn r discusses the types of encipherment on almost the
same lines as al-Kind , starting from Chapter 3 through Chapter 6.
We have summed up his citation in a tree-diagram similar to that of
al-Kind 20 . A quick comparison between the two diagrams shows that
ibn Dunayn r’s drops the encipherment method No. 13., probably
inadvertently due to scribing omission or a scribe’s oversight. This
possibility is supported by the fact that he does mention this method
later when he tackles cryptanalysis. In fact there is nothing
particularly novel in ibn Dunayn r’s discussion of the types of
encipherment except his separating up composite encipherment into
two divisions, which will be explored in detail later in this study, in
the course of handling algorithms of cryptanalysis.
It is worthy to note that these divisions of encipherment include the
three established conventional divisions adopted to date of this
science. These are:
1. Concealment Cipher
This includes all the cases pertaining to encipherment by changing
letters with conceptual relationship and diffusion. It is done by
choosing words for each letter, with a relation of some kind between
them. The true letters are replaced by words, chosen such as to form a
plausible-sounding plaintext in which it is impossible to suspect the
existence of a secret message. This method is customarily attributed to
the German Trithemius (1462-1516); modern findings, however,
confirm, beyond a doubt, that it was documented by the Arabs several
centuries before.
2. Transposition Cipher
This involves all the cases that belong to the encipherment by retaining
the forms (identities) of letters, by changing their relative positions.
3. Substitution Cipher
This embraces all the cases that fall under encipherment by
changing the forms (identities) of letters without relationship and
diffusion.
20 See al-Kind ’s treatise (Volume One of this series), p.87 and p.144.
13

Linking
separate
letters
Some
letters
Composite (or Super-) Encipherment
Corollaries of combining
simple methods
All
letters
Qualitative
Letters retain their forms
Separating
linked
letters
Some
letters
All
letters
Combining simple methods
Repetition
of letters
Some
letters
Quantitative
All
letters
Merging
letters
Some
letters
All
letters
Figure 1.1.
ibn Dunayn r’s Types of Encipherment
One
null
Simple Encipherment
Addition or
omission
nulls
Without relationship
and diffusion
14
Letters change their forms
With relationship
and diffusion
Transposition Simple substitution Species Genus
No nulls
Several
nulls
Simple
Transposition
Transposition
(word or line)
Transposition (letter)
?
Cipher alphabet
of devised shapes
or symbols
Polyword
Polygraphic Monographic
Monoword
Polyword
Monoword

1.3.1.3. Algorithms of Cryptanalysis
ibn Dunayn r elaborates, in eleven chapters (i.e. Chapters 7 through
17), the different cryptanalysis algorithms related to simple
encipherment methods, outlining the quantitative (statistical) and
qualitative (textural) methods. In the next seventeen chapters (i.e.
Chapters 18-35) he turns to discuss composite encipherment, its
methods and algorithms of cryptanalysis.
The following table depicts some of the algorithms for
cryptanalysing individual cipher methods, identified by their numbers
in al-Kind 's tree diagram 21 against their corresponding chapter
numbers in ibn Dunayn r’s book:
Cryptanalysis of cipher method no. 14 Chapter 7
Cryptanalysis of cipher method no. 15 Chapter 7
Cryptanalysis of cipher method no. 13 Chapter 11
Cryptanalysis of cipher method no. 14 Chapter 12
Cryptanalysis of cipher method no. 19 Chapter 13
Cryptanalysis of composite cipher method no. (15+19) Chapter 13
Cryptanalysis of cipher method no. 20 Chapter 13
Cryptanalysis of cipher method no. 21 Chapter 14
Cryptanalysis of cipher method no. 22 Chapter 15
Cryptanalysis of cipher method no. 22 Chapter 16
Cryptanalysis of cipher method no. 7 and 8 Chapter 17
Next, each chapter will be examined individually as follows:
Chapter 7
Cryptanalysis of Simple Substitution Cipher 22
This method is known, in today's terminology, as the
monoalphabetic simple substitution. In this method "every letter is
represented by a symbol that is unique to it," 23 ibn Dunayn r says.
The cryptanalysis is accomplished according to the following steps:
21 See Volume One (of this series ), p.87.
22 Methods Nos. 14 and 15.
23 See his book, p.84.
15

1. Counting the enciphered forms (symbols), and arranging them in
a list.
2. Establishing the frequency of occurrence of each form, and
affixing the frequency numbers to the respective forms.
3. Disposing the forms in descending order of frequency.
4. Writing down the language letters, conformably with their order
of frequency, against the corresponding forms in cipher.
5. Maneuvering for correct combination of letters and intelligible
articulateness of words.
6.Turning over intractable forms again and over again, assuming all
possible alternatives and combinations, and using fair
conjecture, until the cipher makes sense.
ibn Dunayn r then goes to mention the orders of the letters of
highest frequency of occurrence in the Arabic language. These are:
ا, ي, ٚ, َ, ـ٘, ٞ, and ْ. Perhaps his full awareness of the importance of
this group of letters makes him reiterate them elsewhere, but with the
slight difference where the letter َ comes before the letter ٚ. 24
Chapter 8
Orders of Arabic Letters,
or the Quantitative Method
The application of the approach described in Chapter 7 demands a
knowledge of the orders of Arabic letter frequency of occurrence in
typical clear texts. ibn Dunayn r states that he has come to know
these orders from al-Kind 's treatise, and that he has conducted his
own count of letter frequency in a three-sheet Arabic text. As he puts
it: "It so occurred to me to take up [other] written sheets myself and
count the letter frequency orders in them. Thus I took three sheets of
prose epistolary texts and I calculated the frequency of the letter ا (alif);
it turned out to be… So it came home to me the validity of the
statement of Ya q b ibn Is q [al-Kind ], peace be on his soul." 25 ibn
Dunayn r's statement bespeaks an exquisite scientific technique that is
worthy of note: He begins by studying the works of his predecessors,
then he systematically verifies his results, through the independent
24 See his book, p.86.
25 Ibid., p.86.
16

examination of samples of appropriate data. This, needless to say, is a
principle of vital importance in statistical linguistics today, and a
prerequisite for sound results, taking into account a period of eight
long centuries that separate him from us. It should be pointed out that
the total number of letters contained in those sheets was 3430,
amounting to around 1100 letters per sheet and 550 letters per page.
The following table (Table 1.1.) lists ibn Dunayn r's statistical
findings as regards frequencies, in three sheets, of the letters of the
Arabic alphabet, rendered in descending order of occurrence.
17

Letter
Frequency of
occurrence
Percentage of
occurrence
ا 575 16.76 %
ي 360 10.50 %
َ 265 7.73 %
ـ٘ 260 7.58 %
ٚ 250 7.29 %
ٞ 230 6.71 %
ْ 225 6.56 %
ه 195 5.69 %
ع 170 4.96 %
ف 145 4.23 %
د 115 3.35 %
ة 105 3.06 %
ن 95 2.77 %
ك 80 2.33 %
ً 75 2.19 %
ق 62 1.81 %
ػ 50 1.46 %
ط 43 1.25 %
م 32 0.93 %
ص 28 0.82 %
ُ 17 0.50 %
ؿ 13 0.37 %
س 11 0.32 %
ى 9 0.26 %
ط 8 0.23 %
ظ 7 0.20 %
ؽ 5 0.14 %
ض 0 0.00 %
Total/ % 3430 100 %
Table 1.1. ibn Dunayn r's work on the orders of letter frequency 26
(statistical cryptanalysis)
One point that is highly relevant, and probably unknown to some,
is that the computation of Arabic root-letters differs from the
computation of word-letters as such; hence the disparity in the orders
of letter occurrence in each case. The letter ه (r), a moderatefrequency
letter in words, takes precedence over high-frequency
letters in Arabic roots. It goes without saying that, to cryptologists,
26 -Cf. al-Kind 's table in Volume One, p.58.-
18

letter orders relate to full words including affixes (rather than roots
only).
Chapter 9
Preamble to Letter Combination
In this chapter ibn Dunayn r discusses the second principle of
cryptanalysis; it is based on making use of linguistic knowledge
associated with the combination and non-combination of letters in
language. The effective utilization of this principle is related to the
length of the message or the sufficiency of the number of its letters.
A very short cryptogram implies a shortage of constituent words and
letters ـــa factor that precludes the proper application of the statistical
laws and calls for using the qualitative tool of cryptanalysis instead.
This in itself is a skilful gesture on the part of ibn Dunayn r, reflecting
his familiarity with the principle of the so-called law of large numbers.
He says: "If the cryptogram is very short, there exists insufficiency in
it of the frequency of letter occurrence. The expedient for cryptanalysis
to be used here is to determine those letters [of the alphabet] which
admit combination with each other, and those which do not…until
[the cryptologue] elicits the intended meaning of that scant cipher." 27
ibn Dunayn r, however, is not the first to point out to this issue;
al-Kind takes the lead on that score when he states in his treatise on
cryptanalysis that "it could happen sometimes that short cryptograms
are encountered, too short to contain all the symbols of the alphabet,
and where the order of letter frequency cannot be applied. Indeed the
order of letter frequency can normally be applied in long texts, where
the scarcity of letters in one part of the text is compensated for by their
abundance in another part. Consequently, if the cryptogram was too
short, then the correlation between the order of letter frequency in it
and in that of the language would no longer be reliable, and thereupon
you should use another, qualitative expedient in cryptanalysing the
letters."
28 A simple comparison immediately shows that al-Kind 's
statement, though three centuries earlier than ibn Dunayn r's, is richer,
more precise and transparent.
27 See ibn Dunayn r's book, p.88.
28 See al-Kind 's treatise in Volume One, p.124 and p.126.
19

Some of ibn Dunayn r's successors also make reference to how
critical the length of the cryptogram is. An example is ibn Adl n (d.
29
AH 666/ AD 1268) , who goes a step further to set a minimum
length to the cipher sought for cryptanalysis. He writes: "The length of
the text to be cryptanalysed should be at least in the neighborhood of
ninety letters as a rule of thumb, because the letters thus would have
had three rotations, Yet, the number of letters may be less than that in
certain cases." 30
ibn Dunayn r concludes this chapter by maintaining that decryption
by the qualitative means requires considerable professional expertise.
He undertakes to establish, in the next chapter, what he terms "the
rules of this art", by means of a "simplified" table of those Arabic
letters which are combinable and those which are not.
Chapter 10
Combination of Letters,
or the Qualitative Method
This chapter can be aptly described as a summary of al-Kind 's
ideas regarding letter combination and non-combination, although
ibn Dunayn r falls comparatively short of al-Kind 's finesse in
expounding the combination phenomenon. He states towards the end
of the chapter: "…and I abridged that considerably such that my
version should suffice instead of al-Kind 's treatise and its longwinded
prolixity". 31 In point of fact, however, al-Kind 's investigation
of the laws regulating combination and non-combination of each
Arabic letter, although sometimes characterized by repetition, proves
otherwise very useful because these laws are, by nature, so prone to
ambiguity, misspelling or distortion that their repetition by al-Kind
guards against any possible misrepresentation. ibn Dunayn r's
contribution in this respect has been to round up the scattered rules,
bring them together, and eliminate repetition by means of presenting
them in one table, which itself is not without repetition in more places
than one.
29 -In fact ibn Adl n was a contemporary, rather than a successor, of ibn Dunayn r,
although he outlived ibn Dunayn r by some 40 years.- (Translator)
30 See ibn Adl n's treatise (Volume Two of this series), p.52.
31 See ibn Dunayn r's book, p.94.
20

ibn Dunayn r divides Arabic letters into four groups:
1. Letters which combine with all other letters in both anterior and
posterior positions, i.e. pre-positively and post-positively. These
are: ا a, ة b, د t, ف f, ن k, ي l, َ m, ْ n, ـ٘ h, ٚ w/ , and ٞ y/ .
2. Letters that do not combine with some others neither in anterior
nor in posterior position. This relates particularly to the letters
that belong for their utterance to points quite close together in
the human articulatory system, such as the apical letters ( ى z, ً
s, ص ) in relation to each other, gingival letters (س , م , ظ ),
and some of the guttural letters.
3. Letters that combine with some others in anterior position, but
do not combine in posterior position, such as the letter (ُ )
with ى z, ً s, ظ , ص , س , م ,…
4. Letters that combine with some others in posterior positions, but
do not combine in anterior positions, such as the letter (م ) with
ُ and ؽ ; and (ى z) with ُ and ض …
ibn Dunayn r's table of letter combination covers the last three
groups, excluding the first, since it is considered as being the
32
baseline. Immediately noticeable in his table is the needless
repetition of letters in his treatment of the second group (i.e. letters
non-combinable anteriorly nor posteriorly). This is due to his citing a
certain letter against all those non-combinable with it, then citing it
again upon handling each of those letters individually. For example,
he starts his table with the letter ً s, citing all the letters noncombinable
with it anteriorly nor posteriorly. He then reiterates the
letter ً s when he treats each of those letters non-combinable with it.
Consequently, we have opted to make a table of our own (Table 1.2.),
incorporating the content of ibn Dunayn r's without repetition, along
with another table (Table 1.3.) presenting the letters in alphabetical
order, flanked on the right-hand side by the anterior non-combinables,
and on the left-hand side by the posterior ones. Besides, a third table
(Table 1.4.) is given representing non-combinable letters in Arabic
roots (radicals); it is based on the outcome of a comperhensive
statistical study we have conducted on five major Arabic dictionaries,
foremost of which are Lis n al- Arab and al-Q m s al-Mu . al-
32 However, al-Kind mentions it "in the interest of making the statement most
explicit". See al-Kind 's treatise, p.200.
21

Kind 's table (Table 1.5.) has also been found useful to quote here for
comparative purposes. Together, these tables would serve to facilitate
comparison and educe the results that follow.
Letter(s) non-combinable with it
ى ض ص ظ م س
ظ ض ص ى م
ض ص ظ ى ط
ض ظ ط
ُ ظ ط
ط ط ك
ؽ ػ
ؽ ط ق
ظ ص
ع ػ
ع
ؽ ُ
ض ُ
ُ ط
ق
ض ى ص
ى
ؽ ؿ ُ ق ػ
س ً
ؽ
ُ
22
Sign Letter
ً
س
م
ص
ض
ظ
ؿ
ط
ى
ؽ
ػ
م
ى
ص
ض
ك
ط
ظ
ُ
ق
س
Table 1.2. Noncombinable letters (in texts) as observed by ibn Dunayn r
(without repetition).
N.B. non-combinable in anterior position (pre-positively)
non-combinable in posterior position (post-positively)
non-combinable in both anterior and posterior positions (pre- and
post-positively)

Posterior non-combinables
ظ ض ص ُ ً ى م
ق ؽ ظ ط
ؽ ع ؿ
ؽ ػ
ض ص ظ ى
ؽ ظ ط ض ص ُ ً ى س
ظ ض ص ُ ً م س
ظ ض ص ُ ى م س
ض
ظ ط ض ُ ً ى م ط س
ق ظ ط ص ُ ً م س
ظ ض ص ى م
ق ؽ ط ض ص ُ ً ى م ك ؿ ػ ط س
ع ؿ ػ ط
Letter Anterior non-combinables
س ظ ض ص ً ى م
ط ق ؽ ظ ط
ػ ؽ ع ظ ؿ
ؿ ؽ ظ ػ
ك ظ
م ظ ط ض ص ً ى س
ى ظ ط ص ً م ك س
ً ظ ض ص ى م س
ُ ظ ض ص ً ى م س
ص ظ ط ض ً ى م ك س
ض ظ ط ص ُ ً ى م ك س
ط ظ ض ص م
ظ ط ض ص ً ى م ك ط س
ؽ ق ع ظ م ؿ ػ ط
Table 1.3. Noncombinable letters (in texts) according to ibn Dunayn r,
arranged alphabetically (with repetition).
23

Letter(s) non-combinable with it pre-positively Letter
ع ء
ء
ف
ة
ط ض ص م ظ
د
ُ ظ ض ص ً ى م
س
ظ ق ؽ د
ط
ؿ ـ٘ ؽ ع
ػ
ن ػ ـ٘ ؽ ء
ؿ
ظ ض ط د
ك
ط ك ظ ض ص ُ ً ى س د
م
ظ
ه
م ظ ض ص ُ ً س
ى
ظ ض ص ُ ى س
ً
ض ُ
ى م ظ ض ُ ً س ص
ق ُ س د ظ ص ً م
ض
ظ ض ص م د
ط
ُ ً ى م ك
ن
ؿ
ق
ػ
ؽ
ط
ط
س
ض
د
ص
ظ
ؽ ؿ ػ ء
ع
ن ع ؿ ط ػ ء
ؽ
ة
ف
ن ط
ق
ق ط
ن
ف ة
َ
ظ ؿ ػ
ـ٘
Table 1.4. Noncombinable letters as demonstrated in our statistical
analysis of Arabic roots 33 .
33 Extracted from al-Mu am al- Arab : dir sa 'i 'iyya lidawar n al- ur f f alu
r al- Arabiyya (The Arabic Dictionary: A Statistical Study of Letter
Frequencies in Arabic Roots); Table no. 60, p.205.
24

Resultant noncombinable bigrams
25
Letter(s)
noncombinable with it
Sign
Letter
Table 1.5. Table of noncombinable letters as observed by al-Kind
Key: pre-positively (anteriorly)
post-positively (posteriorly)
neither post- nor pre-positively.

Results of Comparison
A. Between ibn Dunayn r's table and al-Kind 's table:
Upon checking ibn Dunayn r's table against that of al-Kind , we see
that ibn Dunayn r correctly adds one bigram of non-combinable letters
to those of al-Kind , i.e. the bigram (ؽ ظ), while he incorrectly misses
one, i.e. the bigram (ط ك).
B. Between ibn Dunayn r's table and that of the Arabic-root
statistical findings:
An essential difference between the table of ibn Dunayn r (and that
of al-Kind before) and our Arabic-root table is that while the former
deals with Arabic words just as they occur in context, the latter treats
of Arabic roots only (without affixation); hence its inclusion of noncombination
cases not covered by ibn Dunayn r. This is quite natural a
phenomenon because the area of non-combining letters grows wider
the narrower the word inflection becomes, and the more the word is
divested of its affixes, so much so that the non-combination scope
culminates in root-words. Conversely, the non-combining letters grow
less and progressively dwindle the broader the word inflection
becomes, and the more the word is linked up with prefixes and
suffixes. Thus the scope of non-combination keeps tightening until it
becomes narrowest in words usually used in context and ordinary
speech, regardless of their being bare, augmented, prefixed, suffixed,
etc.
As a matter of fact, al-Kind ـــ and indeed all later cryptologists,
including ibn Dunayn r ـــ does not state explicitly the technique he
adopts in constructing his rules of non-combination. However,
contextual connections show his intention to be the ordinary speech as
such. This is in evidence first from the fact that the examples he
invokes of letters that combine pre-positively only or post-positively
only do involve augmented as well as uaugmented words alike.
Second, and this is no slight evidence, is his division of letters into
basic ( ur f 'a liyya), which are always original and form an intrinsic
part of words; and variable ( ur f muta ayyira), which may be now
basic and now affixing ( ur f az-ziy da) and include the well-known
affixing letters ـــthose making up the Arabic word (بٙ١ّٔٛزٌؤٍ), plus the
letters: ة, ف and ن. His addition of these last three to the affixing
letters is an extra indication that he actually intends words ordinarily
used in speech and writing, because the affixings alone do not cover
all the letters that may be added to root words, so as to consummate a
26

word inflection in time, number, gender, genitive, comparison,
causality, succession, and the like 34 .
One more point that is crucially important to note is that these rules
of non-combination are effectively utilized in cryptanalysis so long as
the ciphertext is "spaced", that is provided with word spacers, but they
practically prove useless in no-word-spacers. That is so on account of
the possibility then of the occurrence of two consecutive
non-combinable letters from two originally separate (but adjacent)
letters, such as the occurrence of the letter (ً s) at the end of a word
and the letter (م ) at the beginning of the next word, e.g. … ٚم ًِهلِ.
In fact no-word-spacer encipherment is considered among the most
intricate types of simple encipherment, since the cryptologue then fails
to make use of a good few cryptanalysis algorithms, such as initial and
final letters of words, word lengths (bigrams, trigrams, etc.), the
frequency of the space symbol, and combination and noncombination
of letters.
Chapter 11
Simple Substitution
This chapter handles encipherment by simple substitution 35 . It is
done by substituting for each letter the form of another, such as using
the form of the letter (a) to mean the letter (b), and the form of (b) to
indicate (a); (d) for (c) and (c) for (d), and so forth. In today's
terminology this method of encipherment is called monalphabetic
simple substitution. ibn Dunayn r here makes reference to his other
book a ih a i i a at-tar i (The shooting star in
the science of making ciphers), where he elaborates the cryptanalysis
algorithms of this method. However, he indicates that the process has
been outlined earlier, meaning in Chapter 7, as part of treating the
quantitative principles of cryptanalysis.
34 See al-Kind 's treatise in Volume One, p.174.
35 This is the method no.13 in al-Kind 's tree diagram of the types of encipherment;
see Volume One, p.144.
27

Chapter 12
Substitution Using Devised Forms
This is a variety of monographic substitution [corresponding to the
method no.14 in al-Kind 's tree diagram], in which encipherment is
accomplished by changing letter forms into symbols not pertaining to
letter forms (substitution by symbol). For example, given that a= =m ,ٱ
Ø , n= Ω, the word "man" is enciphered: ØٱΩ.
A possible variation of this method is to retain some of the
plaintext letters beside their respective devised forms. The above
example may look like this: a= ٱ, m= Øm , n= Ωn, and the word "man"
becomes: ØmٱΩn.
Cryptanalysis of this method would also entail the utilization of the
quantitative expedient afore-stated.
Chapter 13
Simple Transposition
ibn Dunayn r addresses three types of encipherment by
transposition. The first is the simple transposition based on changing
the relative positions of letters without changing their forms. This
method is easy to cryptanalyse, by restoring the letters to their original
order through continuously re-arranging letter positions until a
comprehensible message emerges. Most probably ibn Dunayn r's
intention here is the simplest method of transposition, i.e.
transposition within a single word. Accordingly, the message: "Fold
the paper" is ciphered: "dlof eht repap".
The second type, a composite one, is based on implementing both
transposition and simple substitution. Undoubtedly this type is of
paramount importance, since it incorporates the core of today's most
sophisticated encipherment methods (for instance the current
international Data Encryption Standard (DES), and the newer
Advanced Encryption Standard (AES), both grounded on the principle
of encipherment using substitution and transposition together, but
carrying it to a higher degree of complication, using a binary number
system).
ibn Dunayn r expands on the decryption of this method, first by
means of the quantitative resource, and then by transposition. As he
puts it: "If the letters are devised forms [i.e. employing simple
substitution] and interchanged as we have already stated [i.e. by
transposition], the way for cryptanalysing them consists in the
28

utilization of the first instrument [i.e. the quantitative technique via
letter computation]. Once the cryptologue works out the letter orders
[of frequency], and places each letter of the alphabet against its
devised counterpart in the cryptogram, he interchanges their relative
positions reciprocally, shifting the letters backward and forward in
relation to one another, until they slot into place and the intended
meaning shows up."
36 It is such a pity ibn Dunayn r does not state
explicitly that this is composite encipherment, nor does he give it due
deliberation, much proud as he is of understanding what others fail to
understand for that matter!
The third type is the encipherment by changing the position of the
letter in relation to itself (i.e. its standard orientation), just by altering
the angle of its setup (without changint its relative position within the
word), assuming various angles of presentation such as writing it
upside down or standing on its end.
Example:
A B C D E Plain
29
Cipher
OR Cipher
Obviously, this type is so easy to unfold that "it would never miss
the common sense of anyone with perceptive insight," ibn Dunayn r
says.
Chapter 14
Encipherment by Adding Nulls
ibn Dunayn r's discussion of this method is something of an
37
elaboration of al-Kind 's notions. Here two distinct cases can be
identified:
a) Addition of nulls within the single word, by splitting it and
embedding one or more nulls in between its constituent letters. Note
that nulls can be letters chosen from the alphabet, or devised forms
irrelative to the alphabet. For Example:
36 See ibn Dunayn r's book, p.100.
37 See al-Kind 's treatise, p.138.
Clear: familiar
Cipher: fazmidlizard

The nulls used in this example are the letters "z" and "d" introduced
alternately after every other letter.
The algorithm for cryptanalysing this type of encipherment, when
used in message cryptograms, is rendered through applying the
quantitative tool, namely, counting the letters. If the occurrence
frequency of the letters or forms in the cryptogram is found to be
greater than the typical letter frequency in the alphabet of the language
concerned, one ascertains that they are nulls, and are left out.
ibn Dunayn r says: "The cryptanalysis of this encipherment is
reasoned out by calculating the forms and sorting them out. If you find
them in excess of the letter orders, try to work out some of them by
the first expedients we have previously mentioned."
38
b) Addition of one or more nulls at the end of words, indicating the
space or the word spacer. ibn Dunayn r's frequent use of the word
"null" in the plural indicates that he utilizes more than one null to
represent a space.
The cryptanalysis of this type of cipher involves manipulating
those letters that are still covert amongst others already identified. The
nulls-spacers are then dropped. As ibn Dunayn r says: "You now look
into the letters none of which has yet shown, and seek their identical
instances among those already puzzled out. If, by eliminating those
letters sought for solution, the context makes sense and word
composition straightens, you conclude the letters left out are all nullsspacers.
When the encipherment is done using one null only, in that
case you have already solved it ipso facto, since the single null is
employed as a word-spacer."
39
Chapter 15
Cryptanalysis of Composite Cipher
ibn Dunayn r refers to his experience in cryptanalysing a composite
cipher that is difficult to solve. Although not expressly stated, the fact
that it is of the composite type manifests itself in the example he
invokes, which is composed of the following three methods:
38 See his book, p.102.
39 Ibid., p.102.
30

(a) Changing letter forms (simple substitution).
(b) Changing letter positions (transposition).
(c) Omitting some letters and using null forms instead.
In this connection he says: "By changing the forms of letters,
altering their positions, and at the same time omitting [certain] letters
of the alphabet to replace them with null forms, the cipher would be
very hard to solve indeed. Nevertheless, and by the good assistance of
the Almighty, I managed to solve it straightway."
40
Chapter 16
Encipherment by Omitting a Letter
In this chapter ibn Dunayn r explains the algorithm for
cryptanalysing the method of encipherment conducted by omitting one
letter of the alphabet throughout the whole encrypted message. It
seems that the employment of this method is always concomitant with
the use of simple substitution. This is clear from ibn Dunayn r's
exposition of the method: "The cryptanalysis here lies in computing
the forms; if they are found less in number than the alphabet count,
you detect them through the first expedients we have mentioned
earlier in this book. Work out some letters of the cryptogram sought
for cryptanalysis. If you notice, by seeking their identical counterparts
elsewhere therein, the existence of one and the same letter omitted so
that the context does not straighten, examine the context closely and
weigh up what is [purposely] omitted, as the words and import would,
in all likelihood, point to it."
41
ibn Dunayn r illustrates this method by an example, maintaining
that the purposely omitted letter is retrieved by sampling the vacancy
(in several places) against all the letters of the alphabet, one by one, so
as to exhaust all likely possibilities, until the dropped letter is
determined once and for all.
40 See his book, p.104.
41 Ibid., p.106.
31

Chapter 17
Encipherment by Changing the Forms of Letters
with Conceptual Relationship and Diffusion
This method is analogous to the current "key-dependent
encryption". In his discussion, ibn Dunayn r obviously relies on al-
42
Kind 's ideas as cited in his treatise. The fullness of the explanation
there should suffice for its reiteration here. Further, ibn Adl n
concludes his treatise with a rich practical example of cryptanalysing
one variety of this method, where the relationship is bird species; each
43
letter being replaced by the name of a bird.
1.3.1.4. Composite Encipherment
Having demonstrated in the previous eleven chapters (7 through
17) some of the simple encipherment methods and algorithms for their
cryptanalysis, ibn Dunayn r shifts to discuss what he calls composite
encipherment. In eighteen chapters (18 through 35) of his book he
dilates on his own perception of composite encipherment, which
differs from al-Kind 's and also the present-day established views on
that respect. Examining the encipherment methods that ibn Dunayn r
terms composite, as well as those he classifies under simple
encipherment while considered composite in today's criteria, one can
list the following conclusions regarding ibn Dunayn r's perception of
composite encipherment:
1. The current view of composite encipherment is that it is a
product of simple methods combined 44 . This is in conformity with al-
Kind 's notion, so impressively demonstrated in his treatise.
2. In the context of addressing simple methods of encipherment,
ibn Dunayn r goes (in Chapters 13, 15 and 16) to handle composite
methods, mistakenly considering them, as simple. However, he
specifically declares earlier that composite encipherment "falls into
42
See al-Kind 's treatise, p.93, and pp. 158-160.
43
See ibn Adl n's treatise, pp.104-113.
44
-I choose to dub it "eclectic encipherment", using a wide range of cipher
methods.- [Translator].
32

two divisions: the one is a combination of simple methods, and the
other is what ensues in consequence."
45
3. It is evident from ibn Dunayn r's book that the concept of
"composition" according to him is to manipulate the letters to be
enciphered in such a way as to disguise the intended meaning through
enveloping it in any device or medium that has nothing to do with the
purport aimed at. This encipherment may take a host of forms such as
building on a tale, a dream, a chessboard, beads, the motion of planets,
or the arithmetic using decimally-weighted numerical alphabet ( is b
al- ummal). In fact these methods bear no relation to composite
ciphering, and would more correctly be associated with what is known
as "concealment cipher", which is intended to pass without being
suspected as the conveyor of a secret communication.
To ibn Dunayn r's credit, it should be noted, he has developed a
number of encipherment methods, which he might have taken over
from his predecessors, and which are based on such accessory devices
as the punctured wood sheet with a thread, folded paper, colour beads,
etc.
Chapter 18
An Overview of Composite Encipherment
ibn Dunayn r seems fully conscious of the fact that the range of
composite encipherment is so wide it is not confined to any limits;
thus it is impossible to deal with all its multiplicity of forms. He states
that what he is going to discuss is just an example for handling other
composite instances. He argues that al-Kind has not considered these
examples of composite encipherment ـــand indeed so, because they
are worlds apart in their views about it. To ibn Dunayn r it is more of
a concealment cipher than proper composite encipherment, as we shall
see in subsequent chapters.
Chapter 19
A Preamble to Solving Composite Cipher
Of all types of encipherment the composite type is regarded by
ibn Dunayn r as the most complicated. Its decryption requires a lot of
45 See his book, p.82.
33

expertise and thorough training. The algorithm for cryptanalysis is
attained by:
1) Experimenting with each and every type of simple
encipherment. If, after all, the cipher remains inscrutable, it is
concluded to be composite.
2) Experimenting with the types of composite encipherment, some
of which ibn Dunayn r will mention in the following chapters.
Chapter 20
Encipherment by Replacing Letters with Generic Names
ibn Dunayn r considers this method as composite encipherment,
although it, in fact, belongs under simple substitution using the
principle of conceptual relationship and diffusion. It is based on the
idea of enciphering letters in terms of genera, thereby a letter can be
represented by more than one symbol. This type is analogous to
polyalphabetic encipherment, but with a symbol-letter relationship,
i.e. relationship of the different symbols to each letter. For instance,
the letter (ا a) may be enciphered using the "people" genus through
employing any proper name to symbolize it.
Keen to help his reader in cryptanalysing this type of cipher, ibn
Dunayn r proposes a table of generic names (relationships)
representing each letter of the Arabic alphabet, followed by a practical
illustrative example. The cryptanalysis assumes taking up the generic
names and combining the letters that they stand for.
ibn Dunayn r suggests that this cipher defies cryptanalysis. That is
probably so, because each letter is replaced by more than one symbol
ـــa process which turns void the quantitative as well as the qualitative
techniques of cryptanalysis. Furthermore, a message enciphered this
way, if put in a well-chosen context, is likely to mislead the
cryptanalyst and distract his/her thought from suspecting the message
to be a cryptogram. It is patently evident that ibn Dunayn r's
demonstration of this type of encipherment puts him one up over his
fellow scholars for that matter. His predecessor al-Kind gives only a
brief account of it 46 ; his contemporary ibn Adl n restricts himself to a
46 See al-Kind 's treatise, p.132, and pp.158-160.
34

simple example towards the end of his treatise 47 ; whereas his
successor ibn ad-Durayhim makes use of his description, as can be
readily observed from the uniformity of generic denominations of ibn
ad-Durayhim in his treatise 48 and ibn Dunayn r in this chapter.
Chapter 21
Encipherment Using the Arithmetic of Decimally-Weighted
Numerical Alphabet (ADWNA)
Or " is b al- ummal"
Important as it is, this method of encipherment has been
overlooked by al-Kind in his treatise on cryptanalysis, despite his
awareness of is b al- ummal, and his reference to it elsewhere 49 . The
Author of the Two Essays, however, does refer to it in his First Essay,
and ibn Dunayn r seems to have quoted from him particularly the use
of the "quarter" and "half" fractions.
" is b al- ummal" is an old method of encipherment, well-known
to the Arabs at an early stage of their civilization, and was practised
later in other languages such as Hebrew. ibn Dunayn r addresses this
method in its two divisions, the major and the minor, expanding on its
significant applications by developing highly relevant ways of
ciphering that have subsequently been adopted by ibn ad-Durayhim.
The following table (Table 1.6.) shows the letters of the numerical
alphabet, with corresponding decimal numerical values in ADWNA.
47 See ibn Adl n's treatise, p.104 ff.
48 See ibn ad-Durayhim's treatise, pp.76-80.
49 As reported by ibn an-Nad m in his al-Fihrist, p.21 quoting al-Kind .
35

ا
ة
ط
ك
ـ٘
1 2 3 4 5 6 7 8 9
ٞ
ن
ي
َ
ْ
10 20 30 40 50 60 70 80 90
ق
ه
ُ
د
س
100 200 300 400 500 600 700 800 900
ؽ
1000
x 1 2 3 4 5 6 7 8 9
1 ا
10 ٞ
100 ق
1000 ؽ
ة
ن
ه
ط
ي
ُ
ك
َ
د
36
ـ٘
ْ
س
Table 1.6. Numerical values of letters.
Thus, the numerical cipher of the proper name ل٠ى, for example, can
be expressed: 7, 10, 4; or (in words): seven, ten, four.
Equally important is that this type of encipherment is simple
substitution, with each letter substituted by a single symbol throughout
the cryptogram. Cryptanalysis is accomplished by utilizing the
quantitative technique stated earlier.
According to ibn Dunayn r, the concept of composition in the areadependant
decimal numerical alphabet as a "composite" method of
encipherment is predicated on making the cryptogram look like a
peasant-farming financial register. The measurement is done through
adopting length units in common use at the time, such as al- ar b, alqaf
z, and al- a r. The cryptogram is composed by representing the
letters as land dimensions, simulating an outward semblance of
buying, selling, or otherwise similar bargains. This, ibn Dunayn r
suggests, tends to boost the concealment of the cipher and renders it
even more difficult to cryptanalyse. He says: "If you fail to do like we
have told you as regards giving the cryptogram the semblance of a
financial register of expenditure, an episode about somebody, taking,
buying or giving, you would incur a raw and unhappy [state of
affairs], over and above an unmistakable clue to exposing the intended
ٚ
ً
ؿ
ٚ
ً
ؿ
ى
ع
م
ى
ع
م
ػ
ف
ض
ػ
ف
ض
ط
ص
ظ
ط
ص
ظ

encipherment. Otherwise, this course of action would be quaint and
pretty efficient."
50
Chapter 22
Encipherment by Communication through Finger-Spelling,
Using the Manual Alphabet and ADWNA
In this type of encipherment ADWNA is instrumental in letter
substitution; letters are replaced with numbers communicated by
bending the fingers in specific shapes so as to convey to a recipient
the numerical values corresponding to the respective letters. This kind
of esoteric communication is particularly used by those specially
initiated, in the presence of another who is not meant to understand
the discourse.
Such a "manual alphabet" is an already well-known Arab signaling
method of communication. It can assume many different shapes.
ibn Dunayn r's method is based on representing the intended number
by relative finger configurations. Thus he represents the units and
number ten, referring to other numbers by analogy. The following
table (Table 1.7.) demonstrates the Arabic numerical alphabet, with
the corresponding values in ADWNA of the individual letters, and the
finger configuration for each; the units being quoted from
ibn Dunayn r, the rest from other sources.
50 See his book, p.116.
37

Hand Letter Value Finger Configuration
Right ا (a) 1 Ring finger folded and pinkie rested on it from behind.
Right ة (b) 2 Little and ring fingers folded to their base in palm.
Right ط ( ) 3
Little, ring, and middle fingers folded to their base in
palm.
Right ك (d) 4 Pinkie spread up; ring and middle fingers folded.
Right ـ٘ (h) 5
Middle finger folded in palm, with little and ring fingers
spread out.
Right ٚ (w/ ) 6
Ring finger folded in palm, with middle finger spread
up.
Right ى (z) 7 Little finger bent inside, with all the rest spread.
Right ػ ( ) 8 Little and ring fingers folded.
Right ط ( ) 9 Little, ring, and middle fingers folded.
Right ٞ (y/ ) 10 Thumb and index fingers made into a loop.
Right ن (k) 20 Thumb tip placed between index and middle fingers.
Right ي (l) 30 Index inner tip placed on thumb inner tip.
Right َ (m) 40 Inner tip of thumb placed on outer tip of index finger.
Right ْ (n) 50
Tip of thumb placed on back of index finger while
stretched out.
Right ً (s) 60 Index tip placed on thumb tip.
Right ع ( ) 70
Tip of thumb nail placed between inner joints of index
finger that is twisted.
Right ف (f) 80 Thumb tip placed in the index joint towards its tip.
Right ص ( ) 90 Index-finger tip placed on thumb tip.
Left ق (q) 100
Index-finger tip placed in joint of thumb while spread
out.
Left ه (r) 200
Thumb tip placed between index and middle fingers
towards their base.
Left ُ ( ) 300 Inner tip of index finger joined to inner tip of thumb.
Left د (t) 400 Inner tip of thumb placed on outer tip of index finger.
Left س ( ) 500
Tip of thumb placed on back of index finger while
stretched out.
Left ؿ ( ) 600 Index tip mounted on thumb tip.
Left م ( ) 700
Tip of thumb nail placed after inner joints of index
finger that is twisted.
Left ض ( ) 800 Thumb tip placed in the index joint towards its tip.
Left ظ ( ) 900 Index-finger tip placed on thumb tip.
Left ؽ ( ) 1000
Pinkie folded to its base in left palm, with ring finger
mounted on it.
Table 1.7. Finger-spelling (dactylology) using ADWNA
38

Chapters 23 & 24
Encipherment by "Composing" Letters on the Chessboard
This method is based on simple substitution. It is originally
intended to address someone who is present, but can also be employed
to communicate with absent people ـــa method which ibn Dunayn r
credits to himself, maintaining that he establishes the precedent for it.
His explanation is lucid enough to spare any elucidation. One
noteworthy remark here is that ibn ad-Durayhim, in his Mift alkun
z f ' al-marm z, seems to have taken over this method from
51
his predecessor ibn Dunayn r.
Chapter 25
Cryptanalysis of Cipher "Composed" on the Arithmetic of
Decimally-Weighted Numerical Alphabet (ADWNA)
ibn Dunayn r asserts, right from the outset, that this type of cipher
is "very easy to cryptanalyse,"
52 and rightly so, because that kind of
arithmetic was then widespread and in common use. The cryptanalysis
is effected by reconstructing letters against their corresponding
numbers in ADWNA. It is interesting to remark here that
ibn Dunayn r discusses encipherment using ADWNA twice in his
book, but he has not been consistent in the symbols he uses to denote
the orders of tens, hundreds, and thousands. While in the first instance
(that composed on area) he uses numbers with super-dots to indicate
the tens order, and numbers with under-dots to indicate the hundreds
order, he in this chapter opts to use numbers preceded by one circle to
indicate the tens, two circles to indicate the hundreds, and three circles
to denote the thousand. Nevertheless, it is understood that the circles
here are equivalent to the dots there.
Moreover, ibn Dunayn r observes the nicety that is b al- ummal
is basically one of three varieties of the Hindi calligraph (cipher
alphabet). In his words: "The algorithm is to place each letter of the
alphabet against its Indian decimal numerical equivalent in the
system… Consequently, if you wanted to encipher the statement
51 See ibn ad-Durayhim's treatise, p.66.
52 See his book, p.124.
39

ك١فٛزٌا ٌٟٚ للها by this method, you would have to replace the letters with
their corresponding Indian characters…" 53 .
ibn Dunayn r's description of this method as easy to solve may be
meant to serve as a preamble to what he is about to develop in the next
chapter. Through the introduction of sophisticated improvements this
encipherment turns out to be complicated and difficult to decrypt. This
fact is attested by his repetition in the following chapter of the same
illustrative example " ك١فٛزٌا ٌّٟٚ للها", probably to enable the reader to
appreciate how far the method has been developed.
Chapter 26
Encipherment by ADWNA Using Further
Numerical Processing
Though simple substitution in substance, this method of ciphering,
which is credited to ibn Dunayn r as its originator, is extremely
important in terms of its content and effect. Its importance stems
especially from the fact that it lends itself to a special numerical
processing, through arithmetical operations governed by a set rule,
that makes it assume more complicated forms. This may be
represented by the following model (Figure 1.2.).
The
Cleartext
(LETTERS)
Substitution
of Numbers
for Letters
Figure 1.2. Encipherment by numerical processing using ADWNA.
Numerical processing involves making the representative numbers
two, three, four, etc. times as great in value, thus increasing the
difficulty of cryptanalysis. For example, we encipher the phrase
ك١فٛزٌا ٌّٟٚ للها as follows:
53 See his book, p.124.
Numerical
Processing
40
Resubstitution
of Numbers
for Letters
The
Cipher-text
(CRYPTOGRAM)

Cleartext ق
Numerical
value in
ADWNA
Encipherment
by doubling
the number
(twofold)
Reconversion
to letters
Encipherment
by
quadrupling
the number
(fourfold)
Reconversion
to letters
ٞ
ف
ٚ
د
ي
41
ا
100 10 80 6 400 30 1 10 30 6 5 30 30 1
200 20 160 12 800 60 2 20 60 12 10 60 60 2
ه
ن
ٌل
ت٠
ض
ً
ة
400 40 320 24 1600 120 4 40 120 24 20 120 120 4
د
َ
هش
لو
ـغ
هل
Fully awake to the significance of this method, ibn ad-Durayhim
later takes up this method from where ibn Dunayn r left off,
developing it and further expanding on it. He makes the numerical
processing take other forms by breaking up the number into a sum of
two or more numbers of various choices, each corresponding to its
respective letter in ADWNA. For instance, enciphering the proper
name لّؾِ this way gives:
ك
Plaintext ك َ ػ َ
Numerical value in ADWNA 4 40 8 40
Numerical processing of one choice (3+1) (10+30) (6+2)
Corresponding letters طا ٌٟ ٛث ٌٟ
Numerical processing of another choice (2+2) (20+20) (7+1)
Corresponding letters تث هو ىا هو
ٞ
ن
َ
ي
ً
هل
ٚ
ت٠
لو
ٖ
ٞ
ن
ي
ً
هل
ي
ً
هل
ا
ة
ك
(10+30)
(20+20)
It is well worth emphasizing that although far more sophisticated
numerical processing is used in cipher algorithms nowadays, this
54 See ibn ad-Durayhim's treatise, pp.24-25 and p.68.
54

method forms, in principle, the basis of many algorithms in
present-day cryptography.
Chapter 27
Encipherment by Substituting For Letters the Days of
the Week and Hours
In this type of encipherment the cryptogram is "composed" on the
seven days of the week, by coining seven words that cover all the
letters of the Arabic alphabet in such a way as to avoid the repetition
of any of them. The words are then associated with the days of the
week one apiece, assigning to each letter of the cryptogram a specific
hour of the day. ibn Dunayn r elucidates this method by enciphering
the phrase: لله لّؾٌا as follows (with a slight change, as most of the
seven words in the original Arabic manuscript are illegible):
Days of
the week:
Coined
words:
Number
of letters
Friday Saturday Sunday Monday Tuesday Wednesday Thursday
5 + 4 + 5 + 4 + 3 + 4 + 3 = 28
ـ٘ + ي + ي + ك + َ + ػ + ي + ا = لله لّؾٌا
ا = the second hour of Friday
ي = the last hour of Sunday
ػ = the second hour of Wednesday
َ = the second hour of Thursday
ك = the first hour of Tuesday
ي = the last hour of Sunday
ي = the last hour of Sunday
ـ٘ = the last hour of Wednesday
ibn Dunayn r concludes by establishing that "the algorithm of
cryptanalysing such ciphers is pursued through the application of the
quantitative expedients, namely by computing the order of letter
occurrence frequencies. This type of encipherment is most
conveniently performed by way of a tale."
55
55 See his book, p.128.
42

Chapter 28
Encipherment by Folded Paper
This method of encipherment is not based on letter substitution, but
has more the appearance of a concealment than real cipher. One
should think, in all probability, that ibn ad-Durayhim has picked it up
56
from ibn Dunayn r. It is more or less similar to a cryptographic
device that dates back to the Spartans of ancient Greece, as early as
the fifth century B.C., called the "skytale", which is "the earliest
apparatus used in cryptology and one of the few ever devised in the
whole history of the science for transposition ciphers."
57 The idea is
to write the secret message down a narrow strip of papyrus or
parchment wrapped round a staff of wood close-packed, with edges
meeting uniformly at all points. The parchment is then unwound and
sent on its way. The disconnected letters and fragments make no sense
unless the parchment is rewrapped (by the recipient) round a baton of
the same thickness as the first, thus forming the message. The
decryptor of today, however, would make short work of such a
system.
Another related encipherment method is achieved by writing the
secret message on a sheet of paper folded in pleats, and concealed by
unfolding it, filling up the spaces by adding extra letters that, together
with the original letters of the cryptogram, make new innocentlooking
context of different import from the one intended.
Chapter 29
Encipherment by a Punched Board
Much as this method employs a device, it belongs under simple
substitution cipher. Encipherment is achieved by puncturing holes, in
a sheet of wood, equal in number to the language letters (28 for
Arabic), not necessarily arranged alphabetwise but according to an
agreed succession. The cryptogram is represented by a thread driven
through the intended holes, marking a route which defines the letters
of the message. The recipient reads the letters represented by the holes
through which goes the thread. Obviously, decrypting this kind of
56 See ibn ad-Durayhim's treatise, p.82.
57 Kahn, D. The Codebreakers, New York: Macmillan, 8 th printing, 1976, p.82; and
Gaines, Helen Fouché Cryptanalysis: A Study of Ciphers and their Solutions,
New York: Dover Publications, 1956, p.14.
43

cipher depends on the quantitative technique, explained by ibn
Dunayn r so fully as to make any addition here redundant.
Chapter 30
Encipherment by Coloured Beads
This method uses beads distributed, according to their colours,
among the letters of the alphabet. Encipherment is done by threading
or "composing" letters represented by beads on a string as a rosary, in
which the succession of colours tallies with the succession of letters of
the text to be enciphered. Note that colour-bead encipherment can take
numerous methods, as ibn ad-Durayhim later states in his Mift al-
Kun z: "This type gives rise to scores of ramifications."
The algorithm for cryptanalysing this cipher is also through the
employment of the quantitative technique of counting the frequency of
coloured beads against each letter.
ibn Dunayn r's method of coding, however, is by no means
economical; alternative methods can be utilized, pursuing an agreed
rule, to produce the same result with a fewer number of beads. Morse
code (alphabet) is a case in point much in evidence; with just a couple
of colours the Code permits the representation of the whole gamut of
letters.
Chapter 31
Encipherment by Concealment within Context
In this method the true message is "concealed" within another
context by spreading the intended words at the beginning, middle, and
end of lines, according to some rule known only to the sender and the
recipient.
To exemplify this let us agree that the message is to be read
clockwise starting end first. The concealed message would read:
"Don't just stand there, do something":
There's a lot to say and do before I leave, darling. Say something;
stand before me. Let's just not forget our love; please don't.
58 pp. 80-82.
44
58

Chapter 32
Encipherment by Letters Embedded in Words
The message is "composed" on the words of a written epistle,
conformably with a fixed rule. This can be accomplished by taking the
first, second, last, etc. letter of each word. The following example
demonstrates enciphering the name ٍٟػ لّؾِ in this way twice: the one
by taking the last letter, the other by taking the first.
ٞ ي ع ك َ ػ َ
ٍٟػ ًضِ غفاه َكوف ُى١ٍػ ؼٌبص ٍٍَُ
ٖاو٠ ٟىٌ وِبػ هاك ًب٠مبؾِ لِبؽ ٝشِ
ibn ad-Durayhim later handles this method down to the smallest
59
detail, citing several varieties and giving many examples.
Chapter 33
Encipherment by Reversing Letter Order of a Word
This type comes under encipherment by transposition, and is
60
performed by writing each word of the cryptogram in reverse order.
The name لّؽا,
for example, is enciphered: بؾِك and ْاٛضه (plain)=
وضٚبٔ (cipher). It would have been more accurate if ibn Dunayn r were
to classify this method under simple rather than composite
encipherment. We do not know for certain the reason for his choice,
but it is probably motivated by a personal confused definition of
composite encipherment.
Chapter 34
Encipherment by Numerical Calculations
This method is closely akin to the method of encipherment
"composed" on area (Chapter 21), with the slight difference of
employing whole dinars for the units order, fractions of quarters of the
dinar for the tens, fractions of halves for the hundreds, and fractions of
both halves and quarters for the thousands. It seems likely that
ibn Dunayn r has taken this method from the Author of the Two
59 See his treatise, pp.26-27 and p.70 ff.
60 This type of encipherment has been later handled by ibn ad-Durayhim in more
detail and diversification. See his treatise under the "transposition" type of
encipherment, p.56 ff.
45

Essays (in his First Essay). In both manuscripts, however, the
transcription suffers much from corruption and misrepresentation,
owing to omission on the part of the scribes. It might be for this
reason that ibn ad-Durayhim does not make any reference to this
method in his treatise. Indeed we have managed, by studying the
examples in both manuscripts, to make out the following correct form
of ibn Dunayn r's example illustrating this method:
ا ة ط ك ـ٘ ٚ ى ػ ط
1 2 3 4 5 6 7 8 9
46
dinar
ٞ ن ي َ ْ ً ع ف ص quarters of the dinar, indicating
1 2 3 4 5 6 7 8 9 the number times 10
ق ه ُ د س ؿ م ض ظ
1 2 3 4 5 6 7 8 9
ؽ
1
halves of the dinar, indicating
the number times 100
Three-quarters of the dinar, indicating the number times 1000
Thus, the proper name ٍٟػ ٓث لّؽأ, for instance, can be enciphered:
ٞ ي ع ْ ة ك َ ػ أ
1 3 7 5 2 4 4 8 1
quarter Quarters quarters quarters dinars dinars quarters dinars dinar
Chapter 35
Encipherment by Conditions of planets
and Other Celestial Bodies
With this chapter ibn Dunayn r concludes his discussion of prose
encipherment. Here the cryptogram is "composed" on an astronomical
text addressing planets and other heavenly bodies: their motions,
distances, durations, mansions, revolutions, rotations, etc. He brings
forth an example of enciphering the name لّؾِ by this method:
"Having completed forty revolutions, the Moon eclipsed at such and
such degrees of such and such constellation. Eight revolutions thence
remained. Its motion straightened after it had waned in appearance
and faded in colour. Thereafter it moved to Sagittarius and completed
forty revolutions thus far. At the end of Sagittarius the planet Venus
approached it. Four turns elapsed before its motion evened out in

orbit, and its light became as bright as to emulate planets". 61 It is clear
that the algorithm for cryptanalysis lies in the realization of the letters
corresponding to the numbers [set in boldface] in ADWNA.
ibn Dunayn r attributes this type of encipherment to Hermes
Trismegistus of wisdom and learning, the legendary author of
mystical, astrological and alchemical works, and one of seven wise
men known to have possessed calligraphs of their own, barred off to
all but the "sons of wisdom", hence the epithet "hermetic" (in English)
or "hermetique" (in French), meaning completely sealed or impervious
to external influences. Many ciphers were ascribed to Hermes; ibn
Wa iyya an-Naba , in his awq al-mustah m f ma rifat rum z al-
'aql m (The seeker's joy in identifying the written symbols of
languages) gives a detailed account of the Hermetic calligraphs.
ibn Dunayn r concludes this chapter by pointing out the following
two notions:
1. that "the cryptanalyst of this cipher should be knowledgeable
about arithmetic and astronomy" 62 , and rightly so, in order that he/she
can identify the text as a cryptogram, and that the astronomical
content is not what is intended.
2. that the cryptanalyst "should make use of the first statistical
principles of calculating the frequencies of letter occurrence" 63 ,
namely the quantitative technique. Here ibn Dunayn r is wide of the
mark. It may be an unfortunate oversight on his part, because
cryptanalysing such a cipher requires nothing else but an acquaintance
with the arithmetic using decimally-weighted numerical alphabet, or
is b al- ummal.
1.3.2. Cryptanalysis of Poetry Ciphers
ibn Dunayn r's work, much important as it is, is not without
precedent of its kind; it is simply one link of an integral chain in
which every scholar make good use of, and adds to, the contributions
of his predecessors. It has already been noted (1.2.1.) that ibn
Dunayn r tends to draw upon quite a few of his earlier peers, quoting
61 See ibn Dunayn r's book, p.140.
62 Ibid., p.140.
63 Ibid., p.140.
47

their ideas, recapitulating their concepts, or building on their findings.
This tendency, in fact, is even more pronounced in this part, where he
seems to lean notably on al-Kind , ibn ab ab and the Author of
'Adab a - u ar ' (The Art of Poets).
1.3.2.1. Tools for Cryptanalysing Poetry Ciphers
Chapters 36 and 37 of ibn Dunayn r's book serve as an introduction
to cryptanalysing poetry ciphers. In Chapter 36 he reiterates the tools
of cryptanalysis that are common to both prose and poetry; these are:
1. Determining the orders of letter frequency of occurrence;
2. Familiarity with the variable and basic letters; and
3. Knowledge of letter combination and non-combination.
In Chapter 37 he mentions those principles of cryptanalysis
exclusive to poetical ciphers, considering them as indispensable
conditions to any cryptanalyst of poetical cryptograms: "Thereafter,
the keynote element of this science is that the cryptologue should be:
1. widely conversant with prosody and metrical structures;
2. thoroughly acquainted with rhymes;
3. deeply familiar with the science of poetry [the art of appreciating
poetical delicacy];
4. a person of insight into the knack of writing;
5. a person with capacious memory for committing to heart poetry
galore; and
6. skilful and resourceful in cryptography."
64
To be noted is the fact that poetical ciphers do not typically exceed
65
a few verses. It follows that the letter order of frequency is scarcely
sufficient to render the quantitative techniques reliably applicable in
cryptanalysis. Nevertheless, adopting the afore-stated principles is apt
to make the process less difficult.
64 See ibn Dunayn r's book, p.142.
65 See the practical examples of ibn ad-Durayhim and ibn Adl n in their respective
treatises, p.102 ff and p.104 ff.
48

1.3.2.2. On Prosody (Metrics)
� Metrical Circles (Chapter 38)
ibn Dunayn r dedicates this chapter to the five circles of Arabic
prosody, from which all poetical meters (measures of versification)
originate. This is so because the meters themselves are so engaged or
overlapped that one meter disengages itself from the other. Each
group of meters that are capable of undergoing such disengagement
share in a circle designated according to the nature of its parts. These
metrical circles are: circle 1 of the different, circle 2 of the consistent,
circle 3 of the similar, circle 4 of the extraneous, and circle 5 of the
harmonious.
� Poetical Meters (Chapters 39 & 40)
Chapter 39 deals with the sixteen meters of Arabic poetry and the
feet [the basic units] that are peculiar to each meter. In Chapter 40 the
meters are distributed to their respective circles. Then ibn Dunayn r
points out to three prosodic terms, all belong under metrical variations
in Arabic poetry, namely, az-zi f, (an optional variation that befalls
the second of a couple of letters, called sabab, in a line of verse),
al- arm (a measured omission of the first vocalized letter of a threeletter
foot segment, called watid, occurring at the beginning of a line
of verse), and al- azm (a measured addition of up to four letters made
at the beginning of a verse, not considered in scansion).
ibn Dunayn r's specific reference to these variations is apparently
due to their direct effect on poetic meters ـــan effect that could turn
them away from what is familiar in Arabic poetry. Other variations,
however, do not have such an effect.
1.3.2.3. On Rhymes
ibn Dunayn r devotes Chapter 41 to rhymes in poetry
[correspondence of terminal sounds in lines of verse, involving
identity of sound rather than spelling. "Fix" and "sticks", like "buffer"
and "rougher" are perfect rhymes]. He refers to their names, letter
structures ( aw ri ) and defects, inasmuch as is necessary for the
cryptanalyst.
49

1.3.2.4. Insight into Writing Knack
This term, also used by the Author of Adab a - u ar ', means the
penetrating discernment in the art of writing, its rules an principles.
ibn Dunayn r discusses this topic at length, covering more than ten
chapters (42-52) of his book. Arranged along the same lines as the
Author of Adab a - u ar ', these rules and principles include the
following:
� The letters ا ( ) and ي (l) (Chapter 42)
This bigram is of highest frequency and combinability, since it
occurs, more often than not, as the definite article. Definition is a
prevalent feature in most Arabic nouns.
� Two-letter words (Chapter 42)
These words are bigrams either inherently (words like ِٓ, ٓػ) or by
inflection (e.g. imperative verbs like عك, ًٍ, and letters governed by
prepositions such as ٗث, هٌ, etc.). Pure bigrams, in fact, are limited in
number (there are 115 of them according to our statistics on Arabic
root-words). Seeking words of this kind (called "word-spotting" in
today's terminology) in a cryptogram contributes favourably towards
solution; indeed it is an algorithm of cryptanalysis, as ibn Dunayn r
states.
� The relation between the number of letters of a verse
and its meter (Chapter 43)
The number of letters contained in a line of verse is likely to
indicate its meter. ibn Dunayn r sets boundaries to the approximate
number of letters in a verse for each meter. Example: the number of
a - aw l (the long) and al-bas (the simple) meters ranges between 40
and 50 letters. The shortest meter in Arabic poetry, however, consists
of seven letters and is called manh k ar-ra az.
He proceeds to consider algorithms of cryptanalysis, which include
the following in order:
1. Cryptanalysing the letter (ا ) ـــmainly through the well-known
quantitative fact that the letter (ا) has the highest frequency of
occurrence of all the letters of the alphabet.
2. Cryptanalysing the letter (ي l) ـــdepending either on its
combinability with the letter (ا), or on its combinability with itself, i.e.
its occurrence repeated in words such as: للها, ش١ٌٍا, ت١جٌٍا.
50

3. Cryptanalysing the letter preceding or following (ا) ـــtaking into
account that decrypting (ا) often makes for working out two-letter
words starting or ending with it, particularly those frequently
occurring bigrams such as:
ٚأ, مإ, ْإ, ٞأ (starting with ا); and بِ, ب٠, ام (ending with ا).
4. Cryptanalysing the letter preceding (يا al) ـــdepending on the
fact that, in one word, (يا) is preceded mostly by one of the letters: (ٚ
w), (ف f) or (ن k).
5. Spotting five- and seven-letter words ـــconcentrating especially
on the six labials in them, i.e. the letters: ي, ة, ْ, ٚ, ف and َ. Linguists,
however, include the letter (ه) in place of (ٚ), dubbing these letters as
the "liquid letters" or al- ur f a - ulq. No pentagram or heptagram,
ibn Dunayn r maintains, is practically devoid of at least one of these
letters, with very rare exceptions.
� Silent letters: letters written but not pronounced (Chapter 44)
ibn Dunayn r draws attention to a set of properties inherent in the
Arabic language, which are beneficial to cryptologues. He begins with
those letters that are orthographically written, but not vocalized, and
therefore they are not considered in metrical scansion since, in
prosody, it is only the enunciated letters that count. Of these letters
ibn Dunayn r mentions:
1. the letter (ا) that is added to the letter (ٚ) in verbs denoting
plurality, e.g. اٚهبص, اٍٛهك (the functional (ا) of differentiation, called
alif at-tafr q or al-f riqa), as distinguished from the intrinsic (ٚ)
terminating verbs like ٚيغ٠, ٚلج٠, etc.
2. the terminal "hamza" in some words such as ءبش, ءبٕث, which used
to be written as بش, بٕث and nonetheless pronounced. This is common
practice in ancient manuscripts. In fact this item would have been
more aptly subsumed by ibn Dunayn r under the following heading,
i.e. letters pronounced but not written.
3. the terminal (ٚ) of the proper name ٚوّػ ( Amr), written to
differentiate it from another proper name وّػ ( Umar). ibn Dunayn r
favours not writing this (ٚ) in enciphered poetry lest it should cause
ambiguity. However, since poetry is metrically measured, there would
be no possibility of any mix-up in these two proper names.
� Voiced letters: letters pronounced but not written (Chapter 45)
These are mainly ا's (alifs) within proper names, often dropped by
scribes since times of old, probably in the interest of damping the
51

vocalization. Examples: ُ١٘وثإ (for ُ١٘اوثإ ), ً١ؼٍّإ (for ً١ػبٍّإ).
ibn Dunayn r favours spelling out such (ا) in poetry, as the meter
necessitates its retention.
� The letters ( ٚ : w, ) and ( ٞ : y, ) (Chapter 46)
Being of high frequency, these two letters are of service towards
cryptanalysis; hence the need, on the part of the cryptanalyst, to spot
them "in mid- and end-positions", 66 and consider their different modes
of usage with vowel points. They occur as "geminated (mu addad),
67
neutral (s kin) and vocalized (muta arrik)", says ibn Dunayn r.
� On glottal stops (hamzas) (Chapter 47)
ibn Dunayn r refers briefly to examples of hamzas that might prove
problematic, such as the mid-glottal catch (or medial hamza).
� Prefixes and suffixes (Chapters 48 & 49)
Also helpful in cryptanalysis is a fair knowledge of Arabic prefixes
and suffixes ـــletters that, when joined to other letters make up integral
entities of significance. Of the prefixes ibn Dunayn r states the letters:
ٚ (w), ف (f), ة (b), ن (k), and ي (l); and of the suffixes he makes
reference to the letter د (t) in three modes.
� Doubled letters (Chapter 50)
Consecutive repetition of the same letter contributes towards
cryptanalysis. ibn Dunayn r gives examples of words containing a
letter repeated:
ًٍَف (in which the letter ي repeated)
كَلَِ (in which the letter ك repeated)
ُّل (in which the letter َ repeated).
� Word patterns defined with (يا) (Chapters 51 & 52)
If the letter (ي) is repeated, after (يا) at the beginning of a word, this
word is all but certain to be the name of God (للها). However,
ibn Dunayn r suggests alternatives. By that he is alluding to the
possibility of cryptanalysing certain letters by an assumption based on
their positions in a word, and on the structure and measure of the
word. This principle of cryptanalysis is further expounded by the
Author of Adab a - u ar '.
66 See ibn Dunayn r's book, p.162.
67 See ibn Dunayn r's book, p.162.
52

1.3.2.5. Other Useful Observations
In chapters 53 through 59 ibn Dunayn r draws attention to a
number of special problems that may crop up and hinder the
cryptologue's endeavour towards solution:
1) long words which are devoid of the definite article (يا), such as:
ُٙعهلزََٕف (10 letters); ُٙى١فى١َف (9 letters); ْٕٛ٠لزَزٍ (9 letters).
2) nonsensical verses, though with sound meter ـــwhich requires
the cryptanalyst to be conversant with such tools as rhyme,
language, prosody, and competent to cope with any possible
metrical variations and defects. This kind of meaningless poetry
is described by ibn Dunayn r (in Chapter 59) as "sheer raving". 68
3) absence of letter-dotting, either through the deliberate use of
undotted letters alone, or by choosing not to dot letters whose
shape causes ambiguity. For example, the first letter of the
undotted word ( ) might just as well be one of these letters:
ة , س , ٞ or ْ .
4) employing separate letters (letters that cannot be linked with
following letters); e.g. ػٚه هاك كٚاك هاى .
5) using each letter just once without repetition, as in the verses
that round up all the letters of the alphabet ـــthe so-called
"keys", such as the following line attributed to al- al l ibn
'A mad al-Far h d :
6) the verse sought for cryptanalysis being of a new form and
unheard-of before.
7) the intended verse being too short to allow sufficient letter
frequency; the longer the verse the better for the cryptologue.
8) unsound meter and language scales, owing to the poet being of
inferior class or shallow knowledge.
9) problematic peculiarities in rhyme and meter, such as curtailing
the seven-unit metric foot (ٍٓ١ػبفِ) by at once omitting the fifth
and seventh neutral units of the foot, which is unacceptable in
poetry.
68 ibn Dunayn r's book, p.174.
53

ibn Dunayn r, moreover, cautions (in Chapter 58) against the
possibility of erroneous conclusions in cryptanalysis resulting from
some default on the part of the encipherer. This might well impede
cryptanalysis, too.
- COMMENT ON AN IMPORTANT CIPHER METHOD (Chapter 60)
ibn Dunayn r puts forward this method in the context of his
discussion of cryptanalysis barriers. It is actually quoted from the
Author of the Two Essays: "Towards the end of his Second Essay, the
Author of the Two Essays on cryptanalysis states that we are destined
to follow an intricate path."
69 ibn Dunayn r settles for propounding
the basis of the method, which involves assuming for the same letter
[of the plaintext] three different symbols [in the cryptogram], to be
used, one at a time, to represent that letter. On the other hand, a single
symbol is assumed to represent three letters [often of the same
orthographic pattern such as ة , د , س ]. He criticizes the method and
its proponent on the basis of its susceptibility of equivocality, and
concludes by saying that the Author of the Two Essays was "not wellinformed
in ciphers". 70
It turns out, however, that ibn Dunayn r's statement is not without
prejudice for that matter. Complicated as it may seem, this method is
deemed one of the important substitution methods that answer to the
latest theories and principles of encipherment, in which two or more
letters are substituted for one letter (homophonic substitution).
1.3.2.6. Practical Examples (Chapters 61 & 62)
In keeping with the common practice of most writers in this
science, ibn Dunayn r works out practical examples to illustrate his
71
ideas. He therefore chooses two lines of verse, the first
(Chapter 61) is of his own composition:
in which the letters ا , ي , ٚ are found to be especially frequent. He
restricts himself to disposing the letters of the verse, attaching to each
69
See ibn Dunayn r's book, p.176.
70
Ibid., p.176.
71
See also ibn Adl n's treatise, p.104 ff., and ibn ad-Durayhim's treatise, p.102 ff.
54

letter its symbol. The following table (Table 1.8.) shows these letters
arranged in descending order according to their frequency of
occurrence. Note that all symbols are chosen to be three-letter words
ending with the letter (ه), with the middle letter diacritically marked
with the neutral "suk n".
Letter Symbol Frequency
ا
وفظ 9
ي
وفٍ
8
ٚ وؼش 8
ع وغف
3
ة وّغ 2
ك
وؼٍ 2
د وؾث
2
َ وغؽ 1
ْ
هلث
1
ى وٙش 1
ف ومش
1
ق
هنٔ
1
م
وّش 1
ً وفص 1
ن
وٙف
1
SPACE ْ
7
Table 1.8. The first of ibn Dunayn r's two practical examples.
In the other verse (Chapter 62) ibn Dunayn r expands on the
algorithm of cryptanalysis, which is conducted according to the
following steps:
1. Calculating the number of letters that constitute the verse (34 in
this example), to deduce its meter (al-bas in our case).
2. Based on step 1, inferring that the rhyme is of the overlapping
type.
3. Preceiving that the final letter of the verse is the same as that at
the end of its first hemistich ـــa phenomenon in Arabic poetry
called at-ta r .
4. Sorting out the letters according to their order of frequency, and
thereupon eliciting the name of God للها , utilizing the repetition
of the letter (ي). Three letters are thus determined, i.e. ا, ي and ـ٘.
55

5. Checking the next high-frequency letters (after ا and ي ), holding
that they would probably be َ and then ٞ .
6. Experimenting with probable words, based on letters so far
uncovered.
7. Composing a word-group that carries meaning and meter:
... ٟٔأ ٍُؼ٠ للها
8. Carrying on after this pattern, always building on what has
already come out, and guessing yet unknown letters in three- or
four-letter words, until the following verse develops:
Right from the outset, ibn Dunayn r lists the letters of the verse,
together with their respective symbols. In the following table (Table
1.9.) these letters are re-arranged according to their descending order
of frequency.
Letter Symbol Frequency
َ
لٍِ
6
ي
لٙف
4
ا
لؼٍ
3
ٞ
لجٌ
3
ن
لٍع
3
ـ٘ كهٚ
2
ْ
لٍٙ
2
ه
لٔى
2
ة
لؼث
2
ػ
كوِ
2
ع
لجػ
1
ؽ
لمػ
1
ٚ
لغٔ
1
ط
لٕ٘
1
د كوغ 1
Table 1.9. The second of ibn Dunayn r's two practical examples.
1.3.2.7. Conclusion (Chapters 63-66)
ibn Dunayn r brings his book to a close by priding himself on
having broken fresh ground, suggesting that he manages to run the
56

gamut of encipherment from simple to composite on the one hand, and
from prose to poetry on the other. He insinuates that al-Kind 's and
ibn ab aba's treatises on cryptanalysis "both failed to develop the
topic exhaustively in either case". 72
He then cites lines of verse [cipher alphabets or cryptographic
keys], each embracing the Arabic alphabet in such a way as to avoid
the repetition of any letter. These are quoted almost entirely from the
treatise extracted from Adab a - u ar ', to be followed by verses
sometimes used in encipherment, and intended for sustained mental
exertion in pursuit of solution. The difficulty underlying these verses
stems from one or more of the following practices:
1) using undotted letters of identical spelling patterns.
2) repeating such letters in a manner so unfamiliar as to upset the
principle of letter frequency.
3) purposely using letters that do not admit linking with one
another all through the verse; e.g.
4) repeating in the second hemistich the same words of the first
hemistich, but in different order. Example:
5) writing the verse adroitly such that the first hemistich is read
forward as the second hemistich is read backward. Example:
6) using odd or out-of-the-way poetic meters, or yet neo-meters
that never belong to the well-known meters of al- al l. Also,
failure to observe a uniform rhyme or rhyme letter.
ibn Dunayn r subjoins a statement restricting the limits of the
cryptanalyst by analogy: "The cryptanalyst is not obliged to puzzle out
ciphers intended for mental exertion, just as the grammarian is not
bound to enter into intricate issues."
73
72 See ibn Dunayn r's book, p.184.
73 Ibid., p.186.
57

1.4. Originality of ibn Dunaynir
Regardless of his drawing upon the works of his predecessors,
ibn Dunayn r stands great amidst cryptological figures. The features of
his originality are manifested first and foremost in the following
contributions:
1. The utilization of numbers in substitution encipherment.
2. The employment of several numbers in ciphering each letter by
substitution. This method as developed by ibn Dunayn r (though
tackled before him by the Author of the Two Essays,
substituting several symbols for a single letter) underscores his
profound cryptographical knowledge, and is known today as the
principle of "frequency reversals". To be noted is that the
earliest instances of using this method in Europe date from the
reign of King Henry IV of France, in his correspondence with
74
the Landgrave of Hesse between 1602-1606, that is four
hundred years after ibn Dunayn r.
3. The demonstration of composite methods of encipherment such
as the one implementing transposition and substitution together,
which has proved important in today’s block cipher algorithms
such as the Data Encryption Standard (DES) and the more
recent Advanced Encryption Standard (AES), both are based on
the principle of encipherment using both methods
simultaneously, but carrying it to a higher degree of
sophistication by means of a binary number system.
4. The abundant use of encipherment by concealment, which he
describes as composition on a background or medium that
disguises the actual intent, such as composing on a tale, dream,
chessboard, financial register, planets, etc.
5. The utilization of encipherment devices such as coloured beads,
punched board and thread, folded paper, etc.
6. The use of encipherment by signaling, applying the arithmetic of
decimally-weighted numerical alphabet (ADWNA) and the
finger-spelling method of communication between two
individuals (manual alphabet).
74 See Treatise on Cryptography, A. Lange and E. A. Soudart; Laguna Hills, CA:
Aegean Park Press, 1981, p.10.
58

It would finally be just as well to remark that most of ibn Dunayn r's
contributions listed above relate to prose encipherment. Not that his
contribution in poetry is any less worthy, but contributions there are
common ground among fellow authors of similar treatises; hence the
difficulty defining clear-cut aspects of ibn Dunayn r's originality.
Suffice it to say that it is to his credit that he could exhaust the subject
of encipherment and cryptanalysis of both prose and poetry at such
length that is unique to him among all those who have written on this
art.
59

Section 2
ibn Dunayn r's Edited Book:
Expositive Chapters on Cryptanalysis
60

2.1. Editing Methodology
The main purpose of editing is the reproduction of a text as close to
the author's original as possible. In line with this objective we have
opted for preserving the statement of the original whenever possible.
� The very nature of the original manuscripts required the
addition -where appropriate- of explicatory titles in the
interest of marking out divisions or classifications. This
would prove useful for easy understanding and clarity of
ideas.
� No effort has been spared in the interpretation of citations
(Koranic verses, Prophetic traditions, lines of poetry,
sayings, etc.) contained in the treatises. We have given brief
biographical identification of personalities (in footnotes to
Arabic text only), relegating interested readers (in Arabic)
to such authorities as al-A l m by ayr al-D n al-Zirkily or
Mu am al-mu'allif n by Omar Ri Ka la, for further
and more detailed biographical reference. Those citations
and personalities that our efforts fell short of their
interpretation or identification have also been properly
recorded.
� In explaining the linguistic terms included in the treatise we
have made use of various dictionaries, old and modern,
foremost of which are: Lis n al- Arab and Matn al-lu a.
Unless otherwise helpful, no reference has been made to
any dictionary.
� We have adopted the same symbols and signs commonly
employed by editors of Arabic manuscripts, and conformed to
the modern spelling norms. We have enclosed requisite
contextual additions -i.e. explanatory insertions and comments
other than the writer's own words- within square brackets [ ];
examples illustrating rules of encipherment have been set off by
round brackets (parentheses) ( ); book titles in italics; quoted
material and Prophetic traditions have appeared within
quotation marks ― ‖ , while floral brackets �� have been used to
enclose Koranic verses. 75
75 Translator's explanatory additions are placed between pairs of hyphens: -…-.
62

2.2. Description of the manuscript
ibn Dunayn r’s book is one of several treatises making up the
assemblage of cryptology, which is part of the stock of the F ti
Library, preserved in as-Sulaym niyya Ottoman Archives in Istanbul
under number 5359. The largest in that aggregate, ibn Dunayn r’s
book spans the sheets 54/A to 80/A. The first sheet contains the title:
Zubad fu l ibn Dunayn r f all at-tar im (The gist of ibn
Dunayn r’s chapters on cryptanalysis), followed immediately by six
lines of poetry on rhymes and related topics. 76 The second sheet bears
the title: Maq id al-Fu l al-Mutar ima an all at-Tar ama.
Following are photocopies of these two sheets, as well as the last sheet
of the book.
76 It has been found appropriate to shift the contents of this sheet to the end of the
book, where it fits more snugly in the context of cryptanalysing poetry.
63

Figure 2.1. A photocopy of the first sheet of ibn Dunayn r's book
(Document No. 5359, as-Sulaym niyya Ottoman Archives, Turkey)
64

Figure 2.2. A photocopy of the second sheet of ibn Dunayn r's book
(Document No. 5359, as-Sulaym niyya Ottoman Archives, Turkey)
65

Figure 2.3. A photocopy of the last sheet of ibn Dunayn r's book
(Document No. 5359, as-Sulaym niyya Ottoman Archives, Turkey)
66

2.3. ibn Dunaynir’s Book
Expositive Chapters on
Cryptanalysis
(Original Arabic Text and English Translation)
67

In the name of God
the Compassionate, the Merciful.
Maq id al-Fu l al-Mutar ima
an all at-Tar ama
68

He said, following the honorific opening statement in praise of God
and the introduction: This book is divided into two parts: the first
tackles the cryptanalysis of prose ciphers; the other deals with
cryptanalysing poetry ciphers. I have further divided each part up into
well-organized chapters, covering all types of encipherment and their
respective algorithms for cryptanalysis. In so doing I always turn to
God for right guidance and support; most sufficient unto me is He, the
Holy One, in whom I trust.
[PART ONE]
[Cryptanalysis of Prose Ciphers] 77
I say: It is true that cryptanalysis is achieved first and foremost
through conjecturing about the cipher sought for solution. The
cryptanalyst keeps trying alternatives and assuming possibilities until
all the forms of the ciphertext reveal all their corresponding letters of
the alphabet. However, there are measured principles and rules
governing this art, so that what is assumed by the cryptanalyst is an
outcome of reasoning and argument by analogy, and not an issue of
haphazard, hit-or-miss endeavour. Successful cryptanalysis involves
two aspects: First, familiarity with the order of letter frequency of
occurrence; namely knowledge of the letters of high occurrence
[abundant letters], those of medium occurrence [common letters], and
those of least occurrence [scarce letters].
77 Square brackets contain useful explanatory additions to the original text.
70

The second aspect is a thorough knowledge of letter combination
and non-combination; namely having cognizance of the combinable
and non-combinable letters, letters combinable in both pre- and post-
positions [anteriorly and posteriorly], those non-combinable both in
pre- and post-positions, those combinable pre-positively only, and
those combinable post-positively in relation to each other. I am herein
stating them in a way that serves the purpose well without much toil.
Moreover, every pursuit needs some kind of instrument expressive
of, and responsive to, one’s intention. The requisite instrument of this
art is the familiarity with the methods of encipherment I am going to
mention in the course of the book.
Any person involved in this science should be endowed with
intelligence, observation, insightful delicacy, keen intuition,
equanimity of mind, proper flair and apt speculation. Otherwise he
would never stand to benefit by any of the methods conducive to
cryptanalysis. Nay, some may have the plaintext already right under
their very nose, yet they are not well-guided to read the cipher
message contained therein, let alone to put to use or even grasp my
say!
Chapter [1] 78
Cryptanalysing enciphered letters can be done through the
utilization of either quantitative or qualitative expedients. By
―quantitative‖ is meant the frequency of occurrence of a letter sought
for cryptanalysis in a ciphertext. By ―qualitative‖ is meant the mode of
the letter occurrence [as regards combinability] in the ciphertext.
78 Chapter numbering is an addition for easier cross-referencing.
72

Chapter [2]
As for cryptanalysis by the quantitative occurrence of a letter in a
ciphertext, I say:
Of all the letters of the alphabet, long and soft letters, or what is
called ―vowel letters‖, have the highest frequency in the Arabic
tongue. These are ا ( ), ٚ (w/ ) and ٞ (y/ ). Some give preference to
the letter ي (l) over ٚ on account of the fact that the letter ي is of high
occurrence with the letter ا, specifically to form the Arabic definite
article (يا), although it often occurs with other letters or doubled.
Because of its high frequency in use, which exceeds the frequency of
the letter ٚ, the letter ي takes precedence [over ٚ], and so is the case
with the letter َ (m), which has priority over ٚ and ٞ 79 .
The letters ا , ٚ and ٞ are called the vowel letters because they
represent the voiced speech sounds created with air passing out free
without causing undue friction. That is why they have the highest
frequency among all letters in all tongues. Other letters vary in their
frequency from one language to another. The letter ً (s), for example,
is more abundant in Latin than all other letters except for the vowels.
Turkish and Mongol are abundant in the letter ْ (n), and so forth. If
we set out to describe the algorithms of cryptanalysis in each tongue,
the book would grow larger. Let us now start to address the methods
of encipherment in the Arabic language, and their algorithms for
cryptanalysis.
79 Thus the frequency count of abundant letters according to ibn Dunayn r, in order
of precedence, is: ا, ي, َ, ٚ and ٞ.
74

Chapter [3]
Encipherment of letters falls naturally into two major types: i.e.
simple encipherment and composite (or super-) encipherment.
SIMPLE encipherment is divided into two parts: in the first part
letters change their forms; in the other, letters retain their forms.
Simple encipherment where letters change their forms can either be
with conceptual relationship and diffusion, or without conceptual
relationship and diffusion.
That with relationship and diffusion can be either relation by
species, or relation by genus. In each case the symbol indicative of a
letter may be either one symbol or numerous symbols. By one we
mean representing the letter ط ( ), for instance, by a symbol suggesting
a single bird such as a pigeon. By numerous is meant the
representation of the letter ط by a symbol suggesting any bird, since
the bird genus includes all species of birds.
76

Chapter [4]
The other division [of simple encipherment where letters change
their forms] is that without relationship and diffusion. This splits up
into two subdivisions: EITHER by changing the forms of letters
-substitution-, OR by keeping the forms of letters -transposition-.
Changing the forms of letters is accomplished by adopting a cipher
alphabet of devised shapes [or symbols] not having the usual forms of
letters. This may be done EITHER by replacing each letter by one
symbol, OR by assuming symbols for those letters that often go
together.
Simple encipherment by keeping the forms of letters branches into
two types: the one involves changing the original positions of letters;
the other is without changing the original positions.
Changing the original positions of letters is divided into two
methods: the one is transposition by changing the position of a letter
in relation to surrounding letters, viz in anterior and posterior
positions; the other is transposition by changing the position of a letter
in relation to itself, viz in terms of only changing its angle of
presentation.
As for enciphering without changing the original positions of
letters, there are two methods: EITHER by the addition of extra
symbols -nulls-; OR without adding such symbols [rather by omitting
one or more symbols]. If nulls are used, they may be either one or
numerous.
78

Chapter [5]
The other part of simple encipherment [where letters retain their
forms] is achieved via two principles: the one is quantitative; the other
is qualitative.
The quantitative principle divides into two subdivisions: the one is
to double, triple, quadruple, etc. the letter. Duplication may be applied
to all or some of the letters. The other subdivision of the quantitative
principle is to merge all the letters that can be merged, by assuming
one common symbol for those which have the same contour. This may
be exercised over all the letters, or only over some.
The qualitative principle, on the other hand, can be accomplished
either by linking all or some of the letters that are inherently
separated, or by separating all or some of the letters that are inherently
linked.
80

Chapter [6]
The other major type of encipherment of letters, i.e. COMPOSITE
(or super-) encipherment, falls into two divisions: the one is a
combination of simple methods, and the other is what ensues in
consequence 80 .
Now then, I have gone through with all the types of simple as well
as composite encipherment, numerous and diverse as they are 81 . This
is all that is necessary for the encipherer to know, as these divisions
cover the long and the short of encipherment. If we set out to dilate on
them all, it would take long, and time would press. Now let us start
with simple ciphers that are prerequisites for the encipherer in
practice. Then we state the relevant algorithms of cryptanalysis,
before we embark on composite ciphers. What applies to
cryptanalysing simple ciphers also applies to cryptanalysing
corresponding composites; and thus developing a thorough knowledge
of simple methods of encipherment will render superfluous the
exposition of all composite methods, since these would then never
miss the cryptologue’s perspicacity and insight a priori. Nevertheless,
I am to mention the various divisions of composite encipherment, and
algorithms for their decryption [in due course].
80 There is no mention to the latter division in al-Kind ’s treatise (q.v., p.142). ibn
Dunayn r is probably referring to composing through a medium, as we shall see.
81 In fact ibn Dunayn r’s handling of the types of encipherment here tends to be
more of an honest rendition of his predecessor al-Kind than an original
investigation. Compare with al-Kind , Volume One, p. 132 ff.
82

Chapter [7]
I say: The type of encipherment characterized by changing the
forms of letters is achieved by devising shapes or symbols not
attributed to letters at all. In this method every letter is represented by
a symbol that is unique to it. The cryptanalysis is accomplished by
counting the symbols of the cipher message, and establishing the
frequency of occurrence for each symbol, by affixing the frequency
number to the respective symbols of the cipher. Having done that, you
dispose the symbols in order of frequency precedence, designating the
most frequently-occurring symbol in its locations throughout the
cryptogram. Do the same with the next frequently-occurring symbol,
and so forth until you exhaust all the symbols of enciphered letters.
Now place the highest-frequency symbol against the highest-
frequency letter of the Arabic alphabet, doing the same with the rest,
conformably with their order of frequency. Keep going in the same
vein until you use up all the letters and symbols. Make sure to place
the symbol of highest frequency against the Arabic letter (ا), for it has
the highest frequency of all letters in all languages, as we have already
stated in the context of discussing the vowel letters. Remember also
that the letter (ي) is the next highly frequent letter after (ا) in all
tongues, followed by the letter (ٚ), then (َ), ( ـ٘), (ٞ) and (ْ)
respectively. You keep on matching letters until they begin to show
intelligible relationship. Symbols defying solution should be tracked
down time and again, using fair conjecture until their purport comes
right for you.
84

Chapter [8]
I have considered the orders of letter frequencies according to the
reckoning of Ya q b al-Kind , peace be on his soul. He said he had
turned to seven parchments and counted all the orders of letter
frequency of occurrence in them, to find that the frequency of the
letter ا ( ) was 600. the frequency of the letter ي (l) was 437, that of the
letter َ (m) was 320, and so on till the end of his citation 82 . It so
occurred to me to take up [other] written sheets myself and count the
letter frequency orders in them. Thus I took three sheets of prose
epistolary texts and calculated the frequency of the letter ا ( ); it turned
out to be 575. the frequencies of other letters were found to be as
follows [in descending rank]: the letter ي (l) occurred as often as 360
times; the letter َ (m) 265 times; ـ٘ (h) 260; ٚ (w/ ) 250; ٞ (y/ ) 230;
ْ (n) 225; ه (r) 195; ع ( ) 170; ف (f) 145; د (t) 115; ة (b) 105;
ن (k) 95; ك (d) 80; ً (s) 75; ق (q) 62; ػ ( ) 50; ط ( ) 43; م ( ) 32;
ص ( ) 28; ُ ( ) 17; ؿ ( ) 13; س ( ) 11; ى (z) 9; ط ( ) 8; ظ ( ) 7;
ؽ ( ) 5. 83 So it came home to me the validity of the statement of
Ya q b ibn 'Is q [al-Kind ], peace be on his soul.
82
See other letter frequencies according to al-Kind and ibn Adl n in Volume One,
p.168 and Volume Two, p.48 respectively.
83
The letter ض ( ) does not appear in this count, neither does it in al-Kind ’s count;
see al-Kind ’s treatise, p.168. Its frequency according to ibn Adl n is 23; see his
treatise, p.48.
86

Chapter [9]
If the cryptogram is very short, there exists insufficiency in it of the
frequency of letter occurrence. The expedient for cryptanalysis to be
used here is to determine those letters [of the alphabet] which admit
combination with each other, and those which do not. The cryptologue
should be ambly experienced to cope, until he elicits the intended
meaning of that scant cipher. Let us then start to address combinable
and non- combinable letters, so as to guide the seekers of
cryptanalysis to this honourable science, and acquaint them with the
rules of this art. In the following table, we shall demonstrate the
various divisions of letters and their relative non-combinability,
numerous and diverse as they are, with the good assistance of God.
88

ً (s)
س م ى
م ( ) س ى
ى (z) س م
ص ( ) س م
does not
ض ( ) س م
combine
ظ ( ) س مك
with
ػ ( ) ؿ ع
ؿ ( ) ػ ؽ
ط ( ) ق ط
ؽ ( ) ط ػ
س ( ) م ى
ط
ص
ى
ص
ى
ؽ
ظ
ؿ
ص
90
ص
ظ
ظ
ط
ط
ط
ؽ
ع
ض
ض
ص
ً
ظ
ظ
ص
ظ
ض
ً
ً
ط ض
[Relative non-combinability of letters]
ظ
ً
ً
ض
ُ
ً
anteriorly
nor
posteriorly

Chapter [10]
I say: Letters are divided into four groups: the first group represents
letters that combine with each other in both anterior and posterior
positions; the second group covers those letters that do not combine
with other letters neither in anterior nor in posterior position; the third
designates those letters combinable with other letters anteriorly, but
non-combinable posteriorly; and the fourth group embraces letters that
combine with some others posteriorly rather than anteriorly. These are
the possible divisions of all letters with respect to their combinability,
disparate as they are in their characteristics and peculiarities.
Letters combinable anteriorly as well as posteriorly are all the
[variable] letters, with the exception of those that I am to exclude for
you. These are: ا ة د ً ف ن ي َ ْ ـ٘ ٚ ٞ , of which the letter
(ً) combine with some letters rather than some others. It does not
combine in anterior nor posterior position with these letters:
س م ظ ص ض ى ; but it does combine [in both positions] with:
ط ػ ؿ ك م ه ُ ط ع ؽ ف ق ن ي َ ْ ـ٘ ٚ ٞ ا ة د.
The basic letters, sixteen in number, are these:
س ط ػ ؿ ك م ه ى ُ ص ض ط ظ ع ؽ ق , which are intrinsic and
never change. Variable letters are not sheer basics, but they occur now
as basic now as affixing letters.
92

Basic letters are so designated because some of them are not
combinable with one another prepositively nor postpositively; some
are combinable prepositively only; while some others are combinable
postpositively only. Variables are so denominated owing to the fact
that they vary, i.e. can combine with all letters anteriorly and
posteriorly, save the letter ً as already stated.
Let us now draw up a comprehensive table of non-combinable
letters, letters combinable anteriorly, and those combinable
posteriorly; also those letters that are used and that are not used. This
is particularly helpful to elucidate the matter at issue, and expose it
smoothly without striking snags to its pursuer, who should be keen to
attend to it, ponder on it, and seek the advice of those who know
better.
This table, together with the previous one, portrays all letter
potentials of combinables, non-combinables, variables, basics, letters
used and not used. And I abridged that considerably such that my
version should suffice instead of al-Kind ’s treatise and its long-
winded prolixity. 84
84 Contrary to ibn Dunayn r’s belief, al-Kind 's treatise is far from prolix; it is a
typical example of brevity and depth of investigation.
94

Letters not used
are these
Letters used are
these
96
(2) (1)
These letters do
combine
anteriorly with
all letters in
column 1
These letters do
not combine
anteriorly with
any letter in
column 2

Chapter [11]
Encipherment by changing the forms of letters [monoalphabetic
simple substitution] is accomplished by substituting for each letter the
form of another, such as using the form of the letter (ق) to denote the
letter (ؽ), and (ن) to indicate (ك), and the like. I have already
elaborated this method fully in my book [a - ih b an-n im f ilm]
wa at-tar im, which serves well instead of restatement here. The
algorithm of cryptanalysis thereof has been outlined earlier.
Chapter [12]
Encipherment by changing the forms of letters can also be attained
by devising a symbolic cipher alphabet, not in the least pertaining to
the plaintext letters [substitution by symbol]. These devised forms
may be substituted one for each letter and aligned beside one another.
However, substitution can be applied to all or only some of the letters.
The algorithm of cryptanalysing this method entails the utilization of
the [quantitative] expedients mentioned earlier.
98

Chapter [13]
I say: If encipherment is done by maintaining the forms of letters
but changing their relative positions in relation to the surrounding
letters, it is very easy to cryptanalyse. Observing the incoherence of
the connection, you realize that letters have been interchanged. You
try to restore their original arrangement time and again, and you are in
line for hitting the mark.
If the letters are devised forms [i.e. employing simple substitution]
and interchanged as we have already stated [i.e. by transposition], the
way for cryptanalysing them consists in the utilization of the first
instrument [i.e. the quantitative expedient]. Once the cryptologue
works out the letter orders [of frequency], and places each letter of the
alphabet against its devised counterpart in the cryptogram, he
interchanges their relative positions reciprocally, shifting the letters
backward and forward in relation to one another, until they slot into
place and the intended meaning shows up 85 .
Encipherment by changing the position of a letter in relation to
itself is done simply by altering the angle of its setup, assuming
various angles of presentation, such as writing it upside down or
standing on its end. Cryptanalysing this type is so easy that it would
never miss the common sense of anyone with perceptive insight. It is
to set straight the forms by turning the angles of their setup. Once any
of the letters is adjusted, you take that form as a clue to that letter in
all places.
85 This is the first indication to a composite cipher achieved by substitution and
transposition together.
100

Chapter [14]
Encipherment without changing the positions and forms of letters is
rendered by embedding [within or between words] additional
insignificant letters [nulls], that must not be vowels. The cryptanalysis
of this encipherment is reasoned out by calculating the forms and
sorting them out. If you find them in excess of the letter orders, try to
work out some of them by the first expedients we have previously
mentioned. You now look into the letters non of which has yet shown,
and seek their identical instances among those already puzzled out. If,
by eliminating those letters sought for solution, the context makes
sense and word composition straightens, you conclude the letters left
out are all nulls-spacers. When the encipherment is done using one
null only, in that case you have already solved it ipso facto, since the
single null is employed as a word-spacer.
102

Chapter [15]
I was asked to cryptanalyse a ciphered message, but found it
incompatible with any of the [simple encipherment] divisions. I
pondered on it, sorted out its characters against the letters of the
alphabet, but it was still impenetrable through utilizing those
algorithms. When I dropped certain characters and re-composed the
letters they fell into place and turned out well. I did the same
elsewhere in the cipher, and words also tied in. So I kept dropping
those letters wherever they occurred in the cryptogram, and the thread
came right for me. I grasped its content to the end, and realized that
the characters dropped were all nulls, and that some letters of the
alphabet might be omitted, to be replaced by nulls. That is perhaps the
most intricate and problematic encipherment possible. By changing
the forms of letters, altering their positions, and at the same time
omitting [certain] letters of the alphabet to replace them with null
forms, the cipher would be very hard to solve indeed. Nevertheless,
and by the good assistance of the Almighty, I managed to solve it
straightway.
104

Chapter [16]
There is another method of encipherment [without relationship and
diffusion] and without changing the forms of letters, their positions or
setup, and implemented not by adding nulls, but by omitting letters
from the cipher message 86 . The cryptanalysis here lies in computing
the forms; if they are found less in number than the alphabet count,
you detect them through the first expedients we have mentioned
earlier in this book. Work out some letters of the cryptogram sought
for cryptanalysis. If you notice, by seeking their identical counterparts
elsewhere therein, the existence of one and the same letter omitted so
that the context does not straighten, examine the context closely and
weigh up what is [purposely] omitted, as the words and import would,
in all likelihood, point to it. For example, instead of writing للها َُث you
write للها ٌث, dropping the letter َ. You will soon realize that the
context tends to bespeak its existence. To establish the identity of the
missing letter, you sample the vacancies against all the letters of the
alphabet [one by one]. If, in two or three places of the cipher, the
cryptanalyst finds that the same letter is missing, he concludes, in
positive assertion, that it has been [deliberately] dropped.
Chapter [17]
The next type of [simple] encipherment to consider is that where
letter forms are changed with relationship and diffusion; namely the
letters here are conceptually related by species or by genus. Their
relationship by species involves representing the ciphered letter ط ( ),
for instance, with the symbol of a single bird, say a dove. Their
relationship by genus entails designating the same letter ط using the
symbol of every bird, as flight is a feature that all birds have in
common. This is the most demanding aspect of this type of
encipherment. Once it is observed, the rest would be manipulated by
the first afore-stated technique.
86 This is the method ibn Dunayn r drops in his discussion of the types of
encipherment; see p.13.
106

Chapter [18]
In the preceding chapters we have tackled simple ciphers
accomplished via the qualitative principle, given that there are just a
few simple methods which remain unmentioned. Now let us enter
upon composite ciphers here as they also pertain under the qualitative
principle. So I say: Ciphers that are intended to be composite could
really be a combination of practically all the afore-mentioned simple
methods. Composition of [simple] methods tends to give rise to quite
a large multitude of ciphers, too many to be addressed all herein. But I
mentioned a good few of them to serve as a guideline in deciding on
unmentioned cases, if any. al-Kind never attended to composite
encipherment except incidentally 87 [without dwelling on details].
Whoever attempted to deal with it, other than al-Kind , certainly raved
and went astray on that score. I am going to present it to you on the
spot, along with the algorithm for its cryptanalysis, by the good
assistance of God Almighty.
87 In fact al-Kind ’s treatment of composite encipherment and the algorithms for its
cryptanalysis is precise and in conformity with the system of brevity and
compactness that he adopts and observes throughout. See his treatise p.142 and
p. 164.
108

Chapter [19]
To identify a cipher as composite, check it against all types of
simple encipherment individually. If, after all, the cipher remains
abstruse, it is concluded to be composite; thereupon it should be
matched up against the type by which a part of the cryptogram has
been worked out, until it makes sense. Bear in mind that the composite
type of encipherment is definitely the most complicated; its
cryptanalysis for those with insufficient expertise is virtually
impossible. Let us proceed to mention some of the types [of composite
encipherment], as they are the ultimate in cryptanalysis.
Chapter [20]
One type of composite encipherment is to represent each letter of
the alphabet by instruments, foods, clothing, jewellery, animals, and
such other items listed in the following extensive table of generic
names. It is rewarding to always be at pains to study this table over
and over again until you exhaust it and comprehend its content
perfectly well. We pray to God, the Ever-Nigh, the All-Hearing for
that He has guided us to, and from Him we invoke support.
110

of people: someone, whom you know or whom you do not.
b of herbs: endive, cress, etc.
t of dates: varieties of dates, e.g. makt m, barn , etc.
of clothing: shirt, turban, etc.
of leather: hide (raw or dressed),skin, etc.
of iron: swords (varieties of swords, e.g. Damascene,
Indian, etc.), steel
of wood: sandal, fir, etc.
d of animals: horse, bull, etc.
of gold: varieties of gold, e.g. Egyptian, etc.
r of aromatic plants: lily, lotus, violet, etc.
z of glass: bottle, cup, etc.
s of fishes: carp, mackerel, etc.
of chess: pawns, individual chess pieces.
of brass: brassware, e.g. (drinking) glass, tazza, etc.
of regions: specific regions.
of birds: hawk, falcon, etc.
of deer: gazelle, stag, roe, etc.
of perfumes: specific makes and types of scents.
of sheep: goats, ewes, rams, lambs, etc.
f of fruits: apples, quinces, etc.
q of villages: so-and-so’s village, etc.
k
of books: names of books, e.g. al-'A
lu a, etc.
, al-mu mal f al-
l of milk: types of milk (e.g. colostrum), milk products, etc.
m of towns: Mosul, Cairo, etc.
n of stars [and planets]: Sirius, Canopus; Saturn, Jupiter, etc.
h of vermin, pests, etc.: scorpion, snake, etc.
w/ of paper: varieties of paper, e.g. papyrus, stock paper, etc.
Y/ of jewellery: emerald, diamond, etc.
112

To take up one of these letters, you turn to each genus and to the
species thereof relevant to that letter. From that species you name one
of its types. For example, to encipher the statement " " you
may write: "Mr. so-and-so bought colostrum and yoghurt in which he
found a scorpion. He bought stockpaper and used it to wrap wet
cheese in which he found a sapphire stone. He went with such-and-
such a person somewhere on the outskirts of the town, to buy wet
cheese and dates. He put them in a paper, along with some apples. He
saw a crystal kohl jar. Together they walked to the judge's village."
Our saying "so-and-so"signifies the letter ا ( ); the words "colostrum"
and "yoghurt" indicate the letter ي (l) twice; the word "scorpion"
stands for the letter ـ٘ (h), and so on you proceed to the end by
analogy. This is one type of composite encipherment that defies
cryptanalysis. The words in between are inane redundancy; the
intended purport is sought via the nouns placed against the letters
indicative of cryptanalysis. Note that such a cipher can be [and is
better] presented in the framework of a dream, a tale, an episode or the
like.
114

Chapter [21]
Another type of encipherment is the one that is "composed" on
numbers. Each letter is designated by its numerical value in the system
of is b al- ummal (the arithmetic using decimally-weighted
numerical alphabet) the minor and the major. That numerical value
having been written indicates the letter it represents. I am about to
elucidate the manipulation of letters according to is b al- ummal in
both its minor and major divisions, God being willing. 88
The highest degree of concealment using this type is attained in an
area-dependent cipher, where letters are rendered in terms of numbers
suggestive of what used to be called ar bs, qaf zes and a rs [old-
fashioned length units]. Qaf zes and a rs are expressed by upper dots
and lower dots respectively. The technique is based on making the
cryptogram look like a peasant-farming financial record or something
of the kind, simulating an outward aspect of buying, selling, or other
similar bargains. Meanwhile you state the number of ar bs placed
against the letters, one by one. Letters with upper dots 89 serve to
represent qaf zes; letters with lower dots 90 serve to represent a rs.
These should go after ar bs. If you fail to do like we have told you as
regards giving the cryptogram the semblance of a financial register of
expenditure, an episode about someone, taking, buying or giving, you
would incur a raw and unhappy [state of affairs], over and above an
unmistakable clue to exposing the intended encipherment. Otherwise,
this course of action would be quaint and pretty efficient.
88
See Chapter 25.
89
i.e. the letters (ٞ, ن, ي, َ, ْ, ً, ع, ف, ص) according to the numerical-alphabet
order, representing the tens places.
90
The rest of letters, i.e. (ق, ه, ُ, د, س, ؿ, م, ض, ظ) designating the hundreds places,
followed by the letter (ؽ) in the thousands position.
116

Chapter [22]
This type is used to address a person who is in attendance, through
finger signaling the numbers [numerical values] corresponding to the
respective letters. It is a straightforward method of composition. To
express a letter you give its numerical equivalent [in ADWNA] by
means of relative finger configurations using the right-hand fingers for
the numbers one to hundred, 91 and the left-hand fingers for the
numbers hundred to thousand. I shall demonstrate the method for the
numbers one to ten to serve as a clear example for representing other
numbers. The communicator signals the number one [designating the
letter ] by folding his ring finger and mounting his pinkie onto it from
behind. He folds the little and ring fingers inwards to represent the
number two [for the letter ]. Then he joins the middle finger to both
of them to represent the number three [corresponding to ]. He now
spreads the little finger whilst keeping the ring and middle fingers
folded, thus expressing the number four [i.e. the letter ]. Next he
spreads out the ring finger leaving the middle finger folded to
represent the number five [i.e. the letter ]. Now he spreads the
middle finger whilst keeping the ring finger folded, and so
representing the number six [ ]. Thereafter he spreads out all fingers
but the pinkie, and that is the number seven [ ]. If he folds the ring
finger and the pinkie together, then he is representing the number
eight [ ]. With the middle finger also folded, the number nine [ ] is
thereby demonstrated. The number ten [ ] is indicated by spreading
out all fingers, with the thumb and index made into a loop. After this
pattern he proceeds to the number [ninety]; and, now using the left
hand, to hundred and to thousand until what he intends to
communicate is figured out exactly right.
91 -Rather "ninety"-.
118

Chapter [23]
A cipher that is rendered by composing its letters on a chessboard
is also addressed to someone who is present. It may be employed to
address an absent person in a way I shall tell you without precedent.
For instance, to convey to your fellow a private message intended
solely for him, you resort to a chessboard and two chessmen: black
and white. Putting on an air of play, you leave the piece in the square
assigned for the first letter of your message, then you move it to the
square assigned for the next letter, then to that meant for the letter that
follows, until you exhaust all you have got to say. Your fellow, in
turn, does the same until the message is driven home to both of you. It
can be outlined as follows:
Example: To convey the word " " you place the chessman in the
first, sixth, twenty-fourth and eighth squares representing the letter ,
, and respectively.
120

Chapter [24]
Thus to set down a cryptogram opening with the word " ", you
write: Two men were on hand and started a game of chess. They took
two playing pieces. One of the two guys left his chessman in the first
square, then moved it to the twenty-third square twice, thereupon he
moved it to the twenty-sixth square.
What does that mean? The first square signifies the letter , the
twenty-third square denotes the letter twice, and the twenty-sixth
square indicates the letter . It is after this pattern that you should
reason and identify cases of the kind.
122

Chapter [25]
Ciphers rendered by is b al- ummal (the arithmetic utilizing
decimally-weighted numerical alphabet) are very easy to cryptanalyse.
The algorithm is to place each letter of the alphabet against its Indian
decimal numerical equivalent in the system. The following are the
shapes of the Indian numerical character units:
When the number one is preceded by a small circle it becomes ten.
If the circle is placed before the number two it becomes twenty; and
that is how you get the tens orders. If the number one is preceded by
two circles it becomes a hundred. If these two circles go prior to the
number two, it is then two hundred; and these are the hundreds orders.
Likewise, the use of three circles in front of the number one makes it a
thousand, and in front of the number two makes it two thousand, etc.
Consequently, if you wanted to encipher the statement ( ) by
this method, you would have to replace the letters with their
corresponding Indian characters, as follows:
10 30 6 5 30 30 1
(ten) (thirty) (six) (five) (thirty) (thirty) (one)
ٞ ي ٚ ـ٘ ي ي ا
100 10 80 6 400 30 1
(one hundred) (ten) (eighty) (six) (four hundred) (thirty) (one)
ق ٞ ف ٚ د ي ا
This is an example of encipherment using the decimal numerical
alphabet. Examine it carefully, and always keep this book within your
reach.
124

Chapter [26]
One method of composite ciphering is to multiply the numerical
value of a letter twofold, threefold, or more— a process which makes
the cryptogram even more complicated to solve. For instance, you
may write the statement ( ك١فٛزٌا ٌّٟٚ للها ) in cipher like this:
" ه ن ٌل ت٠ ض ً ة ن ً ت٠ ٞ ً ً ة",
increasing the numerical values twofold; the letter ة whose value in
ADWNA is 2 represents the letter ا whose value is 1. Similarly, the
letter ً (= 60 in ADWNA) is twice the value of the intended ي, and so
on for the rest of letters and other multiplications. Note how
interesting this nicety is.
126

Chapter [27]
Encipherment may be accomplished by having the letters of the
alphabet rounded up in seven words, specially coined to represent the
days of the week, a word apiece. Each letter of the word is further
assigned a specific hour of that day, so that you may say: the first
hour, the second hour, the third hour, etc., thereby building your
cipher as follows:
Thursday Wednesday Tuesday Monday Sunday Saturday Friday
ٌّش خظؾٌ هٚك قوجع ي ٓ١زٕص ا
For example, to encipher the phrase ( لله لّؾٌا) you write: the second
hour of the day of Friday, the last hour of the day of Sunday, the
second hour of Wednesday, the second hour of Thursday, the first
hour of Tuesday, the last hour of Sunday (twice), and the last hour of
Wednesday. Our statement "the second hour of Friday" denotes the
letter (ا), "the last hour of Sunday" indicates the letter (ي), and all the
other hours signify the rest of the letters. The algorithm of
cryptanalysing such ciphers is pursued through the application of the
quantitative expedients, namely by computing the order of letter
occurrence frequencies. This type of encipherment is most
conveniently performed by way of a tale.
92 Most the words in the Arabic original are practically illegible; see p.42.
128
92

Chapter [28]
Ciphers can also be effected by folding a scroll [writing sheet], on
which pleats the sender writes whatever they want to convey. Upon
unfolding it, writing would look something like dots and strokes on
those pleats. The concealment is done by unfurling the scroll and
making the dots and strokes into [extra] complete letters until all
pleats are covered. Employing the same technique you can also write
the message on the back of a sheet which has already been used to
write irrelevant material. The dots and letter fragments give the
impression that the sheet was folded while still wet, and that the back
therefore soiled. The exposure of the intended text is very easy. All
you have to do is to re-fold the sheet and read the message.
130

Chapter [29]
Encipherment can be implemented by puncturing twenty-eight
holes in a sheet of wood, one hole for each letter of the alphabet. The
cryptogram is rendered by a thread driven through the intended holes.
For example, to write the word ( لّؽأ) using this method the thread is
driven into the first, sixth, twenty-fourth and eighth holes in
succession. Uncovering the message requires correct identification of
the letters in relation to their respective threaded holes. You remove
the thread from the holes one after another, marking the representative
letters in their due positions. Having done that, you read the letters in
reverse, starting with the hole from which the thread has been
removed last, and ending up with the one from which the thread has
been removed first. The same process is also applicable with long
cryptograms. This method is illustrated as follows:
132

Chapter [30]
Another method of encipherment [using cipher devices] is that
which uses beads of different colours substituted for the letters of the
alphabet. One way of so enciphering is to designate specific colour
beads to represent a letter. The beads are threaded on a string as a
rosary, with identical colours separated by a distinctive mark. For
example, to represent the proper names ( لّؾِ) and (ٍٟػ) using this
method, you thread one of the beads designated to the letter (َ), then
you thread one of those designated to the letter (ػ), followed by one
assigned to (َ) again, and another of those designated for (ك). Now you
carry on with individual beads corresponding to the letters (ع), (ي) and
(ٞ) respectively. Do the same for whatever message you want to
convey. The algorithm of solution comes down to perceiving the
colour bead of highest recurrence and judging it to be against the
letter (ا). The next highest would be determined to stand for the letter
(ي); the following one for (َ), and so on, utilizing the [quantitative]
expedients stated earlier.
134

Chapter [31]
Encipherment may be accomplished by concealing the intended
message within another context. The procedure is to take a white sheet
of paper, on which to write any form of account. The cipher message
is embedded within the context by dispersing it abroad at the
beginning, end, or middle of the account, or yet diagonally, splitting
the sheet into two triangular parts [according to an agreed rule]. The
algorithm of cryptanalysis is very easy by carefully considering the
contextual connection, or otherwise setting apart the beginnings, the
ends, the middle sections, and the diagonal. On such basis the message
bids fairly to come out.
Chapter [32]
And we have straightforward methods out of composites. One such
method is implemented by simulating words [consistently with a set
rule], of which the intended letters are made to be the first, the second,
the third, etc. For instance, the name ( ٍٟػ لّؾِ) may be enciphered:
ٍٟػ ًضِ غفاه َكوف ُى١ٍػ ؼٌبص ٍٍُ [taking the last letter of each word]. This
method is within easy reach of the enlightened people of this
profession, who consider it carefully.
Chapter [33]
Another of these methods is to encipher by writing each word of
the cryptogram in reverse order. That is easy indeed; to render the
word (لّؽأ), for example, in cipher you write ( بؾِك). Cryptanalysis is
also very easy, by experimenting with various algorithms, or
otherwise trying to read it inversely, if the cryptogram is made up of
letters.
136

Chapter [34]
This type of encipherment is fulfilled using special numerical
calculations based on whole numbers and fractions of quarters and
halves. Whole [dinars] are employed to express the units order [i.e.
numbers from 1 to 9]; quarters are utilized to indicate the tens order
[10-90]; halves for the hundreds [100-900]. Thus, the name لّؽأ, for
example, can be written in cipher: 93
Four [dinars] Four quarters
[of the dinar]
138
Eight [dinars] One [dinar]
Cryptanalysing such ciphers requires the cryptologue to be
knowledgeable about arithmetic and keen on investigation. To him
one dinar means the letter (ا) and eight dinars are equivalent to the
letter (ػ), and like this he proceeds till he exhausts all.
93 ibn Dunayn r's example in the Arabic original does not consist with his above and
subsequent explanation; it takes the same lines as simple ADWNA rather than
the fraction concept of quarters and halves. It is herein set right, however .

Chapter [35]
Encipherment can be rendered on an astronomical text
demonstrating the conditions of planets [and other celestial bodies]:
their motions, distances, periods, durations, mansions, revolutions,
and their mutual relationship. The technique is to impart numbers to
some planets in terms of distance covered in orbit or in the
constellation, or suchlike.
For instance, to encipher the name (لّؾِ) you may write: Having
completed forty revolutions, the Moon eclipsed at such and such
degrees of such and such constellation. Eight revolutions thence
remained. Its motion straightened after it had waned in appearance
and faded in colour. Thereafter it moved to Sagittarius and completed
forty revolutions thus far. At the end of Sagittarius the planet Venus
approached it. Four turns elapsed before its motion evened out in
orbit, and its light became as bright as to emulate planets.
Our statement "forty revolutions" designates the letter (َ); the
"eight revolutions" suggests the letter (ػ); and so on for the rest. This
method of encipherment is complicated, and is ascribed to [the
learned] Hermes in his treatise entitled: The war of planets, denoting
the generous nature. The cryptanalyst of this cipher should be
knowledgeable about arithmetic and astronomy, and should make use
of the first statistical principles of calculating the frequencies of letter
occurrence. 94
Thus far I have addressed the bulk of simple and composite
encipherment types encompassed by the first part of this book, viz.
prose ciphers, numerous and diverse as they are, with the good
assistance of Almighty God.
94 -As a matter of fact the cryptanalysis of this method has more to do with
ADWNA than with the quantitative technique.- (Translator)
140

PART TWO
Cryptanalysis of Poetry Ciphers
Chapter [36]
I am going to provide you with rules that serve for a basis in this
highly sought-after art, and also to guide you to the right way therein.
I say: Among the tools that are utilized in cryptanalysing cipher
rendered in poetry [as well as prose] is a thorough knowledge of the
orders of letter frequency of occurrence stated earlier. Frequency of
certain forms is, more often than not, an indication of expected letters.
The pursuer of this art also need to be familiar with the variable and
basic letters, and well-informed in the letter combination and noncombination
phenomenon—letters that combine pre-positively
(anteriorly), those that combine post-positively (posteriorly), others
that combine both pre- and post-positively, and those that do not
combine pre-positively nor post-positively. He should also be
acquainted with letters that are used and those that are not used, as
discussed in PART ONE. 95
Chapter [37]
Thereafter, the keynote element of this science is that the
cryptologue should be widely conversant with prosody, rhymes, and
metrical structures; deeply familiar with the science of poetry; a
person of insight into the knack of writing, with capacious memory for
committing to heart poetry galore, and skilful and resourceful in
cryptography [consequent on long experience and exercise]. Meeting
such requisites, the cryptologue is apt to be able to handle the more
difficult aspects of poetical ciphers.
95 Chapters 8, 9 & 10.
142

Chapter [38]
Prosody has five metrical circles: (1) the circle of the different
(al-mu talif), the pentameters and heptameters of which tend to vary;
(2) the circle of the consistent (al-mu'talif), the heptameters of which
are regular and steadily in tune; (3) the circle of the extraneous (almu
talab), whose measures are drawn from the first circle; and (4) the
circle of the similar (al-mu tabih), whose constituent meters are
marked by correspondence or resemblance; (5) the circle of the
harmonious (al-muttafiq), whose pentameters are in agreement.
Further expansion on these circles would take long, and is outside our
terms of reference.
Chapter [39]
Poetical meters, according to al- al l [ibn 'A mad al-Far h d ], 96
are fifteen in number, supplemented or "redressed" later by 'Ab alasan
al-'A fa [Sa d ibn Mas ada al-'Awsa ] 97 with one more meter,
the so-called al-mutadarak [=the redresser], thus scaling up the
number of meters to sixteen. The poetical meters are: a - aw l, based
on the feet of fa lun maf lun; al-mad d, based on the metrons of
f il tun f ilun; al-bas , its basic units being mustaf ilun f ilun;
al-w fir, which is based on muf alatun; al-k mil, based on
mutaf ilun; al-haza , with its feet maf lun [six times]; ar-ra az,
mustaf ilun; ar-ramal, f il tun; as-sar , mustaf ilun mustaf ilun
maf l tun; al-munsari , mustaf ilun maf l tu mustaf ilun; al- af f,
f il tun mustaf ilun f il tun; al-mu ra , maf lun f il tun
maf lun; al-muqta ab, maf latu mustaf ilun mustaf ilun; al-mu ta ,
mustaf ilun f il tun f il tun; al-mutaq rib, based on fa lun.
Ab al- asan said: and al-mutad rak, which is based on f ilun.
Each of these meters has its own particularities, ramifications, and
views on it, which are not of interest for our purpose.
96 d. AD 786.
97 d. AD 830.
144

Chapter [40]
As for the first [metrical] circle, it has three meters, i.e. a - aw l,
al-mad d and al-bas ; the second circle has two meters, i.e. al-w fir
and al-k mil; the third has three, i.e. al-haza , ar-ra az and ar-ramal;
the fourth has six, i.e. as-sar , al-munsari , al- af f, al-mu ra ,
al-muqta ab and al-mu ta ; the fifth circle contains one meter, i.e.
al-mutaq rib (according to al- al l), or al-mutad rak (according to
al-'A fa ).
He [The cryptanalyst] must also be familiar with such metrical
variations as az-zi f, al- arm, and al- azm.
As for az-zi f, it may occur in all meters, and varies with them. Its
occurrence is peculiar to the so-called sabab. In a - aw l meter, for
example, the ْ of the foot ٌٓٛؼف can be omitted and يٛؼف remains. This
phenomenon is called qab .
As to al- arm, it is the omission of the first vocalized letter of a
[three-letter] foot segment called watid, that occurs at the beginning of
a stich.
al- azm, on the other hand, concerns the addition [of letters] made
at the beginning of a stich, that is taken into consideration in terms of
meaning and counted insignificant in terms of poetic scanning.
146

Chapter [41]
Rhymes 98 are five, namely al-mutak wis, al-mutar kib, almutad
rik, al-mutaw tir, and al-mutar dif.
al-Mutak wis is that rhyme in which are found four vocalized
letters located between two neutral letters (suk ns). al-Mutar kib is
that rhyme in which are found three vocalized letters between two
neutral letters. al-Mutad rik is a rhyme in which are found two
vocalized letters between two neutrals. al-Mutaw tir of rhymes is the
one in which is found one vocalized letter between two neutrals. The
last of rhymes is al-mutar dif, in which are found two [consecutive]
neutral letters.
These rhymes has six letter structures or aw ri , namely the exit,
the relief, the basal (ا), the linkage, the extraneous, and the rhyme
letter.
The rhyme letter (or raw ) is that on which the entire poem is built.
For example, in the following verse,
the letter ق of the word قاّوط is the rhyme letter, and the rhyme of the
whole poem is also ق. Note that all letters may occur as rhyme letters
except for the three vowel letters, i.e. ا ( ), ٚ (w/ ), and ٞ (y/ ) which
often form the so-called release letters (i l q). Supposing the final
word of a stich be بػٌٛٚ, you see that the rhyme is عٌٛٚ, the letter ع is
the rhyme letter, and the letter ا is for release. The same is true with
ِٛب١قٌا or ِٛلاٌَا in which the rhyme, according to some, is َلاٌَا, the َ is
the rhyme letter, and the ٚ the release letter. Similarly, the rhyme in
ٟؼثوٌا and ٟػوغٌا is غثوٌا and عوغٌا.
98 See also ibn Adl n's treatment of drawing on prosody and rhyme towards
cryptanalysis in his treatise (Volume Two of this series), rules 16 & 17, pp.88-98.
148

The relief letter (or ridf) is a vowel letter ( ا, ٚ or ٞ) that occurs
immediately before the rhyme letter. It is a common practice [in
Arabic poetry] to alternate ٚ with ٞ as relief letters in one poem. 99
The basal (or ta's s) is the letter (ا) occurring prior to the rhyme
letter but one. It is not counted basal if it occurs in a word while the
rhyme letter is in another word. Moreover, if the rhyme letter is an
implicit noun or part of such a noun, it is possible that the (ا) emerging
from it be now basal now not. [To be noted is that the basal (ا) is a
requisite element; once used in a poem, it should be observed
throughout.]
The linkage letter (or wa l) is a vowel ( ا, ٚ or ٞ) resultant [among
other things] from fully lengthening the sound value of the rhymeletter
diacritic; or the letter ـ٘, neutral or vocalized, that follows the
rhyme letter.
The exit (or ur ) is any one of the vowel letters (ا, ٚ or ٞ)
occasioned by the linkage ـ٘ when fully lengthened in articulation.
[Like the basal (ا), the exit is a requisite element that, when adopted,
should be adhered to throughout the poem without fail.]
The extraneous (or da l) is the letter that lies between the basal (ا)
and the rhyme letter. 100
99 -Example:
(Translator)
100 -It is interesting to note that in one rhyme it is possible to have a combination of
the basal (ا), the extraneous, the rhyme letter, the linkage, and the exit
simultaneously. In the following verse:
the letter (ا) of the word ٗؼعبضِ is basal, The letter (ط) is extraneous, the (ع)
rhyme letter, the (ـ٘) linkage, and the (ٚ) that results from lengthening the sound
value of the (ـ٘) diacritic is the exit.
Also possible is a combination of the relief letter, the rhyme letter, the
linkage, and the exit. In the following verse:
the letter (ا) of the word ِٗبضٌ is relief, the (َ) rhyme letter, the (ـ٘) linkage, and the
(ٚ) resultant from lengthening the final (ـ٘) exit.-
(Translator)
150

Rhyme, however, may undergo some flaws or defects; these are:
al-'ikf '—the use [in one poem] of two rhyme letters that belong to
slightly different points of articulation. 101
al-'iqw '—the use in one poem of different rhyme-letter
diacritic. 102
al-' '—the repetition of rhyme by using two rhyming words that
agree in form and meaning (identical rhyme). 103
at-ta m n—the state in which the rhyme of one stich, though
metrically complete, is dependent upon the following stich so that
both lines incorporate an integral whole as far as meaning is
concerned. 104
as-sin d—the occurrence, in one poem, of a line with a basal (ا),
and another without one. 105 This has many ramifications that are not
within our scope here.
101 Example: and in this verse:
102 Example: and in the following:
103 Example: and in the following lines:
104 Example: and in:
105 Example: and in:
152

Chapter [42]
It is those with expertise and discernment in orthography who are
the aptest to break ciphers, since they are likely to recognize the
mainstream principles underlying proper writing. The letters (ا) and
(ي), forming the [Arabic] definite article يا [=the] as in ًعوٌا [=the
man], حوغؾٌا [=the room], and the like, are of highest frequency among
all letters. The cryptologue should be able to spot two-letter words
[bigrams], three-letter words [trigrams] and four-letter words
[tetragrams], as these are favourably promotive to cryptanalysis. Pure
bigrams are words such as the following: ِْٓ, َِْٓ, َ سـَـ , َ سـُـ , َةُه, ِةَه, ٓػ,
َيػ, ًََع, ْ نُِ,
َلَِ, َوَِ, ّوُِ, َلَػ, ْلُػ , َُه, ّوث, ّكه, ٌّؽ, َك, ل٠, ؿأ, ةأ, ُػ, َأ, ُّغ, ّلَع,
ّلف. Bigrams, however, may be single letters governed by prepositions
such as: هث, ٗث, هٌ, ٌٗ, etc. They could also be verbal nouns like َْٗص and
َِْٗ, or even verbs expressing command as ْعَك, ْوٍِ and َْ ـ ُـل.
Trigrams are
words such as ل٠ى, ٚوّػ 106 , وىث, لجػ, ًعه, هاك, ةٛص, ػٛٔ, طٌٛ, فوؽ, et
cetera. Spotting some words of the kind is likely to conduce towards
spotting the rest, seeing that they lend significant indications indeed.
Thus we have established rules wherewith algorithms of cryptanalysis
are fulfilled.
106 Numbered by ibn Dunayn r among 3-letter words in respect of its utterance. The
extra final in it he will discuss soon (in Chapter 44).
154

Chapter [43]
Upon trying to work out a line of poetry ciphered for you by
someone else, you start by counting the number of constituent letters.
Should they be found between forty and fifty, the verse would
probably belong to the aw l or bas meter in view of the fact that
these are of the longest meters. If the number is found to be forty more
or less, the meter would probably be one of the whole meters such as:
a - aw l, al-mad d, al-bas , al-w fir, al-k mil, perfect ra az, perfect
ramal, as-sar , al-munsari , al- af f, or perfect mutaq rib. Thirty
letters or thereabouts suggest brachycatalectic mad d, brachycatalectic
bas , square k mil, al-w fir, al-haza , ar-ra az, ar-ramal, as-sar , alaf
f, al-mu ra , al-muqta ab, al-mu ta or al-mutaq rib. In case the
number is found some ten odd, it indicates certain varieties of such
short meters as curtailed munsari and ra az. A ten-letter line
expresses a variety of ra az. A line of verse might sometimes consist
of as few as seven letters like:
[How splendid the moon is.
Rain poured down in torrents.]
Such one unit verse is the shortest possible in Arabic poetry; it
rhymes with (ٍٓؼفزَِ). In fact I have here estimated the number to be in
the neighborhood of forty because a line of verse, when enciphered, is
transcribed according to the standards that are familiar to people. Thus
a geminated letter is metrically represented as two letters, while
considered one letter in ordinary writing. A line of poetry may
undergo some foot variations, in which case the letters so affected take
the place of those geminated.
Having decided on the number of letters, and pondered deeply over
relevant poetic meters, you look closely at the names juxtaposed with
each letter of the poetic cipher. The most highly frequent name is held
to represent the letter (ا), although, in some rare occasions, other
letters may take precedence. Of course, by no means do rarities stand
for established rules.
156

The letter (ي) can be sought by observing in the cipher verse long
words beginning with the letter (ا). The letter that follows immediately
is likely to recur once or twice, and it is positively thought to be the
letter (ي), since it is far more combinable with (ا) than any other letter.
Further, a line of verse may contain a signal clue to the definite (يا),
by observing the occurrence of the letter (ي) repeated in words such
as: للها, ً١ٌٍا, ش١ٌٍا, ت١جٌٍا, and the like.
If you encounter, in a cipher verse, a bigram the first of whose
letters has already been identified as (ا), you have a good reason to
hold that, with the other letter, the bigram may be one of the following
(descending from the odds-on probability): ٚأ, مإ, ْإ, َأ or ٞأ.
Conversely, where the first letter is still covert and the other being (ا),
you can then assume the bigram to be one of these: بِ, ب٠, ام, بش or بؽ. 107
Other bigrams are yet possible.
On the other hand, the letter preceding (يا) in one word should, in
all probability, be (ـ٘) 108 or ن.
Having made out most of the highly frequent letters in the cipher,
you now turn to those of less frequent occurrence. Thus you guess on
heptagrams [seven-letter words] and pentagrams [five-letter words].
Such words should incorporate one or more of the labial letters: ي, ة,
ْ, ٚ, ف, [and َ], which are all but inherent in pentagrams and
heptagrams. Exceptions are too rare to merit consideration.
107
The last two bigrams are actually not all that frequent in usage; they can
possibly and more rightly be: لا & ب٘.
108
So in the original Arabic manuscript; perhaps (ٚ) or (ف) is the correct letter.
158

Chapter [44]
Special attention should be paid to the [terminal] letter (ا) [added to
te letter (ٚ) of plurality] in verbs like: اٛٔبو, اٚهبص, اٌٛبل, اٛػبث. Such an (ا)
is not metrically considered, yet it might pose ambiguity for the
cryptanalyst. Also problematic are verbs [with an intrinsic terminal ٚ]
such as: ٚيغ٠, ٚلغ٠, ٛجؾ٠, which might wrongly be written by some with
a terminal (ا) in the same way as they mistakenly write verbs like اِٛبل
and اٛٔبو without one. A cryptologue should also keep an eye on
terminal hamza's in words like ءبش and ءبٕث, and be equally heedful of
the extra (ٚ) subjoined to the proper name ( ٚوّػ) to differentiate it
from another name, i.e. ( وّػ). It might just as well be avoided
altogether in ciphered poetry because it can be problematic. However,
since poetry is strictly qualified by metrical measures, it would be
realized on the spot which of the two names is intended.
Chapter [45]
A cryptologue ought to be aware of the letter (ا) that is often
dropped in writing in the interest of damping the vocalization. In
poetry I favour fixing it in names such as: ُ١٘وثإ [for ُ١٘اوثإ], ً١ؼٍّإ [for
ً١ػبٍّإ] and كؾٍإ [for قبؾٍإ] since poetry calls for its retention to put
up the meter. Likewise, variants in writing the word (يلا٘) are (ًٍ٘)
and (ً١ٍ٘), which are equally baffling and should therefore be avoided.
160

Chapter [46]
He has to be alert to the letters (ٚ) and (ٞ). All-often they occur in
mid- and end-positions as diacritically geminated, neutral and
vocalized. They also occur following the rhyme in the form of release
letters, as has previously been stated.
Their occurrence as neutral is profuse; e.g. ٓ٠ل٠, ٓ١ٕ١ػ, ٗ١ٌإ, ٗ١ٍػ, فٛف,
فٛع, فٛط, ىٌٛ and يٛم٠.
They may occur at end-positions; e.g. ٟف, ٌٝإ, ٍٝػ 109 , ٛ٘, ٛف, ٌٛ.
They may occur geminated; e.g. لّ١ٍ, ّٞك ط,
كّٛع, كّٛػ, كّٛل.
They may occur following the rhyme letter; e.g. بِلاٍ, بِبمٍ, in
which the (ا) is for release; and ِٟلاٍ , ِٟلاغ, ِٝبمٍ, ِٛبمٍ, ِٛلاغ, ِٛلاٍ,
where the (َ) is the rhyme letter, and the next for release.
When they occur as rhyme letters they may be diacritically neutral
(e.g. ُٝٙٔ, ٜلُ٘, ٞٚم, ٚٚم, ََٚٛ٘); or geminated (e.g. بّ٠وص, بّ١َُّؽ, بّ١زٌٍا, بّ٠نٌٍا, ّٚلػ,
ُّٛجُٔ); or vocalized (e.g. ٟػه
ٍ
, ٟمٍ,
ْٚلَػ,
ٚيغ).
ٍ
ٍ
Chapter [47]
He ought to be particularly familiar with the modes of [medial]
hamza; for instance: حلئفأ, حكُٚءِٛ, حكٚؤفِ.
109 It is the graphic representation rather than the way of reading that matters by
cryptanalytical standards; hence, undotted (ٜ) is considered (ٞ), not a special
variant of (ا).
ٍ
162

Chapter [48]
He should also be fully acquainted with:
1) The five types of the letter (ٚ), viz. the conjunctive, the
circumstantial, the comitative, the potential, and that of
oath. Some add to these the so-called "(ٚ) of the
number eight".
2) The eight categories of the letter (ف), i.e. that of
comment and succession; also the (ف) that occurs in
response to command, prohibition, negation,
interrogation, wish, statement, and invocation.
3) The three categories of the letter (ة); i.e. as a
preposition, as a letter for oath-taking, and as a
"narrative" letter underlying an implicit noun, such as:
4) The two categories of the letter (ن), viz. the
superfluous (ن), and that governed by a pronoun.
5) The three categories of the letter (ي); namely as a
preposition, as an initial letter, and as an emphatic
letter. An additional occurrence of (ي) is its use as
emphatic in the predicate of (َْإ).
6) The high recurrence of the definite (يا = the), as in: ان٘
ُءبٌَٕاٚ ًُعوٌا (= This man and the women), ًَعوٌا ُذ٠أه
َءبٌَٕاٚ (= I saw the man and the women), and ُدهوِ
ِءبٌَٕاٚ ِيبعوٌبث (= I walked past the men and the women).
In fact (يا) is a vigorous leading light toward
cryptanalysis. However, it can be problematical if
preceded by such letters as ٚ, ف, ة, and superfluous ن.
164

Chapter [49]
The letter (د) occurs in such words as: ذِبل, دلؼل, برهبٍ, برَلؼل, بزَثوض,
َ
ب٘ ذَثَه ـْـ َضـ , بٙـ ذِ ْـ ـــ ً,
and ب٘ دـْـ مـؿأ.
When repeated it serves as a robust
lead-in to its solution, especially if used immediately next to (يا).
Chapter [50]
You should also see to letters repeated consecutively [doubled
letters] such as (ي/l) in words like: ًٍـ قُـ , ًٍِ, ًٍِػ, ًٍِؽ, ًٍَف; (ك/d) in words
like: ككول, ككوِ, كّلشِ, كّلَِ; and (َ/m) in: ُّ٘, ُّل, ُِأ, and َُِ ـَـ ي.
Moreover, the occurrence of the letter ( ـ٘/h) next to a double (ي/l)
creates an impression that the word sought is likely to be the name of
God (للها). It can also be one of these words: ّتٌٍا, ّظٌٍا, ت١جٌٍا, ف١فٌٍا, ً١ٌٍا,
ٓجٌٍا, ْب٠ ـَـٌٍا,
and نـ ًٌا ّـ –a typical Arab dialect for ٞنٌا.
Chapter [51]
One of the reliable conjectures in cryptanalysis is that the letter
between the definite (يا) and an (ا) is fairly guessed to be َ, ك, or ُ,
making these words: آٌّا, آلٌا or آشٌا. In case the (ا) is followed by
another letter, then you may guess at words like: ًبٌٕا, هالٌا, هبٌٕا, هبؼٌا,
قبٌٕا, قبٌَا, and so forth. If the letter next to (يا) and the final letter were
identical, the word produced would possibly be: ُةبجٌا, ٚاٌٛا, َبٌّإ, ػبؾٌإ,
ٌةبجٌأ (plural of ّتٌُ), or suchlike.
166

Chapter [52]
Two identical letters after the definite (يا), followed by [ا plus]
another letter, are together guessed to be a word such as ىبٌّّا, ْبججٌا (a
Turkish noun), etc. If the two letters were found unidentical, take a
guess at: َبٌّٕا, َبمٌّا, َبّغٌا, ةاٛصٌا, ةاوضٌا. If the (ا) is followed by two
other letters, these words are possible options: تلبٌّٕا, تٔبمٌّا, َهاٛصٌا,
ُغاوضٌا, and the like.
If one letter is there immediately after (يا), and two letters next to
the other (ا), then the possibilities are words such as: تئبغٌا, ل٘بشٌا,
تصبٌٕا, ِٟاوٌا, and ٟفبىٌا.
Chapter [53]
Remember that there exist long words which are devoid of the
definite (يا), such as: ُٙعهلزََٕف, ُٙى١فى١َف, ٍُّٙؼزٍَٕ, and ْٕٛ٠لزَزٍ. The
cipher verse may also be nonsensical though sound in its meter.
Knowledge of metrics often leads to hit the entire verse. The
cryptanalyst ought to be conversant with all the possible cases of the
verse in hand, such as its metrics, rhyme, language, as well as the
predominant trends and variations thereof. Proper familiarity with
these requisites, together with the utilization of the afore-mentioned
directive indicators to letters and words, and also reasoning in the light
of the orders of letter frequency of occurrence, would make
favourably for cryptanalysis. You should also be fully aware to the
[deliberate] use of undotted or non-combinable letters, the stinted
employment of repeated letters, or choosing new or unheard-of verse
as the cipher sought for cryptanalysis. Notice that the longer the verse
the better for the cryptologue, since in that case it allows for sufficient
frequency of letters to be achieved.
168

Chapter [54]
Encipherment may be rendered by the poet himself, who can be
ignorant of, or otherwise deficiently acquainted with, poetic meters,
parsing and the language in general. Subsequently he comes up with a
syntactically erroneous and metrically unsound poetry. This kind of
cipher is very problematic indeed. The following sample
has nothing to do with prosody. To be noted is that much of the poetry
of Ab al- At hiya, among others, does not pertain under prosody,
too. For example, one says:
Chapter [55]
An enciphered line of verse may contain some disincentives in
meter and rhyme that prove to the cryptanalyst extremely
problematical. The meter peculiarities include the occurrence of the
so-called phenomena of al-qab and al-kaff at the end of a verse. This
involves curtailing the seven-unit metric foot ٍٓ١ػبفِ by at once
dropping its fifth unit so that ٍٓػبفِ remains (qab ), and the seventh
unit of the foot so that ًػبفِ remains (kaff). The occurrence of either
of them alone is not much of a problem, but their occurrence
simultaneously poses a knotty problem to the cryptologue. What
augments the difficulty is the occurrence of alm, arm, arm or azm
at the beginning of a verse. We have already addressed the arm and
azm. 110 As for alm, it is like ٌٓٛؼف, if subjected to arm, ٌٓٛػ
remains, which is shifted to ْ ـُـ يـْـع
فـَـ .
110 See Chapter 40.
170

Chapter [56]
Besides, the first hemistich of a verse that belongs to the aw l
meter may undergo the arm phenomenon, making it into the k mil
meter, while the other hemistich remains of the aw l. Example:
(Zuha r ibn Ab Sulm ) 111
Note that the first hemistich is k mil and the other is aw l. Had the
poet said ْطِوػٚ or ْطَوؼر or ْطِوؼف instead of ْطِوػ, the measure would have
straightened. But it seems that he has been more attentive to meaning
than to measure.
Chapter [57]
Bear in mind that you ought to practise on prosody, rhymes and
verse composition in order that you keep your hand in, and get the feel
of this art that I have given you. As for the cryptanalysis of prose
ciphers, use the algorithms propounded towards the end of PART
ONE of this book of mine: they should suffice for the one who
experiences them, and sure enough they should.
111 This verse is rather attributed to Ku ayyir Azza in praise of the Caliph Umar
ibn Abd al- Az z. The exact wording as stated in his poetical corpus (divan) is
as follows:
172

Chapter [58]
And beware of cryptograms that might have been wrongly
enciphered through slipping up on a letter or so. That would prejudice
your chances of success in cryptanalysis.
Chapter [59]
You may encounter cryptograms made up of opaque lines of
meaningless verse, whose component words are sheer raving, intended
only to establish the meter. The following is a case in point:
It goes without saying the meaninglessness of these lines in the
Arabic language. A similar example reads:
Like the preceding lines, this verse is a senseless inanity with
sound metrics.
174

Chapter [60]
Towards the end of his Second Essay, the Author of the Two
Essays on cryptanalysis states that we are destined to follow an
intricate path. Nevertheless we shall be able to cope with it to achieve
cryptanalysis. This method involves assuming for the letter (ا ) a light
name such as ( وفظ), whose component letters [ظ, ف & ه] are
systematically used to represent the letter (ا) wherever it occurs in the
cryptogram. Then he says that a single symbol is also assumed to at
once represent three letters having the same orthographic pattern such
as (ة, د, س) or ( ط, ػ, ؿ), thereby suggesting the method of
encipherment but not the algorithm for cryptanalysis. Obviously that
is something of an idle talk. 112 If the encipherer intends to write a
word containing the letter (ة), for example, then how would he come
to know his own intention so long as this shape ( )suggests (ة) and
two more letters? A cipher rendered by this method is likely to be
equivocal in case it is left over for days and the cipher itself forgotten,
let alone the mix-up expected on the part of the cryptanalyst with
regard to the orders of letter frequency, considering that the letter (س )
is of low frequency, the (ة b) of medium frequency, and the (د t) of
higher frequency than (ة). On the other hand, assigning three symbols
to represent one letter, whilst assigning just one symbol to represent
three letters would make the count of letters versus symbols in the
cryptogram proportionate. This shows the Author of the Two Essays
not well-informed in ciphers. 113
112 See p.54.
113 On the contrary, the Author of the Two Essays has proved himself to be a
seasoned old hand at cryptography and cryptanalysis. This method, which
conforms to the latest principles of encipherment, is intended to augment the
number of cipher symbols.
176

Chapter [61]
Now I am to give you an illustrative example by enciphering the
following verse of my own composition, in which the letters ا, ي and ٚ
are highly frequent, and a few more also circulate:
114
114 From the previous letters one can string together the following verse:
- What made the heart grow fonder is the tattler who said: be obedient!-
178

Chapter [62]
A line of verse has once been given to me in cipher, of which I
contrived to break only the initial words in the first instance. I,
however, managed to go through with it later, and came off well. It
took me several hours of exertion before it ran full and for good as
follows:
115
115 From the letters above one can piece together the following verse:
- God knows how much I am besotted with you heart and soul.-
180

For cryptanalysis I started on telling the occurrence frequency of
letters right through. Having found thirty-four letters, I concluded that
the verse belongs to al-bas al-ma b n meter. It also came home to
me that the last word involved the rhyme, which was of the
overlapping type as it consisted of three vocalized letters lying
between two neutral suk ns. I further perceived that the final letter of
the second hemistich is identical with the final letter of the first
hemistich. Sorting out the letters according to their order of frequency,
I elicited first and foremost the name of God (للها), utilizing the
repetition of the letter (ي) in it and the fact that His name all-often
goes in front position. I thus labeled the letters ( ا, ي and ـ٘). Then I
checked the form of the letter (َ) and found it repeated six times, i.e.
exceeding in frequency the form of the letters (ا) and (ي). Therefore I
held it would probably be (َ). Switching over to the next frequent
form of the letter (ٞ), I found it recurring three times, and I made it
(ٞ). Thereupon I took up the tetragram (four-letter word) following
the name of God, with the letters (ي), (ٞ) and (َ) already known, and
sampled such words as: ٍَُ٠, ٍُؼ٠, ٍُظ٠, ٍُض٠, etc. to reserve judgement on
it for a while. I now sought the next word—a trigram (three-letter
word) the middle letter of which was still covert, the initial and
terminal letters being (ا) and (ٞ) respectively. By sampling words such
as ِٟأ, ٟثأ, ٟٔأ the following got out as possibilities: ( ٚأ ٟثأ ٚأ ِٟأ ٍُظ٠ للها
ٟٔأ), which I immediately dismissed as out of the question. Of these
words I had my heart set on ٟٔأ, promptly turning my assumption to
the word ( ٍُؼ٠) instead of ( ٍُظ٠) by extension, and thus sounding
meaningful and poetical. The next word was another tetragram
beginning and ending with the letter (َ). I guessed at words such as
َوغِ, َيؼِ and the like, but the context soon lent credence to َوغِ as the
apposite choice, and so the word-group read: ( َوغِ ٟٔأ ٍُؼ٠ للها). Now I
looked into the next word which was a trigram ending with the letter
(َ). Experimenting with letters in the light of contextual connection,
the word (ُىث) developed. It was along these lines that cryptanalysis
was carried out.
182

Chapter [63]
I have [herein] adduced something novel that none else had ever
broached before, because al-Kind 's book [treatise] tackles prose
simple encipherment only; and Ab al- asan's book treats poetry
encipherment. Both failed to develop the topic exhaustively in either
case.
Chapter [64]
And I supplement this [discourse] with lines of verse that embrace
the letters of the alphabet [without repetition]. Examples:
1) 116
2)
3)
The second hemistich of this last line has another variant:
4)
116 Termed by ibn ad-Durayhim al-Fahlaw cipher alphabet, and by ibn- Adl n one
of the regulators or cryptographic keys. See Volume Three, p. 62 and Volume
Two, p. 42.
184

Chapter [65]
Many verses have been indited to be used in encipherment, and are
intended for sustained mental exertion in pursuit of solution. The
following are some:
1) 117
2)
3)
4)
Of the poetry that is particularly tough to crack is that composed on
al-mad d meter in its original, rather than catalectic, version. Another
such type is a special reversed form of al-mutaq rib meter (called
bad ), not reported to have been ever used in the refined traditional
poetry.
Chapter [66]
Cryptanalysis can be extremely demanding if poetical ciphers are
rendered using meters that are not based on the established rules of
prosody and uniformity of rhyme. I say: The cryptanalyst is not
obliged to puzzle out ciphers intended for mental exertion, just as the
grammarian is not bound to enter into intricate issues.
Glory be to God, the Lord of grace and favour, the granter of
natural gifts and talents. Sufficient unto me is God! Most Excellent is
He in Whom I place my trust.
Not e: The following verse also encompasses the alphabet:
118
117 This verse appears in the treatise on cryptanalysis of poetry by the author of
'Adab a - u ar ', as an illustrative example of the deliberate use in
encipherment of letters that never link with each other, but are used as separate
disconnected letters.
118 This verse is appended malapropos to the book, probably by the scribe. No
reference to it has been made in any of the treatises incorporating the
assemblage of cryptology.
186

The Gist Of ibn Dunayn r's Chapters
On Cryptanalysis
The rhyme structures are six; take them as concisely as can be:
LETTERS: raw , wa l, ur , ridf, ta's s, and da l.
DIACRITICS: naf , 'i b , mu r , a w, rass, and taw h.
The rhyme defects are five; take them as tractably wrought as
possible: sin d, ' ', ta m n, 'ikf ', and 'iqw '.
� raw : the letter on which the poem is based.
� ridf: the pre-raw vowel letter; e.g. , and respectively
in , and .
� ta's s: the letter ( ) prior to the raw but one; e.g. .
� da l: the letter between ta's s and raw ; e.g. in .
� wa l: one of the vowel letters ( , , ) or the letter ,
next to the raw .
� ur : a post- raw vowel letter; e.g. the final ( ) in ( ).
� naf : the vowel point of the letter of wa l.
� taw h: the vowel point of the restricted pre-raw letter.
� mu r : the vowel point of the raw .
� 'i b : the vowel point of the unrestricted pre-raw letter.
� rass (or ras s): the vowel point of the pre-ta's s.
* * *
188

5
2
3
1
71
4
(1)
(2)
(3)
(4)
(5)

215 1
5
) 2(
] 1[
73
3
1
4
(1)
(2)
(3)
(4)
(5)

6
4
5
1
216
215
1
2
237 236 216 215 1
126
124 3
75
84
3
19 1
2
(1)
(2)
(3)
(4)
(5)
(6)

1
3
77
(1)

4
3
14
13
11
4
79
2
221 1
114 1
1
62
(1)
(2)
(3)
(4)

5
223 1
4
224 1
24
5
23
81
2
1
225 1
3
(1)
(2)
(3)
(4)
(5)

3
224 1
2
5
224 1
6
224
1
83
1
6
4
224 220 1
(1)
(2)
(3)
(4)
(5)
(6)

4
58
3
55
58
] 7[
85
لصف
1
2
(1)
(2)
(3)
(4)

23
274 1
600
6
3
274 1
4307
360
274 1
236 1
7
] 8[
8
236 1
87
2
لصف
236 2
236 1
5
575
4
600
437
1
275
1
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)

1
] 9[
89
لصف
(1)

4
1
3
239 1
239 1
] 10[
2
7
93
5
لصف
240
1
8
240 1
6
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)

4
2
3
1
95
6
5
241 240 238 1
(1)
(2)
(3)
(4)
(5)
(6)

3
�
2
ڤ
x
] 11[
] 12[
ڤ
99
لصف
لصف
81 1
1
62 1
(1)
(2)
(3)

2
5
6
1
Substitution
] 13[
101
لصف
4
7
3
Transposition
(1)
(2)
(3)
(4)
(5)
(6)
(7)

3
5
223 222 1
2
8
] 14[
103
4
لصف
57
1
256
6
7
230
225
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)

1
2
] 15[
105
لصف
(1)
(2)

3
5
2
1
57
16
4
17
107
(1)
(2)
(3)
(4)
(5)

2
] 18[
109
لصف
1
3
234،224 1
234 1
(1)
(2)
(3)

2
] 19[
] 20[
111
لصف
1
لصف
(1)
(2)

113

115

1
7
50 11
92
5
25
92
] 21[
4
67
92
2
117
لصف
0.7456
2304
3
6
147.456
(1)
(2)
(3)
(4)
(5)
(6)
(7)

5
4
3
1
] 22[
119
لصف
5
44
31
4
~
2
(1)
(2)
(3)
(4)

1
331 330 1
] 23[
762
121
لصف
2
(1)
(2)

]
24[
123
لصف

332 331 1
6
5
4
2
74 1
3
] 25[
125
لصف
4
1
10 30
100 10 80
6
6
5 30 30 1
74
1
400 30 1
(1)
(2)
(3)
(4)

75
1
1
] 26[
127
لصف
(1)

] 27[
129
لصف
1
(1)

339
1
1
] 28[
131
2
لصف
3
(1)
(2)
(3)

3
2
1
29
133
(1)
(2)
(3)

10
4
3
7
2
] 30[
لصف
135
1
6
9
5
8
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)

2
325
1
] 31[
] 32[
] 33[
137
لصف
لصف
لصف
1
(1)
(2)

2
4
] 34[
139
لصف
1
3
1000
(1)
(2)
(3)
(4)

1
13
2
] 35[
141
4
لصف
17
15
3
5
(1)
(2)
(3)
(4)
(5)

1
54
3
] 36[
] 37[
143
لصف
لصف
4
204
1
10
2
9
8
(1)
(2)
(3)
(4)

) 3(
2
5
178
) 5(
135
18
4
6
] 38[
] 39[
) 5(
101 3
145
لصف
لصف
194
215
1974
3
1
52
1394
(1)
(2)
(3)
(4)
(5)
(6)

61
4
187
] 40[
147
لصف
1
3
) 2(
2
(1)
(2)
(3)
(4)

7
299 297 1
6
3
] 41[
149
لصف
208
2
5
119
4
1
231
224
(1)
(2)
(3)
(4)
(5)
(6)
(7)

2
4
3
228
151
5
31
29
28
1
228
(1)
(2)
(3)
(4)
(5)

137
134
227
215
153
74
46
1
2
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3
1
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155
4
لصف
2
5
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44
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5
185
1
3
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157
لصف
297 1
4
74
73
1989
2
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1
3
6
5
2
159
4
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1
122
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161
لصف
لصف
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1
5
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2
3
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163
6
لصف
123
(1)
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165
ًصف
[
48
]
1
2
3
4
5
6
7
8
9
10
11
(1)
463
482
(2)
(3)
213
223
(4)
137
151
(5)
(6)
2
366
2
148
1
112
64
1
330
279
3
62
29
8
1
3
2
153
1
6
2
120
9
388
762
(7)
(8)
233
241
(9)
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274
312
(11)
123

124
124
4
3
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167
لصف
لصف
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158
157
124
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3
60
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169
لصف
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4
1
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5
32
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2
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6
178
128
43
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321 1
171
لصف
لصف
4
826
71
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333
2
4
38
5
128
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6
128
173
لصف
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لصف
128
1
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] 58[
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175
لصف
لصف
تفضرجت بوجطمخلاب ىمر امل ِلطْعَبْرَخلا يف ضافو ُهاتفاّرـش
2
4
3
129
1
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4
115
118
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108
115
2
36 1
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لصف
1
177
82
81
6
3
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2
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179
لصف
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3
4
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1
2
لصف
(1)
2
3
4

2
3
183
54
1
4
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322
7
6
5
8
272،327 1
169 168 144 1
4
353
353
352
] 63[
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185
لصف
لصف
81
53
80
2
1
48
559 1
101
3
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(4)
(5)
(6)
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(8)

5
3
6
4
44
1
41
2
173
353
352
169
353
] 65[
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187
لصف
لصف
225
74
47
(1)
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(6)

2
39
205
15
54
1
72
71
70
189
54
41
3
233
221
(1)
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(3)

190