Cryptology - Unofficial St. Mary's College of California Web Site

76 CHAPTER 5. MONOALPHABETIC CIPHERS
Then remove the ciphertext alphabet as in a keyword cipher, ignoring the *’s:
plaintext
ciphertext
a b c d e f g h i j k l m n o p q r s t u v w x y z
C A K T O B M U L D N V F P W E H Q X G I R Y J S Z
Finally, one can use Interrupted Keyword Transposed ciphers, but we won’t.
5.5 Frequency Counts and Exhaustion
Are these new monoalphabetic ciphers any more secure than the ones we saw
earlier Or will frequency analysis once again save (ruin) the day Let’s try
to break a message enciphered with a keyword mixed cipher and see.
Example: KNHHXKK QS PXTDQSB YQFJ NSISCYS HQEJXUK QK LXTKNUXP AO
FJXKX RCNU FJQSBK QS FJX CUPXU STLXP EXUKXVXUTSHX HTUXRND LXFJCPK CR
TSTDOKQK QSFNQFQCS DNHI FJX TAQDQFO TF DXTKF FC UXTP FJX DTSBNTBX CR
FJX CUQBQSTD QK VXUO PXKQUTADX ANF SCF XKKXSFQTD
The letter frequency count of the ciphertext is
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
4 5 10 10 2 17 0 6 2 9 17 3 0 9 4 7 18 4 16 16 12 2 0 27 2 0
Does this look like a Caesar cipher By far the most common letter is X, so
this is likely e. But if so then S and T are y and z, respectively, and it is not
likely that a message would have sixteen each of these letters. In fact, there
is no low sextuple. This is not a Caesar cipher. The ciphertext’s letters have
been well enough mixed that the standard frequency patterns have been totally
destroyed.
⋄
This is the main advantage of the keyword ciphers: unless we know the
method and the keyword, it is quite difficult to directly detect the pattern in
the ordering of the ciphertext alphabet. In a Caesar cipher, once we knew where
the ciphertext version of e was located we were basically done. In Decimation
and Linear ciphers, knowing two letters allowed us to determine the rest. With
a keyword cipher, the ciphertext alphabet is mixed enough that knowing the
meanings of even five or ten ciphertext letters does not necessarily disclose the
pattern of encryption.
What about exhaustion, one might ask We might use a computer and
simply try all the possibilities. Working modulo 26 there are 26 different Caesar
ciphers. There are only 12 decimation ciphers modulo 26, and 26 × 12 = 312
linear ciphers. How many monoalphabetic ciphers are there Well, we have 26
choices for which letter goes is substituted for a. Then we have 25 choices for