Cryptology - Unofficial St. Mary's College of California Web Site
Cryptology - Unofficial St. Mary's College of California Web Site
Cryptology - Unofficial St. Mary's College of California Web Site
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170 CHAPTER 9. DIGRAPHIC CIPHERS<br />
a<br />
b<br />
c<br />
d<br />
e<br />
f<br />
g<br />
h<br />
i<br />
j<br />
k<br />
l<br />
m<br />
n<br />
o<br />
p<br />
q<br />
r<br />
s<br />
t<br />
u<br />
v<br />
w<br />
x<br />
y<br />
z<br />
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<br />
RA XW DT JP PU VQ BN HS NO TK ZP FM LI RN XJ DG JC PH VD BA HF NB TX ZC FZ LV<br />
IB OX UT AQ GV MR SN YS EP KL QQ WM CJ IO OK UG AD GI ME SA YF EC KY QD WZ CW<br />
ZB FY LU RZ XV DS JO PT VP BM HR NN TJ ZO FL LH RM XI DF JB PG VC BZ HE NA TW<br />
QC WY CV IA OW US AP GU MQ SM YR EO KK QP WL CI IN OJ UF AC GH MD SZ YE EB KX<br />
HD NZ TV ZA FX LT RY XU DR JN PS VO BL HQ NM TI ZN FK LG RL XH DE JA PF VB BY<br />
YD EA KW QB WX CU IZ OV UR AO GT MP SL YQ EN KJ QO WK CH IM OI UE AB GG MC SY<br />
PE VA BX HC NY TU ZZ FW LS RX XT DQ JM PR VN BK HP NL TH ZM FJ LF RK XG DD JZ<br />
GF MB SX YC EZ KV QA WW CT IY OU UQ AN GS MO SK YP EM KI QN WJ CG IL OH UD AA<br />
XF DC JY PD VZ BW HB NX TT ZY FV LR RW XS DP JL PQ VM BJ HO NK TG ZL FI LE RJ<br />
OG UC AZ GE MA SW YB EY KU QZ WV CS IX OT UP AM GR MN SJ YO EL KH QM WI CF IK<br />
FH LD RI XE DB JX PC VY BV HA NW TS ZX FU LQ RV XR DO JK PP VL BI HN NJ TF ZK<br />
WH CE IJ OF UB AY GD MZ SV YA EX KT QY WU CR IW OS UO AL GQ MM SI YN EK KG QL<br />
NI TE ZJ FG LC RH XD DA JW PB VX BU HZ NV TR ZW FT LP RU XQ DN JJ PO VK BH HM<br />
EJ KF QK WG CD II OE UA AX GC MY SU YZ EW KS QX WT CQ IV OR UN AK GP ML SH YM<br />
VJ BG HL NH TD ZI FF LB RG XC DZ JV PA VW BT HY NU TQ ZV FS LO RT XP DM JI PN<br />
MK SG YL EI KE QJ WF CC IH OD UZ AW GB MX ST YY EV KR QW WS CP IU OQ UM AJ GO<br />
DL JH PM VI BF HK NG TC ZH FE LA RF XB DY JU PZ VV BS HX NT TP ZU FR LN RS XO<br />
UL AI GN MJ SF YK EH KD QI WE CB IG OC UY AV GA MW SS YX EU KQ QV WR CO IT OP<br />
LM RR XN DK JG PL VH BE HJ NF TB ZG FD LZ RE XA DX JT PY VU BR HW NS TO ZT FQ<br />
CN IS OO UK AH GM MI SE YJ EG KC QH WD CA IF OB UX AU GZ MV SR YW ET KP QU WQ<br />
TN ZS FP LL RQ XM DJ JF PK VG BD HI NE TA ZF FC LY RD XZ DW JS PX VT BQ HV NR<br />
KO QT WP CM IR ON UJ AG GL MH SD YI EF KB QG WC CZ IE OA UW AT GY MU SQ YV ES<br />
BP HU NQ TM ZR FO LK RP XL DI JE PJ VF BC HH ND TZ ZE FB LX RC XY DV JR PW VS<br />
SP YU ER KN QS WO CL IQ OM UI AF GK MG SC YH EE KA QF WB CY ID OZ UV AS GX MT<br />
JQ PV VR BO HT NP TL ZQ FN LJ RO XK DH JD PI VE BB HG NC TY ZD FA LW RB XX DU<br />
AR GW MS SO YT EQ KM QR WN CK IP OL UH AE GJ MF SB YG ED KZ QE WA CX IC OY UU<br />
Figure 9.2: A More Complicated Digraphic Substitution Chart<br />
for etaoinshr, as we would in a monographic cipher, we look for th-he-in-erre-....<br />
But the basic idea is the same: do a (very large) frequency count, guess<br />
that the top occurring pairs come from therein, and start working. So while<br />
we need more data, the techniques are very similar to the ones with which we<br />
are comfortable.<br />
How to make this system better I guess a 26 × 26 × 26 hyper-chart listing<br />
all 17576 three-letter triples. Maybe one would do this as 26 charts, where the<br />
first letter <strong>of</strong> the triple was the name <strong>of</strong> the chart, the second one was on the left<br />
<strong>of</strong> the chart and the third one was one the top The extreme cumbersomeness<br />
<strong>of</strong> a system like this would limits its use to those who have a computer to help. 4<br />
9.2 Hill Ciphers<br />
Lester S. Hill (1881-1961) was an assistant pr<strong>of</strong>essor <strong>of</strong> mathematics at Hunter<br />
<strong>College</strong> in New York when, in 1931, he published the method now named for him<br />
as “Cryptography in an Algebraic Alphabet” in The American Mathematical<br />
4 The idea <strong>of</strong> enciphering letters not individually but in groups, so-called block ciphers,<br />
reappears in almost every modern cipher system.