A History of Cryptography - Introduction to Cryptography with Java Applets - page 6

1.4

FREQUENCY ANALYSIS ON MONOALPHABETIC SUBSTITUTION
CIPHERS
Frequency analysis can be used for any permutation of single letters of an alphabet, not just
a shift as in the Caesar cipher. The relative frequencies of all letters in English text (and
many other languages) are well known. These frequencies can be used to break any cipher
that maps individual letters. The approximate frequency distribution of letters in typical
English text is shown in Figure 1.1.
If analysts have enough ciphertext, they can use this distribution to make fairly good
guesses about how individual letters are mapped in a monoalphabetic substitution cipher.
For example, the most common letter in the ciphertext probably corresponds with the plain-
text letter “E,” the second most common letter in the ciphertext probably corresponds with
“T,” and so on. Once the analyst starts filling in these more common letters, they can begin
to make some good guesses for the other letters, and they eventually fill out enough letters
so that they uncover the secret mapping.

E XAMPLE . Consider the following ciphertext, which was produced by a mapping of the
alphabet A . . . Z to a permutation of the alphabet.

HUFMD JCXNE ONUFZ UFJCX NUYMM TDHLF XTGYT HUFEY KFNEF MXFCD
GTXTQ JFFTZ YNHSJ FNUFM FYCNE FLFNX CFPSX FHGYH FJNUF JFNHD
JFNEO NDSMU FQSXC FNEFX TZYHU NDBJX QUHFD SNTFN NBDJU XNTYE
FNNYK FFAFT HUDSQ UXGYM KHUJD SQUHU FAYMM FODBH UFNUY CDGDB
CFYHU XGXMM BFYJT DFAXM BDJOD SYJFG XHUEF ODSJJ DCYTC ODSJN
HYBBH UFORD EBDJH EFODS ZJFZY JFYHY LMFLF BDJFE FXTHU FZJFN
FTRFD BEOFT FEXFN ODSYT DXTHE OUFYC GXHUD XMEOR SZDAF JBMDG
NNSJF MOQDD CTFNN YTCMD AFGXM MBDMM DGEFY MMHUF CYOND BEOMX
BFYTC XGXMM CGFMM XTHUF UDSNF DBHUF MDJCB DJFAF J

14

12

10

8

6

4

2

0

A BCDEFGH I J KLMNOPQRSTUVWXYZ

Letter

FIGURE 1.1 Relative Frequencies of English Letters (percent)