Math 135 (Summer 2006)Cryptanalysis of Monoalphabetic SubstitutionsNote: There are a few discussions in the textbook about the cryptanalysis of a monoalphabetic sub-stitutions. In particular, read pages 57–59; Example 2.2.7 on pages 77–80; Example 2.3.3 on pages 85–90.Example: Consider the following ciphertext produced by a monoalphabetic substitution:RADHA JCRWC MJCOA NZCSY JVHCY MVAGH WZHSMLTCOH WCAVA SPDLO JLGHV ZASPV LZCII HSLOZCVNZAssumptions, Information, Strategy• It is in English, and has roughly the same statistics as standard English.• Word divisions are not preserved.• Use frequency analysis to guess high frequency letters: E, T, N, O, R, I, A, S make up 70%of letters in English.• Try to identify vowels.• Try to identify digraphs.• Use cribs.• Guess! and rely on luck.Table 2.6: Re lative Letter Frequencies in a Sample of Englishletter frequency (%) letter frequency (%)A 8.399 N 6.778B 1.442 O 7.493C 2.527 P 1.991D 4.800 Q 0.077E 12.150 R 6.063F 2.132 S 6.319G 2.323 T 8.999H 6.025 U 2.783I 6.485 V 0.996J 0.102 W 2.464K 0.689 X 0.204L 4.008 Y 2.157M 2.566 Z 0.025Table 2.7: Com monest Digraphs and their Frequencies in a Sample of Englishdigraph frequency (%) digraph frequency (%)TH 3.319 ES 1.213HE 2.859 TO 1.213IN 2.081 NT 1.200ER 1.596 EA 1.059ED 1.493 OU 1.047AN 1.430 NG 1.034ND 1.430 ST 1.034AR 1.302 AS 0.9957RE 1.302 RO 0.9957EN 1.289 AT 0.9829(Part of) Table 2.8: Commonest Trigraphs and their Frequencies in a Sample of Englishtrigraph frequency (%) trigraph frequency (%)THE 1.82 ING 0.68AND 0.77 HER 0.50When we analyze the ciphertext, we see that the commonest letters, digraphs, and trigraphs are:C A H V Z L S9 7 7 6 6 5 5ZC AS CO GH HW HS JC LO NZ SP VA3 2 2 2 2 2 2 2 2 2 2ASP2That is, we guessplaintext 7→ ciphertext{E, T, N, O, R, I, A, S} 7→ { C, A, H, V, Z, L, S, T, O}{TH, HE, IN, ER, RE, ON, AN, EN, AT} 7→ {ZC, AS, CO, GH, HW, HS, JC, LO, NZ, SP, VA}{THE, AND, ING, HER} 7→ {ASP}Some Known Cribs: F 7→ D and H 7→ ZAnd here is the ciphertext with the word divisions put back in:RADH AJ CRWCMJ C OANZ CSY JVHCYMVAGH WZHS MLT COH WCAVASP DLOJLGHVZASP VL ZCIIHS LO ZCVNZThe quote is from Charlotte’s Web by that famous Cornellian E.B. White.Note: This is an example of a cryptogram, a s hort piece of text encrypted with a simple monoal-phabetic substitution cipher. To solve the puzzle, one must recover the original lettering. Though onceused in more serious applications, they are now mainly printed for entertainment in newspapers andmagazines. A useful tool for solving cryptograms may be found