# CORNELL MATH 135 - Study Notes (2 pages)

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## Study Notes

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## Study Notes

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Cornell University
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Math 135 - The Art of Secret Writing
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Math 135 Summer 2006 Cryptanalysis of Monoalphabetic Substitutions Note There are a few discussions in the textbook about the cryptanalysis of a monoalphabetic substitutions 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 WZHSM LTCOH WCAVA SPDLO JLGHV ZASPV LZCII HSLOZ CVNZ Assumptions 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 Relative Letter Frequencies in a Sample of English letter A B C D E F G H I J K L M frequency 8 399 1 442 2 527 4 800 12 150 2 132 2 323 6 025 6 485 0 102 0 689 4 008 2 566 letter N O P Q R S T U V W X Y Z frequency 6 778 7 493 1 991 0 077 6 063 6 319 8 999 2 783 0 996 2 464 0 204 2 157 0 025 Table 2 7 Commonest Digraphs and their Frequencies in a Sample of English digraph TH HE IN ER ED AN ND AR RE EN frequency 3 319 2 859 2 081 1 596 1 493 1 430 1 430 1 302 1 302 1 289 digraph ES TO NT EA OU NG ST AS RO AT frequency 1 213 1 213 1 200 1 059 1 047 1 034 1 034 0 9957 0 9957 0 9829 Part of Table 2 8 Commonest Trigraphs and their Frequencies in a Sample of English trigraph THE AND frequency 1 82 0 77 trigraph ING HER frequency 0 68 0 50 When we analyze the ciphertext we see that the commonest letters digraphs and trigraphs are C 9 ZC 3 ASP 2 A 7 AS 2 H 7 CO 2 V 6 GH 2 Z 6 HW 2 L 5 HS 2 S 5 JC 2 LO 2 NZ 2 SP 2 VA 2 That is we guess plaintext 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 Z And here is the ciphertext with the word divisions put back in RADH AJ CRWCMJ C OANZ CSY JVHCYM VAGH WZHS MLT

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