Cryptography - Sage

Solution.below.The coincidence index for each of the ciphertext samples is given in the table1. 0.04387225548902192. 0.06570233203879853. 0.04472396925227114. 0.06295453108202115. 0.04128012438455556. 0.06552250683626457. 0.04123391156371738. 0.06749180610660689. 0.068557348267662210. 0.065734175809402411. 0.0665847779993272All but ciphertexts 1, 3, 5 and 7 are consistent with output from a simple substitution ortransposition cipher. It is likely that the exceptional ones employ a polyalphabetic cipher.In order to distinguish substitution and transposition ciphers, it is necessary to look atcharacter distributions, e.g. a close match with the frequency distribution of English (or amodern language) suggests a transposition cipher.Exercise 3.3 For each of the cryptographic texts from the course web page, for variousperiods extract the substrings of im + j-th characters. For those which are not simplesubstitutions, can you identify a period?Solution. Using the average coincidence index of the ciphertext decimations, we find thatthe periods of the ciphertexts 1, 3, 5, and 7 are 11, 6, 14, and 9, respectively. The code toverify this is:sage: ct05 = strip_encoding(open("Ciphertext/cipher05.txt").read())sage: n = len(ct05)sage: for m in range(1,10):cis = [ ct05[i:n:m].coincidence_index() for i in range(m) ]print "%s : %s" % (m, sum(cis)/m)with output:106 Appendix C. Solutions to Exercises