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slides5 - CS 531 Fall 2007 Substitution Ciphers...

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T 1 Substitution Ciphers CS 531, Fall 2007 Copyright © William C. Cheng let A be a alphabet, M be the set of all strings of length t over A , K be the set of all permutations on the set A Substitution ciphers are block ciphers which replace symbols (or groups of symbols) by other symbols or groups of symbols Mono-alphabetic substitution cipher (or simple substitution cipher ) define for each e K an encryption transformation E e as: E e (m) = (e(m 1 )e(m 2 )...e(m t )) = (c 1 c 2 ...c t ) = c where m = (m 1 m 2 ...m t ) M the above means that for each symbol in a t - tuple, replace (substitute) it by another symbol from A according to some fixed permutation e the inverse permutation d=e -1
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distribution of letter frequencies is preserved in the ciphertext (i.e., first-order statistics of plaintext and ciphertext are isomorphic ) T 2 Mono-alphabetic Substitution Ciphers CS 531, Fall 2007 Copyright © William C. Cheng q=26 , size of key space is quite large: q! 4 × 10 26 If A contains q symbols, the number of distinct substitution ciphers is q! and is independent of block size in the cipher however, mono-alphabetic substitution cipher is insecure because the key being used can be determined quite easily by examining a modest amount of ciphertext vulnerable to simple statistics-based cryptanalysis
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T 3 Homophonic Substitution Ciphers CS 531, Fall 2007 Copyright © William C. Cheng a homophonic substitution cipher replaces each symbol a in a plaintext message block with a randomly chosen string from H(a) To each symbol a A , associate a set H(a) of strings of t symbols, with restriction that the sets H(a) , a A , be pairwise disjoint to decrypt a string c of t symbols, one must determine an a A such that c H(a) the key for this cipher consists of the sets H(a) Can use a homophonic substitution cipher to make the
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