Recall the Substitution Cipher. Let A be the set of 26 English alphabet letters,
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Question
Recall the Substitution Cipher. Let A be the set of 26 English alphabet letters, A = {a, b, , z). Recall that in this cipher we have C MA for some integer , and that a key k isa permutation on the set A, ie, it's a one-to-one function f : A A. Notice that if K is a space of all such key A, then IKI = 1 ! = 26!. Recall that if Enc is the substitution cipher and we assume that the message space is M = At for some length I then Ene(k, m) for m = mil lmt outputs c = cl Ice where ci = k(mi) for all i = 1, , 1. (Recall that permutation is a function k : A A, so k(m) stands for the value of function k at argument mE A.) s, i.e. a set of permutations on (a) Show that the substitution cipher is perfectly secret if 1Explanation / Answer
Substitution cipher is a method of encrypting by which units of plain text are replaced with cipher text and based on the fixed system units may be of single letters, pair of letters, triplets of letters, and so on.
(a) prove that Substitution cipher is perfectly secret if l=1.
M : {a,...,z}l , where l is message length
K: permutations on {0,....,25};i:e, each k belongs to K is chosen at randomand is a 1:1 mapping from {0,....,25} to {0,....,25}
c = Enc(k,[m1 to ml]) = [k(m1), k(m2),.....k(ml)], for m = [m1.......ml] belongs to M.
vunerable to brute force effect : key space effect 26!
it is also vunerable to frequency analysis
hence Substitution cipher is perfectly secret if l=1 but it fails to satisfy the secrecy property if l is greater than 2.
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