We describe a cipher which incorporates one of the ideas from the enigma system

Question

We describe a cipher which incorporates one of the ideas from the enigma system used by Germany World War 2. Suppose that pi is a fixed permutation of Z_26 = {0, 1, 2, ..., 25}. The key is an element K Z_26. For all integers i greaterthanorequalto 1, the key stream element z_i Z_26 is defined according to the rule Z_i = (K + i - 1) mod 26. Encryption and decryption are performed using the permutation n and z_r, respectively, as follows: Enc(z, m) = pi(m) + z mod 26 Dec(z, c) = pi^- 1 (c - z) mod 26) pi is the following permutation of Z_26. The following ciphertext has been encrypted using this cipher, use exhaustive key search to decrypt it:

Explanation / Answer

Z E G P R L G D Y F D

encoding A=0,B=1,Z=25,E=4,G=6,P=15,R=17,L=11,G=6,D=3,Y=24,F=5,D=3

THE ENCRYPTED STRING WILL BE = 8 7 14 11 2 1 14 0 3 14 0

As encryption for Z=8,E=7,G=14 hence so on.

the result encrypted string for Z E G P R L G D Y F D

is   8 7 14 11 2 1 14 0 3 14 0

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