Introduction

This page is related to the paper Evolving Keys for Periodic Polyalphabetic Ciphers (PDF).

A genetic algorithm is used to find the keys of Type II periodic polyalphabetic ciphers with mixed primary alphabets. Because of the difficulty of the ciphertext only cryptanalysis for Type II ciphers, a multi-phased search strategy is used, each phase of which recovers a bigger portion of the key.

Background

A polyalphabetic cipher is one in which different alphabets are used to encrypt different letters in the plaintext.

Given d cipher alphabets C₁, ..., C_d then g_i: A → C_i is the mapping from the plaintext alphabet A to the i^th cipher alphabet, C_i.

A plaintext message

M = m1...mdmd+1...m2d

would be decrypted to:

E(M) = g1(m1)...gd(md)gd+1(m+1d)g2d(m2d)

The ciphertext alphabets can take different forms:

• A shifted alphabet -- e.g., defghigklmnopqrstuvwxyzabc
• A mixed (permuted) alphabet -- e.g., zerosumgabcdfhijklnpqtvwxy

One common form of classical cipher is to take a mixed primary alphabet and then derive additional alphabets from it by shifting the letters from 1 to 25 times.

Ciphertext only cryptanalysis of polyalphabetic cipher with a 26-letter alphabet and a period of length d requires search of a keyspace containing 26^ × 26^d-1 possible keys -- approximately 10³² possible keys.

A Parallel GA for Breaking Type II Ciphers

Hands On