An Algorithm for the Complete Automated Cryptanalysis of Periodic Polyalphabetic Substitution Ciphers

FIND_PRIMARY_ALPHABET is a new cryptanalytic algorithm which solves monoalphabetic and periodic polyalphabetic substitution ciphers with 100% accuracy. The algorithm uses probabilistic alphabets, the one-to-many mappings obtained by probabilistic relaxation, to determine the one-to-one mappings of the primary alphabet. First an algorithm for computing the period based on IC calculations is presented. Probabilistic relaxation is then extended to solve polyalphabetic ciphers without word divisions and of unknown key periods in a ciphertext-only attack. FIND_PRIMARY_ALPHABET is then demonstrated by solving Vigenere ciphers encrypted with both standard and mixed primary alphabets, Beaufort, and Variant Beaufort ciphers.