Cryptanalysis of ‘nonlinear-parity circuits’ proposed at Crypto '90

Abstract

In Koyama and Terada proposed a family of cryptographic functions for application to symmetric block ciphers. The authors show that this family of circuits is affine over GF(2). More explicitly, for any specific key K, the ciphertext Y is related to the plaintext X by the simple affine relation Y = MKX ⊕ dK where MK is an n × n non singular binary matrix and dK is an n × 1 binary vector where n is the block length of the cipher. This renders this family of ciphers completely insecure as it can be broken with only n + 1 linearly independent plaintext blocks and their corresponding ciphertext blocks.