Sequence Complexity as a Test for Cryptographic Systems

The complexity of a finite sequence as defined by Lempel and Ziv is advocated as the basis of a test for cryptographic algorithms. Assuming binary data and block enciphering, it is claimed that the difference (exclusive OR sum) between the plaintext vector and the corresponding ciphertext vector should have high complexity, with very high probability. We may refer to this as plaintext/ciphertext complexity. Similarly, we can estimate an “avalanche” or ciphertext/ ciphertext complexity. This is determined by changing the plaintext by one bit and computing the complexity of the difference of the corresponding ciphertexts. These ciphertext vectors should appear to be statistically independent and thus their difference should have high complexity with very high probability. The distribution of com plexity of randomly selected binary blocks of the same length is used as a reference. If the distribution of complexity generated by the cryptographic algorithm matches well with the reference distribution, the algorithm passes the complexity test. For demonstration, the test is applied to modulo multiplication and to successive rounds (iterations) of the DES encryption algorithm. For DES, the plaintext/ ciphertext complexity test is satisfied by the second round, but the avalanche complexity test takes four to five rounds before a good fit is obtained.