Automated statistical methods for measuring the strength of block ciphers
Statistics and Computing
A Layered Approach to the Design of Private Key Cryptosystems
CRYPTO '85 Advances in Cryptology
On the distribution function of the complexity of finite sequences
Information Sciences: an International Journal
Ziv-Lempel complexity for periodic sequences and its cryptographic application
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
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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 complexity 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 distribtion, 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.