The Coincidence Test: a Bayesian Statistical Test for Block Ciphers and MACs

A block cipher or message authentication code (MAC) should behave as a random mapping. The mapping’s randomness can be evaluated with statistical tests. Statistical test suites typically used for this purpose, such as the NIST test suite, are not well-suited for block ciphers and MACs; also, these test suites employ a frequentist approach, making it difficult to obtain an overall evaluation of the mapping’s randomness. This paper describes a statistical test, the coincidence test, that overcomes the aforementioned deficiencies. The coincidence test is well-suited for block ciphers and MACs, and it employs a Bayesian approach that quite naturally yields an overall evaluation of the mapping’s randomness. Results of applying the coincidence test to reduced-round and full-round versions of the PRESENT and IDEA block ciphers and the SipHash and SQUASH MACs are reported; the results are analyzed to determine the algorithms’ randomness margins.