Towards cryptographic function distinguishers with evolutionary circuits

Abstract

Cryptanalysis of a cryptographic function usually requires advanced cryptanalytical skills and extensive amount of human labour. However, some automation is possible, e.g., by using randomness testing suites like STS NIST (Rukhin, 2010) or Dieharder (Brown, 2004). These can be applied to test statistical properties of cryptographic function outputs. Yet such testing suites are limited only to predefined patterns testing particular statistical defects. We propose more open approach based on a combination of software circuits and evolutionary algorithms to search for unwanted statistical properties like next bit predictability, random data non-distinguishability or strict avalanche criterion. Software circuit that acts as a testing function is automatically evolved by a stochastic optimization algorithm and uses information leaked during cryptographic function evaluation. We tested this general approach on problem of finding a distinguisher (Englund et al., 2007) of outputs produced by several candidate algorithms for eStream competition from truly random sequences. We obtained similar results (with some exceptions) as those produced by STS NIST and Dieharder tests w.r.t. the number of rounds of the inspected algorithm. This paper focuses on providing solid assessment of the proposed approach w.r.t. STS NIST and Dieharder when applied over multiple different algorithms rather than obtaining best possible result for a particular one. Additionally, proposed approach is able to provide random distinguisher even when presented with very short sequence like 16 bytes only.