An Improved Evaluation Framework for the Quality Assessment of Hash Functions in Data Communications based on Computational Intelligence and Nonlinear Methodology

摘要

The strength of message authentication, digital signature and pseudonym generation mechanisms relies on the quality of the one-way hash functions used. In this paper, we propose extended tests based on computational intelligence and nonlinear theory to assess the hash function quality, which may be used along with well known methods and thus comprise a testing methodology. We propose four tests, the non-linearity test, the entropy assessment of the digests produced based on genetic operators, the neural-network-based modeling test, and the Lyapunov exponent test. The non-linearity behavior of the hash function is investigated by the first testing method, while the assessment of the amount of information of the hash values indicates the difficulty to find two or more messages that lead to a given digest. On the other hand, the modeling test should show the impossibility to model the one-way hash function by neural network architectures. Otherwise, it would indicate feasibility in modeling the hash functions by artificial intelligence techniques and consequently in reducing the processing effort required to break them. Finally, the Lyapunov exponent test should show the sensitive dependence on initial conditions, regarded as an additional requirement in the cases of imperfect uniform distributions, thus revealing the impossibility to model the digest sequence generation procedure from a corresponding input message sequence by any algorithmic process. The application of the methodology to the well-known MD5 and SHA confirmed the good quality of them, though not as good as supposed theoretically.