An implementation of the differential attacks on cryptographic hash functions MD4 (Message Digest 4) and MD5 (Message Digest 5) by reducing the problems of search for collisions of these hash functions to the Boolean satisfiability problem (SAT) is considered. The novelty of the results obtained consists in a more compact (compared to already known) SAT encodings for the algorithms considered and in the use of modern parallel and distributed SAT solvers in applications to the formulated SAT problems. Searching for single block collisions of MD4 in this approach turned out to be very simple. In addition, several dozens of double block collisions of MD5 are found. In the process of the corresponding numerical experiments, a certain class of messages that produce the collisions is found: in particular, a set of pairs of such messages with first 10 zero bytes is constructed.

Keywords: cryptographic hash functions, collisions, differential attacks, Boolean satisfiability problem, SAT, CDCL (Conflict-Driven Clause Learning), parallel SAT solvers.

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