Logical Analysis of Hash Functions

In this paper we report on a novel approach for uniform encoding of hash functions (but also other cryptographic functions) into propositional logic formulae, and reducing cryptanalysis problems to the satisfiability problem. The approach is general, elegant, and does not require any human expertise on the construction of a specific cryptographic function. By using this approach, we developed a technique for generating hard and satisfiable propositional formulae and hard and unsatisfiable propositional formulae. In addition, one can finely tune the hardness of generated formulae. This can be very important for different applications, including testing (complete or incomplete) sat solvers. The uniform logical analysis of cryptographic functions can be used for comparison between different functions and can expose weaknesses of some of them (as shown for md4 in comparison with md5).