Abstract

In this talk, a polynomial time translation of integer factorization and the cryptographic hash functions MD5 and SHA -1 into propositional formulas will be presented and discussed, along with some interesting experimental results obtained with the use of the current best SAT solvers. Those computational problems can also serve as benchmark for various SAT solvers.

Propositional satisfiability, SAT , is one of the best known NP-complete problems. There is no feasible algorithm known for testing satisfiability of the propositional formulas in general. Nevertheless, there are algorithms (implemented by so-called SAT solvers, or SAT checkers) that turn out to be feasible and very efficient on many instances of propositional formulas.

On the other hand, no one knows any polynomial run-time solving algorithm for the problem of integer factorization. The famous and challenging cryptosystem RSA was built on the problem in 1977 and has been widely applied since then.