In this paper we propose the technology for constructing propositional encodings of discrete functions. It is aimed at solving inversion problems of considered functions using state-of-the-art SAT solvers. We implemented this technology in the form of the software system called TRANSALG, and used it to construct SAT encodings for a number of cryptanalysis problems. By applying SAT solvers to these encodings we managed to invert several cryptographic functions. In particular, we used the SAT encodings produced by TRANSALG to construct the family of two-block MD5 collisions in which the first 10 bytes are zeros. In addition to that we used TRANSALG encoding for the widely known A5/1 keystream generator to solve several dozen of its cryptanalysis instances in a distributed computing environment. Also in the present paper we compare the functionality of TRANSALG with that of similar software systems.