Sparse Boolean equations and circuit lattices

Abstract

A system of Boolean equations is called sparse if each equation depends on a small number of variables. Finding efficiently solutions to the system is an underlying hard problem in the cryptanalysis of modern ciphers. In this paper we study new properties of the Agreeing Algorithm, which was earlier designed to solve such equations. Then we show that mathematical description of the Algorithm is translated straight into the language of electric wires and switches. Applications to the DES and the Triple DES are discussed. The new approach, at least theoretically, allows a faster key-rejecting in brute-force than with COPACOBANA.