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.

A system of algebraic equations over a finite field is called sparse if each equation depends on a low number of variables. Efficiently finding solutions to the system is an underlying hard problem in cryptanalysis of modern ciphers. In this paper the deterministic Agreeing-Gluing algorithm introduced earlier by Raddum and Semaev for solving such equations is studied. Its expected running time on uniformly random instances of the problem is rigorously estimated. The estimate is at present the best theoretical bound on the complexity of solving average instances of the problem. In sparse Boolean equations we observe an exciting difference with the worst-case complexity provided by SAT solving methods.