SPARSE ALGEBRAIC EQUATIONS OVER FINITE FIELDS

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.