On solving sparse algebraic equations over finite fields

A system of algebraic equations over a finite field 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 deterministic AgreeingGluing algorithm introduced earlier in [9] for solving such equations is studied. Its expected running time on uniformly random instances of the problem is rigorously estimated. This estimate is at present the best theoretical bound on the complexity of solving average instances of the above problem. In particular, it significantly overcomes our previous results, see [11]. In characteristic 2 we observe an exciting difference with the worst case complexity provided by SAT solving algorithms.

• Type: Conference
• Year: 2008
• Where: DCC
• Authors: Igor Semaev
• Keywords: Computer Graphics, DCC 2008, SAT Solving Algorithms, Uniformly Random Instances, Worst Case Complexity