**On solving sparse algebraic equations over finite fields II**

*Igor Semaev*

**Abstract: **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
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. 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. In characteristic 2 we observe an exciting difference
with the worst case complexity provided by SAT solving algorithms.

**Category / Keywords: **secret-key cryptography / sparse algebraic equations over finite fields, agreeing, gluing,

**Date: **received 21 Jul 2007, last revised 13 Aug 2007

**Contact author: **igor at ii uib no

**Available format(s): **PDF | BibTeX Citation

**Version: **20070813:125131 (All versions of this report)

**Short URL: **ia.cr/2007/280

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