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Paper: On solving sparse algebraic equations over finite fields II

Authors:
Igor Semaev
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URL: http://eprint.iacr.org/2007/280
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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.
BibTeX
@misc{eprint-2007-13561,
  title={On solving sparse algebraic equations over finite fields II},
  booktitle={IACR Eprint archive},
  keywords={secret-key cryptography / sparse algebraic equations over finite fields, agreeing, gluing,},
  url={http://eprint.iacr.org/2007/280},
  note={ igor@ii.uib.no 13738 received 21 Jul 2007, last revised 13 Aug 2007},
  author={Igor Semaev},
  year=2007
}