International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Fast Exhaustive Search for Polynomial Systems in $F_2$

Charles Bouillaguet
Chen-Mou Cheng
Tony (Tung) Chou
Ruben Niederhagen
Adi Shamir
Bo-Yin Yang
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Abstract: We analyze how fast we can solve general systems of multivariate equations of various low degrees over \GF{2}; this is a well known hard problem which is important both in itself and as part of many types of algebraic cryptanalysis. Compared to the standard exhaustive-search technique, our improved approach is more efficient both asymptotically and practically. We implemented several optimized versions of our techniques on CPUs and GPUs. Modern graphic cards allows our technique to run more than 10 times faster than the most powerful CPU available. Today, we can solve 48+ quadratic equations in 48 binary variables on a NVIDIA GTX 295 video card (USD 500) in 21 minutes. With this level of performance, solving systems of equations supposed to ensure a security level of 64 bits turns out to be feasible in practice with a modest budget. This is a clear demonstration of the power of GPUs in solving many types of combinatorial and cryptanalytic problems.
  title={Fast Exhaustive Search for Polynomial Systems in $F_2$},
  booktitle={IACR Eprint archive},
  keywords={implementation / multivariate polynomials, system-solving, parallelization, Graphic   Processing Units (GPUs)},
  note={Will be an extended version of our paper at CHES 2010 14755 received 25 May 2010, last revised 26 May 2010},
  author={Charles Bouillaguet and Chen-Mou Cheng and Tony (Tung) Chou and Ruben Niederhagen and Adi Shamir and Bo-Yin Yang},