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Solving Boolean equation systems and applications in cryptanalysis

布尔方程组求解及其在密码分析中的应用

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摘要

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本文给出了布尔方程组求解问题近似算法复杂度的最新结果, 说明了随机赋值是近似求解布尔方程组的最佳多项式时间算法。 介绍了求解布尔方程组的特征列算法以及其计算复杂度的最新进展, 通过实验结果说明了该算法能够高效求解若干密码分析中出现的布尔方程组。

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References

  1. Håstad J. Some optimal inapproximability results. J ACM, 2001; 48: 798–859

    Article  MathSciNet  MATH  Google Scholar 

  2. Zhao S, Gao X S. Minimal achievable approximation ratio for MAX-MQ in finite fields. Theor Comput Sci, 2009; 410: 2285–2290

    Article  MathSciNet  MATH  Google Scholar 

  3. Faugère J C. A new efficient algorithm for computing Gr¨oner bases without reduction to zero (F5). In: Proceedings of International Symposium on Symbolic & Algebraic Computation (ISSAC), Lille, 2002. 75–83

    Google Scholar 

  4. Courtois N, Klimov A, Patarin J, et al. Efficient algorithms for solving over-determined systems of multivariate polynomial equations. In: Advances in Cryptology–EUROCRYPT. Berlin: Springer, 2000. 392–407

    Google Scholar 

  5. Mcdonald C, Chernes C, Pieprzyk J. Attacking Bivium With MiniSat. Cryptology ePrint Archive Report 2007/040. 2007

    Google Scholar 

  6. Bouillaguet C, Chen H C, Cheng C M, et al. Fast exhaustive search for polynomial systems in F2. In: Cryptographic Hardware and Embedded Systems. Berlin: Springer, 2010. 203–218

    Google Scholar 

  7. Bardet M, Faugére J C, Salvy B, et al. On the complexity of solving quadratic boolean systems. J Complex, 2013; 29: 53–75

    Article  MathSciNet  MATH  Google Scholar 

  8. Gao X S, Huang Z. Characteristic set algorithms for equation solving in finite fields. J Symb Comput, 2012; 47: 655–679

    Article  MathSciNet  MATH  Google Scholar 

  9. Huang Z Y, Sun Y, Lin D D. On the efficiency of solving boolean polynomial systems with the characteristic set method. ArXiv:1405.4596, 2014

    Google Scholar 

  10. Huang Z Y, Lin D D. A new method for solving polynomial systems with noise over F2 and its applications in cold boot key recovery. In: Selected Areas in Cryptography. Berlin: Springer, 2012. 16–33

    Google Scholar 

  11. Albrecht M, Cid C. Cold boot key recovery by solving polynomial systems with noise. In: Applied Cryptography and Network Security. Berlin: Springer, 2011. 57–72

    Chapter  Google Scholar 

Download references

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Correspondence to Zhenyu Huang.

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Gao, X., Huang, Z. Solving Boolean equation systems and applications in cryptanalysis. Sci. China Inf. Sci. 59, 050104 (2016). https://doi.org/10.1007/s11432-016-5548-2

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  • DOI: https://doi.org/10.1007/s11432-016-5548-2

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