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Evolutionary cryptography against multidimensional linear cryptanalysis

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Abstract

The evolutionary cryptosystem is a new cryptosystem proposed by a Chinese researcher recently. This paper studies its security level resisting against multidimensional linear cryptanalysis in this paper. It is shown that the evolutionary cryptosystem possesses higher resistance than its initial fixed cryptosystem does for resisting against multidimensional linear cryptanalysis. Multidimensional generalizations of Matsui’s Algorithm 1 and Algorithm 2 based on log-likelihood ratio (LLR) statistics are introduced. By the relationship among the data complexity N, the bit advantage a and the success rate P S of these two multidimensional generalized algorithms, it is proven that more data is needed for attacking the evolutionary cryptosystem than that is needed for attacking its initial fixed cryptosystem when the bit advantage and success rate are identical. Moreover, it is shown that both time complexity and memory complexity for attacking the evolutionary cryptosystem are higher than that of attacking its initial fixed cryptosystem with the same data complexity. The research indicates that the evolutionary cryptosystem is more robust than its initial fixed cryptosystem against the multidimensional linear cryptanalysis.

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References

  1. Zhang H G, Feng X T, Qin Z P, et al. Evolutionary cryptosystems and evolutionary design for DES. J China Institute Commun, 2002, 23: 57–64

    Google Scholar 

  2. Zhang H G, Feng X T, Qin Z P, et al. Research on evolutionary cryptosystems and evolutionary DES. Chin J Comput, 2003, 26: 1678–1684

    MathSciNet  Google Scholar 

  3. Meng Q S, Zhang H G, Wang Z Y, et al. Designing Bent functions using evolving method. Chin J Eletron, 2004, 32: 1901–1903

    Google Scholar 

  4. Meng Q S, Zhang H G, Yang M, et al. Analysis of affinely equivalent Boolean functions. Sci China Ser F-Inf Sci, 2007, 50: 299–306

    Article  MATH  MathSciNet  Google Scholar 

  5. Meng Q S, Tang M, Zhang H G. Evolutionary design of trace form Bent function. http://eprint.iacr.org.2005/332

  6. Wang H Z, Zhang H G, Wu Q H, et al. Design theory and method of multivariate hash function. Sci China Inf Sci, 2010, 53: 1977–1987

    Article  MathSciNet  Google Scholar 

  7. Matsui M. Linear cryptanalysis method for DES cipher. In: Helleseth T, ed. Advances in Cryptology-Eurocrypt’93, LNCS 765. Berlin: Springer-Verlag, 1994. 386–397

    Google Scholar 

  8. Matsui M. The first experimental cryptanalysis of the Data Encryption Standard. In: Desmedt Y G, ed. Advances in Cryptology-Crypto’94, LNCS 839. Berlin: Springer-Verlag, 1994. 1–11

    Google Scholar 

  9. Kaliski B S, Robshaw M J B. Linear cryptanalysis using multiple approximations. In: Desmedt Y G, ed. Advances in Cryptology-Crypto’94, LNCS 839. Berlin: Springer-Verlag, 1994. 26–39

    Google Scholar 

  10. Biryukov A, Cannière C D, Quisquater M. Linear cryptanalysis using multiple approximations. In: Desmedt Y G, ed. Advances in Cryptology-Crypto’04, LNCS 3152. Berlin: Springer-Verlag, 2004. 1–22

    Google Scholar 

  11. Murphy S. The independence of linear approximations in symmetric cryptology. IEEE Trans Inf Theory, 2006, 52: 5510–5518

    Article  Google Scholar 

  12. Hermelin M, Cho J Y, Nyberg K. Multidimensional linear cryptanalysis of reduced round Serpent. In: Mu Y, Susilo W, Seberry J, eds. ACISP 2008, LNCS 5107. Berlin: Springer-Verlag, 2008. 203–215

    Google Scholar 

  13. Hermelin M, Cho J Y, Nyberg K. Statistical tests for key recovery using multidimensional extension of Matsui’s Algorithm 1. In: Joux A, ed. Advances in Cryptology-Eurocrypt’09-Post Session, LNCS 5479. Berlin: Springer-Verlag, 2009

    Google Scholar 

  14. Hermelin M, Cho J Y, Nyberg K. Multidimensional extension of Matsui’s Algorithm 2. In: Dunkelman O, ed. Fast Software Encryption, LNCS 5665. Berlin: Springer-Verlag, 2009. 209–227

    Chapter  Google Scholar 

  15. Hermelin M, Nyberg K. Dependent linear approximations-the algorithm of Biryukov and others revisited. In: Pieprzyk J, ed. CT-RSA2010, LNCS 5985. Berlin: Springer-Verlag, 2010. 318–333

    Google Scholar 

  16. Baignéres T, Junod P, Vaudenay S. How far can we go beyond linear cryptanalysis? In: Lee P J, ed. ASIACRYPT 2004, LNCS 3329. Berlin: Springer-Verlag, 2004. 432–450

    Chapter  Google Scholar 

  17. Selcuk A A. On probability of success in linear and differential cryptanalysis. J Cryptology, 2008, 21: 131–147

    Article  MATH  MathSciNet  Google Scholar 

  18. Junod P, Vaudenay S. Optimal key ranking procedures in a statistical cryptanalysis. In: Johansson T, ed. FSE 2003, LNCS 2887. Berlin: Springer-Verlag, 2003. 235–246

    Google Scholar 

  19. Matsui M. On correlation between the order of S-boxes and the strength of DES. In: De Santis A, ed. Advances in Cryptology-Eurocrypt’93, LNCS 950. Berlin: Springer-Verlag, 1995. 366–375

    Google Scholar 

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Authors and Affiliations

  1. School of Computer, Wuhan University, Wuhan, 430079, China

    HuanGuo Zhang, ChunLei Li & Ming Tang

  2. Key Laboratory of Aerospace Information Security and Trusted Computing of Ministry of Education of China, Wuhan University, Wuhan, 430079, China

    HuanGuo Zhang, ChunLei Li & Ming Tang

Authors
  1. HuanGuo Zhang
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  2. ChunLei Li
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  3. Ming Tang
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Correspondence to HuanGuo Zhang.

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Zhang, H., Li, C. & Tang, M. Evolutionary cryptography against multidimensional linear cryptanalysis. Sci. China Inf. Sci. 54, 2565–2577 (2011). https://doi.org/10.1007/s11432-011-4494-2

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