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The analysis of the number of fixed points in the key extending algorithm of RC4

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Abstract

The probabilities of the state transitions of the initial value S 0 in the S table of RC4 are described by a kind of bistochastic matrices, and then a computational formula for such bistochastic matrices is given, by which the mathematical expectation of the number of fixed points in the key extending algorithm of RC4 is obtained. As a result, a statistical weakness of the key extending algorithm of RC4 is presented.

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References

  1. 1

    Fluhrer S R, McGrew D A. Statistical analysis of the alleged RC4 keystream generator. In: Fast Software Encryption, FSE’2000, Berlin-Heidelberg: Springer-Verlag, 2000, 19–30

  2. 2

    Knudsen L R, Mcier W, Preneel B, Rijmen V, Verdoolaege S. Analysis methods for (alleged) RC4. In: Kazuo Ohta, Pei D Y, eds. Advances in Cryptology ASIACTYPT’98, Proceedings of international Conference on the Theory and Application of Cryptology and information Security, Beijing, China, October 18–22, 1998

  3. 3

    Fluhrer S R, Mantin I, Shamir A. Attacks on RC4 and WEP. Cryptobytes, 5(2): 26–34 (2002)

  4. 4

    Liu B L. Theory of Combinatorial Matrices. Beijing: Science Press, 1998

  5. 5

    Fluhrer S R, Mantin I, Shamir A. Weaknesses in the key scheduling algorithm of RC4, In: Selected Areas in Cryptography, Berlin-Heidelberg: Springer-Verlag, 2001, 1–24

  6. 6

    Mantin I, Shamir A. A practical attack on broadcast RC4. In: Fast Software Encryption, FSE’2001, Berlin: Springer, 2001, 152–164

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Author information

Correspondence to KeJian Xu.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 10371061)

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Xu, K., He, L., Dai, Z. et al. The analysis of the number of fixed points in the key extending algorithm of RC4. Sci. China Ser. A-Math. 51, 407–415 (2008). https://doi.org/10.1007/s11425-007-0186-1

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Keywords

  • bistochastic matrix
  • fixed point
  • key extending algorithm
  • RC4
  • state transition
  • probability matrix

MSC(2000)

  • 94A60
  • 37C25
  • 60J10
  • 11A05