Cryptanalysis of the Sidelnikov Cryptosystem

  • Lorenz Minder
  • Amin Shokrollahi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4515)


We present a structural attack against the Sidelnikov cryptosystem [8]. The attack creates a private key from a given public key. Its running time is subexponential and is effective if the parameters of the Reed-Muller code allow for efficient sampling of minimum weight codewords. For example, the length 2048, 3rd-order Reed-Muller code as proposed in [8] takes roughly an hour to break on a stock PC using the presented method.


Sidelnikov cryptosystem McEliece cryptosystem error-correcting codes structural attack 


  1. 1.
    Canteaut, A., Chabaut, F.: A new algorithm for finding minimum-weight words in a linear code: application to primitive narrow-sense BCH-codes of length 511. IEEE Transactions on Information Theory 44(1), 367–378 (1998)zbMATHCrossRefGoogle Scholar
  2. 2.
    Dumer, I., Shabunov, K.: Soft-decision decoding of Reed-Muller codes: a simplified algorithm. IEEE Transactions on Information Theory 52(3), 954–963 (2006)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Huffman, W.C., Pless, V.: Fundamentals of Error-Correcting Codes. Cambridge University Press, Cambridge (2003)zbMATHGoogle Scholar
  4. 4.
    Kasami, T., Tokura, N.: On the Weight Structure of Reed-Muller Codes. IEEE Transactions on Information Theory 16(6), 752–759 (1970)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes. North-Holland, Amsterdam (1978)Google Scholar
  6. 6.
    McEliece, R.J.: A public key cryptosystem based on algebraic coding theory. DSN progress report 42-44, 114–116 (1978)Google Scholar
  7. 7.
    Niederreiter, H.: Knapsack-Type Cryptosystems and Algebraic Coding Theory. Problems of Control and Information Theory 15(2), 159–166 (1986)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Sidelnikov, V.M.: A public-key cryptosystem based on binary Reed-Muller codes. Discrete Mathematics and Applications 4(3) (1994)Google Scholar
  9. 9.
    Sidelnikov, V.M., Shestakov, S.O.: On insecurity of cryptosystems based on generalized Reed-Solomon codes. Discrete Mathematics and Applications 2(4), 439–444 (1992)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Sendrier, N.: On the Structure of a randomly permuted concatenated code. In: EUROCODE’94 (October 1994)Google Scholar
  11. 11.
    Sendrier, N.: Finding the permutation between equivalent codes: the support splitting algorithm. IEEE Transactions on Information Theory 46(4), 1193–1203 (2000)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Lorenz Minder
    • 1
  • Amin Shokrollahi
    • 1
  1. 1.Laboratoire de mathématiques algorithmiques (LMA)EPFL 

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