International Workshop on Post-Quantum Cryptography

PQCrypto 2011: Post-Quantum Cryptography pp 98-116

An Efficient Attack on All Concrete KKS Proposals

  • Ayoub Otmani
  • Jean-Pierre Tillich
Conference paper

DOI: 10.1007/978-3-642-25405-5_7

Volume 7071 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Otmani A., Tillich JP. (2011) An Efficient Attack on All Concrete KKS Proposals. In: Yang BY. (eds) Post-Quantum Cryptography. PQCrypto 2011. Lecture Notes in Computer Science, vol 7071. Springer, Berlin, Heidelberg


Kabastianskii, Krouk and Smeets proposed in 1997 a digital signature scheme based on a couple of random error-correcting codes. A variation of this scheme was proposed recently and was proved to be EUF-1CMA secure in the random oracle model. In this paper we investigate the security of these schemes and suggest a simple attack based on (essentially) Stern’s algorithm for finding low weight codewords. It efficiently recovers the private key of all schemes of this type existing in the literature. This is basically due to the fact that we can define a code from the available public data with unusual properties: it has many codewords whose support is concentrated in a rather small subset. In such a case, Stern’s algorithm performs much better and we provide a theoretical analysis substantiating this claim. Our analysis actually shows that the insecurity of the proposed parameters is related to the fact that the rates of the couple of random codes used in the scheme were chosen to be too close. This does not compromise the security of the whole KKS scheme. It just points out that the region of weak parameters is really much larger than previously thought.


Code-based cryptography digital signature random error-correcting codes cryptanalysis 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Ayoub Otmani
    • 1
    • 2
  • Jean-Pierre Tillich
    • 1
  1. 1.SECRET Project - INRIA RocquencourtLe Chesnay CedexFrance
  2. 2.GREYC - Université de Caen - EnsicaenCaen CedexFrance