A New Efficient Threshold Ring Signature Scheme Based on Coding Theory

  • Authors:
  • Carlos Aguilar Melchor;Pierre-Louis Cayrel;Philippe Gaborit

  • Affiliations:
  • Université de Limoges, XLIM-DMI, Limoges Cedex, France 87060;Université de Limoges, XLIM-DMI, Limoges Cedex, France 87060;Université de Limoges, XLIM-DMI, Limoges Cedex, France 87060

  • Venue:
  • PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
  • Year:
  • 2008

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Abstract

Ring signatures were introduced by Rivest, Shamir and Tauman in 2001. Bresson, Stern and Szydlo extended the ring signature concept to t-out-of-Nthreshold ring signatures in 2002. We present in this paper a generalizationof Stern's code based authentication (and signature) scheme to the case of t-out-of-Nthreshold ring signature. The size of our signature is in $\mathcal{O}(N)$ and does not depend on t. Our protocol is anonymous and secure in the random oracle model, it has a very short public key and has a complexity in $\mathcal{O}(N)$. This protocol is the first efficient code-based ring signature scheme and the first code-based threshold ring signature scheme. Moreover it has a better complexity than number-theory based schemes which have a complexity in $\mathcal{O}(Nt)$.