A New Efficient Threshold Ring Signature Scheme Based on Coding Theory
Carlos Aguilar Melchor, Pierre-Louis Cayrel, Philippe Gaborit, Fabien Laguillaumie · IEEE Transactions on Information Theory · 2011
Ring signatures were introduced by Rivest, Shamir, and Tauman in 2001. These signatures allow a signer to anonymously authenticate a message on behalf of a group of his choice. This concept was then extended by Bresson, Stern, and Szydlo into$t$-out-of-$N$(threshold) ring signatures in 2002. We propose in this article a generalization of Stern's code-based identification (and signature) scheme to design a practical$t$-out-of-$N$threshold ring signature scheme. The size of the resulting signatures is in${\cal O}(N)$and does not depend on$t$, contrary to most of the existing protocols. Our scheme is existentially unforgeable under a chosen message attack in the random oracle model assuming the hardness of the minimum distance problem, is unconditionally source hiding, has a very short public key and has an overall complexity in${\cal O}(N)$. 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${\cal O}(Nt)$. This paper is an extended version of a paper published in the conference PQCrypto 2008, with complete proofs and definitions.