A New Efficient Threshold Ring Signature Scheme Based on Coding Theory

Abstract

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 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 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 O(Nt). This paper is an extended version of a paper published in the conference PQCrypto 2008, with complete proofs and definitions.