A New Efficient Threshold Ring Signature Scheme Based on Coding Theory

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.