A New Efficient Threshold Ring Signature Scheme Based on Coding Theory

Abstract

International audience—Ring signatures were introduced by Rivest, Shamir and Tauman in 2001 [32]. These sig-natures 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 -out-of-(threshold) ring signatures in 2002 [9]. We propose in this article a generalization of Stern's code based identification (and signature) scheme [36] to design a practical -out-of-threshold ring signature scheme. The size of the resulting signatures is in () and does not depend on , contrary to most of the existing protocols. Our scheme is existentially unforge-able 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 (). This protocol is the first efficient code-based ring signature scheme and the first code-based thresh-old ring signature scheme. Moreover it has a better complexity than number-theory based schemes which have a complexity in (). This paper is an extended version of [2] with complete proofs and definitions

An Efficient Code-Based Threshold Ring Signature Scheme with a Leader-Participant Model

“…Existing threshold ring signature schemes are mostly based on the number theory [14][15][16][17]; hence, as mentioned above, such schemes could be insecure in the quantum world. To the best of our knowledge, Dallot and Vergnaud's scheme [18] and Aguilar Melchor et al 's scheme [19] are the only two code-based threshold ring signature schemes published in the literature. Dallot and Vergnaud's scheme [18] combined Bresson et al 's construction [13] and Courtois et al 's signature [20], which results in the signature size twice the number of system users.…”

“…Dallot and Vergnaud's scheme [18] combined Bresson et al 's construction [13] and Courtois et al 's signature [20], which results in the signature size twice the number of system users. Aguilar Melchor et al 's scheme [19] is a generalization of Stern's identification and signature scheme [21] and has low efficiency in the signature size.…”

Post-quantum Cryptography: Code-Based Signatures

“…size in bits Sign. cost in bops Identity Based Signatures PGGG [9] 2 m tm (≈ 0.7 MB) 2 m × r1 (≈ 1.1 MB) t!t 2 m 2 (1/2 + 2 + 6/m)(≈ 2 45 ) Ring Signatures ZLC [44] 2 m tm (≈ 0.7 MB) tm + log 2 ( 2 m t )l (≈ 0.95 kB) t!t 2 m 2 (≈ 2 43.8 ) Threshold(ring) Signatures ACG [28] n 2 N/2 (≈ 2.41 MB) 20000 × N (≈ 0.24 MB) 140n 2 N (≈ 2 32.3 ) DV [17] 2 m tmN (≈ 70 MB) A(m, t, N, l) (≈ 5.2 kB) B(m, t, N, l) (≈ 2 35.4 ) Blind Signatures…”

Provably secure strong designated verifier signature scheme based on coding theory

“…Dallot developed the security proof of CFS signature scheme in a modified version introduced by himself . There are a few provable secure code‐based signatures proposed, such as code‐based ring signature schemes and code‐based undeniable signature scheme . Also a DVS scheme is presented in .…”