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A zero-knowledge identification scheme based on the q-ary Syndrome Decoding problem

Cayrel, Pierre-Louis and Véron, Pascal and Alaoui, Sidi Mohamed El Yousfi (2010):
A zero-knowledge identification scheme based on the q-ary Syndrome Decoding problem.
In: Proceedings of the Seventeenth Workshop on Selected Areas in Cryptography(SAC2010), SAC2010, [Conference or Workshop Item]

Abstract

At CRYPTO’93, Stern proposed a 3-pass code-based identification scheme with a cheating probability of 2/3. In this paper, we propose a 5-pass code-based protocol with a lower communication complexity, allowing an impersonator to succeed with only a probability of 1/2. Furthermore, we propose to use double-circulant construction in order to dramatically reduce the size of the public key. The proposed scheme is zero-knowledge and relies on an NP-complete coding theory problem (namely the q-ary Syndrome Decoding problem). The parameters we suggest for the instantiation of this scheme take into account a recent study of (a generalization of) Stern’s information set decoding algorithm, applicable to linear codes over arbitrary fields Fq; the public data of our construction is then 4 Kbytes, whereas that of Stern’s scheme is 15 Kbytes for the same level of security. This provides a very practical identification scheme which is especially attractive for light-weight cryptography.

Item Type: Conference or Workshop Item
Erschienen: 2010
Creators: Cayrel, Pierre-Louis and Véron, Pascal and Alaoui, Sidi Mohamed El Yousfi
Title: A zero-knowledge identification scheme based on the q-ary Syndrome Decoding problem
Language: German
Abstract:

At CRYPTO’93, Stern proposed a 3-pass code-based identification scheme with a cheating probability of 2/3. In this paper, we propose a 5-pass code-based protocol with a lower communication complexity, allowing an impersonator to succeed with only a probability of 1/2. Furthermore, we propose to use double-circulant construction in order to dramatically reduce the size of the public key. The proposed scheme is zero-knowledge and relies on an NP-complete coding theory problem (namely the q-ary Syndrome Decoding problem). The parameters we suggest for the instantiation of this scheme take into account a recent study of (a generalization of) Stern’s information set decoding algorithm, applicable to linear codes over arbitrary fields Fq; the public data of our construction is then 4 Kbytes, whereas that of Stern’s scheme is 15 Kbytes for the same level of security. This provides a very practical identification scheme which is especially attractive for light-weight cryptography.

Title of Book: Proceedings of the Seventeenth Workshop on Selected Areas in Cryptography(SAC2010)
Uncontrolled Keywords: Secure Data
Divisions: LOEWE > LOEWE-Zentren > CASED – Center for Advanced Security Research Darmstadt
20 Department of Computer Science > Theoretical Computer Science - Cryptography and Computer Algebra
LOEWE > LOEWE-Zentren
20 Department of Computer Science
LOEWE
Event Location: SAC2010
Date Deposited: 30 Dec 2016 20:23
Identification Number: TUD-CS-2010-0188
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