Post-quantum secure fully-dynamic logarithmic-size deniable group signature in code-based setting

Abstract

<p style='text-indent:20px;'>Since its introduction by Chaum and Heyst, <i>group signature</i> has been one of the most active areas of cryptographic research with numerous applications to computer security and privacy. Group signature permits the members of a group to sign a document on behalf of the entire group keeping signer's identity secret and enabling disclosure of the signer's identity if required. In this work, we present the first code-based fully-dynamic group signature scheme which allows group members to join or leave the group at any point of time. We employ a code-based updatable <i>Merkle-tree accumulator</i> in our design to achieve logarithmic-size signature and utilize randomized <i>Niederreiter</i> encryption to trace the identity of the signer. More positively, we equipped our scheme with <i>deniability</i> characteristic whereby the tracing authority can furnish evidence showing that a given member is not the signer of a particular signature. Our scheme satisfies the security requirements of <i>anonymity</i>, <i>non-frameability</i>, <i>traceability</i> and <i>tracing-soundness</i> in the random oracle model under the hardness of generic decoding problem. We emphasize that our scheme provides full-dynamicity, features deniability in contrast to the existing code-based group signature schemes and works favourably in terms of signature size, group public key size and secret key size.</p>