Fiat-Shamir with Aborts: From Identification Schemes to Linkable Ring Signatures

Abstract

Fiat-Shamir with aborts is a technique to transform a lattice-based identification scheme to a signature scheme introduced by Lyubashevsky (in Asiacrypt 2009). The scheme is also provably secure based on some standard lattice problems. In this paper, we show how to generically transform a signature scheme, obtained by Fiat-Shamir transformation from the ring learning with errors problem (RLWE), to a ring signature. The ring signature obtained with this transformation possesses standard security notions like unforgeability and anonymity. We also show how to achieve a linkable ring signature from the ring signature using a collision-resistant hash function. Linkable ring signatures are an important cryptographic tool as it protects signer anonymity and link signatures from the same signer. The linkable ring signature obtained from this transformation performs at par with the other lattice-based solutions for linkable ring signature, which does not require high-end zero-knowledge proofs.