Tightly Secure Threshold Signatures over Pairing-Free Groups

Threshold signatures have been drawing lots of attention in recent years. Of particular interest are threshold signatures that are proven secure under adaptive corruptions (NIST Call 2023). Sadly, existing constructions with provable adaptive security suffer from at least one of the following drawbacks: (i) strong idealizations such as the algebraic group model (AGM), (ii) an unnatural restriction on the corruption threshold being t/2 where t is the signing threshold, or (iii) prohibitively large security loss under established assumptions. Notably, point (iii) has received little to no attention in the literature on this subject. In this work, we introduce Twinkle-T, a new threshold signature scheme which overcomes these limitations. Twinkle-T is the first scheme to have a fully tight security proof under up to t adaptive corruptions without relying on the AGM. It also has a signing protocol consisting of only three rounds and thus matches the currently best threshold signature with full adaptive security Twinkle (Eurocrypt 2024) in the pairing-free discrete logarithm setting. We prove security from a standard non-interactive assumption, namely, the Decisional Diffie-Hellman (DDH) assumption, in the random oracle model.