Paper 2024/214

Distributed Fiat-Shamir Transform

Abstract

The recent surge of distribute technologies caused an increasing interest towards threshold signature protocols, that peaked with the recent NIST First Call for Multi-Party Threshold Schemes. Since its introduction, the Fiat-Shamir Transform has been the most popular way to design standard digital signature schemes. In this work, we translate the Fiat-Shamir Transform into a multi-party setting, building a framework that seeks to be an alternative, easier way to design threshold digital signatures. We do that by introducing the concept of threshold identification scheme and threshold sigma protocol, and showing necessary and sufficient conditions to prove the security of the threshold signature schemes derived from them. Lastly, we show a practical application of our framework providing an alternative security proof for Sparkle, a recent threshold Schnorr signature. In particular, we consider the threshold identification scheme underlying Sparkle and prove the security of the signature derived from it. We show that using our framework the effort required to prove the security of threshold signatures might be drastically lowered. In fact, instead of reducing explicitly its security to the security of a hard problem, it is enough to prove some properties of the underlying threshold sigma protocol and threshold identification scheme. Then, by applying the results that we prove in this paper it is guaranteed that the derived threshold signature is secure.