The many faces of Schnorr: a toolkit for the modular design of threshold Schnorr signatures

Recently, a number of highly optimized threshold signing protocols for Schnorr signatures have been proposed. While these proposals contain important new techniques, some of them present and analyze these techniques in very specific contexts, making it less than obvious how these techniques can be adapted to other contexts, or combined with one another. The main goal of this paper is to abstract out and extend in various ways some of these techniques, building a toolbox of techniques that can be easily combined in different ways and in different contexts. To this end, we present security results for various “enhanced” modes of attack on the Schnorr signature scheme in the non-distributed setting, and we demonstrate how to reduce the security in the distributed threshold setting to these enhanced modes of attack in the non-distributed setting. This results in a very modular approach to protocol design and analysis, which can be used to easily design new threshold Schnorr protocols that enjoy better security and/or performance properties than existing ones.