Adaptive security in the threshold setting: From cryptosystems to signature schemes

Abstract

Threshold cryptosystems and signature schemes give ways to distribute trust throughout a group and increase the availability of cryptographic systems. A standard approach in designing these protocols is to base them upon existing single-server systems having the desired properties. Two recent (single-server) signature schemes, one due to Gennaro et al., the other to Cramer and Shoup, have been developed which are provably secure using only standard number-theoretic hardness assumptions. Catalano et al. proposed a statically secure threshold implementation of these schemes. We improve their protocol to make it secure against an adaptive adversary, thus providing a threshold signature scheme with stronger security properties than any previously known. As a tool, we also develop an adaptively secure, erasure-free threshold version of the Paillier cryptosystem.