Adaptive security for the additive-sharing based proactive RSA

Abstract

Adaptive security has recently been a very active area of research. In this paper we consider how to achieve adaptive security in the additive-sharing based proactive RSA protocol (from Crypto97). This protocol is the most efficient proactive RSA protocol for a constant number of shareholders, yet it is scalable, i.e., it provides reasonable asymptotic efficiency given certain constraints on the corruption threshold. It is based on organizing the shareholders in a certain design (randomly generated, in the asymptotic case) of families of committees and establishing communications based on this organization. This structure is very different than polynomial-based proactive RSA protocols, and the techniques for achieving adaptive security for those protocols do not apply. Therefore, we develop new techniques for achieving adaptive security in the additive-sharing based proactive RSA protocol, and we present complete proofs of security.