Paper 2002/038

A Distributed RSA Signature Scheme for General Access Structures

Javier Herranz, Carles Padró, and Germán Sáez

Abstract

In a distributed digital signature scheme, a set of participants shares a secret information that allows them to compute a valid signature for a given message. These systems are said to be robust if they can tolerate the presence of some dishonest players. Up to now, all the proposed schemes consider only threshold structures: the tolerated subsets of corrupted players as well as the subsets of players who can sign a message are defined according to their cardinality. We propose a framework that is more general than the threshold one, considering a general access structure of players allowed to sign and a general family of dishonest players that the scheme can tolerate. If these general structures satisfy some combinatorial conditions, we can design a distributed and secure RSA signature scheme for this setting. Our construction is based on the threshold scheme of Shoup.