New blind signatures equivalent to factorization

Abstract

In this paper, we present new blind signature schemes based on the factorization problem. They are the first blind signature schemes proved secure relatively to factorization. By security, we mean that no `one-more forgery' is possible even under a parallel attack. In other terms, a user that receives k electronic coins cannot manufacture k+1. Those security definitions have been introduced by Pointcheval and Stern for use in electronic cash. In fact, blind signatures were defined with this aim and it is still their most important application, together with anonymous voting. In the following, we will present an efficient reduction of an attack to a factorization algorithm in the random oracle model.