Strengthened security for blind signatures

Abstract

Provable security is a very nice property for cryptographic protocols. Unfortunately, in many cases, this is at the cost of a considerable loss in terms of efficiency. More recently, a new approach to achieve some kind of provable security was explored using the so-called “random oracle model”. Last year, Stern and the author studied the security of blind signatures in this model. We first defined appropriate notions of security for electronic cash purpose, then, we proposed the first efficient and provably secure schemes. Unfortunately, even if our proof prevents a user from spending more coins than he had withdrawn, this is only if the number of withdrawn coins is poly-logarithmically bounded. In this paper, we propose a generic transformation of those schemes which extends the security even after polynomially many withdrawals. Moreover, this transformation keeps the scheme efficient and so can be used in a secure and efficient anonymous off-line electronic cash system.