Chen, Xiaofeng; Zhang, Fangguo; Mu, Yi; and Susilo, Willy, 2006, Efficient provably secure restrictive partially blind signatures from bilinear pairings, in Financial Cryptography and Data Security Conference, Feb-27-Mar 2006, British West Indies. Lecture Notes in Computer Science, 4107, 251-265.
Restrictive blind signatures allow a recipient to receive a blind signature on a message unknown to the signer but the choice of the message is restricted and must conform to certain rules. Partially blind signatures allow a signer to explicitly include necessary information (expiration date, collateral conditions, or whatever) in the resulting signatures under some agreement with the receiver. Restrictive partially blind signatures incorporate the advantages of these two blind signatures. In this paper we first propose a new restrictive partially blind signature scheme from bilinear pairings. Since the proposed scheme does not use Chaum-Pedersen’s knowledge proof protocol, it is much more efficient than the original restrictive partially blind signature scheme. We then present a formal proof of security in the random oracle model. Moreover, we use the proposed signature scheme to build an untraceable off-line electronic cash system followed Brand’s construction.