Untraceable partially blind signature based on DLOG problem

This paper proposes a new untraceable Partially Blind Signature scheme which is a cross between the traditional signature scheme and the blind signature scheme. In this proposed scheme, the message M that the signer signed can be divided into two parts. The first part can be known to the signer (like that in the traditional signature scheme) while the other part cannot be known to the signer (like that in the blind signature scheme). After having signed M, the signer cannot determine if he has made the signature of M except through the part that he knows. We draw ideas from Brands' "Restricted Blind Signature" to solve the Untraceable Partially Blind Signature problem. Our scheme is a probabilistic signature scheme and the security of our Untraceable Partially Blind Signature scheme relies on the difficulty of computing discrete logarithm.