Ecient Blind and Partially Blind Signatures without Random Oracles

This paper proposes a new ecient signature scheme from bilinear maps that is secure in the standard model (i.e., without the random oracle model). Our signature scheme is more eective in many applications (e.g., blind signatures, group signatures, anonymous credentials etc.) than the existing secure signature schemes in the standard model. As typical applications of our signature scheme, this paper presents ecient blind signatures and partially blind signatures that are secure in the standard model. Here, partially blind signatures are a generalization of blind signatures (i.e., blind signatures are a special case of partially blind signatures) and have many applications including electronic cash and voting. Our blind signature scheme is more ecient than the existing secure blind signature schemes in the standard model such as the Camenisch-Koprowski-Warinsch [9] and Juels-Luby-Ostrovsky [24] schemes. Our partially blind signature scheme is the rst one that is secure in the standard model and it is also ecient (as ecient as our blind signatures). The security proof of our blind and partially blind signature schemes requires the 2SDH assumption, a stronger variant of the SDH assumption introduced by Boneh and Boyen [7]. This paper also presents an ecient way to convert our (partially) blind signature scheme in the standard model to a scheme secure for a concurrent run of users in the common reference string (CRS) model. Finally, we present a blind signature scheme based on the Waters signature scheme.