Beyond the Limitation of Prime-Order Bilinear Groups, and Round Optimal Blind Signatures.
Jae Hong Seo, Jung Hee Cheon · 2012
Abstract. At Eurocrypt 2010, Freeman proposed a transformation from pairing-based schemes in composite-order bilinear groups to equivalent ones in prime-order bilinear groups. His transformation can be applied to pairing-based cryptosystems exploiting only one of two properties of composite-order bilinear groups: cancelling and projecting. At Asiacrypt 2010, Meiklejohn, Shacham, and Freeman showed that prime-order bilinear groups according to Freeman’s construction cannot have two properties simultaneously except negligible probability and, as an instance of implausible conversion, proposed a (partially) blind signature scheme whose security proof exploits both the cancelling and projecting properties of composite-order bilinear groups. In this paper, we invalidate their evidence by presenting a security proof of the prime-order version of their blind signature scheme. Our security proof follows a different strategy and exploits only the projecting property. Instead of the cancelling property, a new property, that we call translating, on prime-order bilinear groups plays an important role in the security proof, whose existence was not known in composite-order bilinear groups. With this proof, we obtain a 2-move (i.e., round optimal) (partially) blind signature scheme (without random oracle) based on the decisional linear assumption in the common reference string model, which is of independent interest.