Paper 2010/133

Signing on Elements in Bilinear Groups for Modular Protocol Design

Masayuki Abe, Kristiyan Haralambiev, and Miyako Ohkubo

Abstract

A signature scheme is called structure-preserving if its verification keys, messages, and signatures are group elements and the verification predicate is a conjunction of pairing product equations. We answer to the open problem of constructing a constant-size structure-preserving signature scheme. The security is proven in the standard model based on a novel non-interactive assumption that can be justified and has an optimal bound in the generic bilinear group model. We also present efficient structure-preserving signature schemes with advanced properties including signing unbounded number of group elements, allowing simulation in the common reference string model, signing messages from mixed groups in the asymmetric bilinear group setting, and strong unforgeability. Among many applications, we show two examples; an adaptively secure round optimal blind signature scheme and a group signature scheme with efficient concurrent join. As a bi-product, several homomorphic trapdoor commitment schemes and one-time signature schemes are presented, too. In combination with the Groth-Sahai non-interactive proof system, these schemes contribute to give efficient instantiations to modular constructions of cryptographic protocols.