International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Signing on Elements in Bilinear Groups for Modular Protocol Design

Masayuki Abe
Kristiyan Haralambiev
Miyako Ohkubo
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Abstract: This paper addresses the construction of signature schemes whose 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 constant-size signatures by presenting an efficient scheme. The security is proven in the standard model based on a novel non-interactive assumption called Simultaneous Flexible Pairing Assumption that can be justified and has an optimal bound in the generic bilinear group model. We also present efficient 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 proof system, these schemes contribute to an efficient instantiation of modular constructions of cryptographic protocols.
  title={Signing on Elements in Bilinear Groups for Modular Protocol Design},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography /},
  note={Digital Signatures, Modular Protocol Design, Groth-Sahai Proofs, Blind Signatures, Group Signatures 14678 received 9 Mar 2010},
  author={Masayuki Abe and Kristiyan Haralambiev and Miyako Ohkubo},