Efficient group signature and identity-based signature schemes

Abstract

This thesis introduces a group signature scheme based on RSA and some identitybased signature schemes based on the bilinear pairings over elliptic curves. A practical group signature scheme is proposed with the introduction of a trusted third party called security mediator. The length of group signatures generated by the proposed scheme is shorter at the security level of 1024 bits than Boneh-Boyen-Shacham scheme. It is suitable for those applications which require short signatures. The implementation of the new group signature scheme is very simple and just requires modulo exponentiations. A new identity-based signature (IBS) schemes is developed which are proven secure in the random oracle model. The security of IBS using random oracles relies on Generalized k-CAA which is an extension version of k-CAA. The experimental results show that the proposed IBS scheme in the random oracle model is the fastest one compared to the published IBS schemes from the bilinear pairings at low security levels. We also investigate methods of building non-supersingular elliptic curves suitable for pairing-based cryptosystems and find a useful property of the Frobenius trace for such curves. Based on this property, some non-supersingular elliptic curves can be built. Batch verification is a very efficient method for speeding up multiple signa-ATTENTION: The Singapore Copyright Act applies to the use of this document. Nanyang Technological University Library iii ture verification. We investigate batch verification of the proposed IBS scheme in the random oracle model. The experimental results exhibit excellent performance in terms of the time for verification of multiple signatures and the implementation complexity. The security analysis shows that batch verification of the proposed IBS scheme is unforgeable under an adaptive chosen message and identity attack. Based on the proposed IBS scheme in the random oracle model, two new signature schemes with special features are developed: identity-based blind signature (IBBS) scheme and identity-based chameleon signature (IBCS) scheme. The security analysis illustrates that the new IBBS and IBCS are provably secure. The performance comparison shows that the efficiency of both new signature schemes is improved compared to the Zhang-Kim IBBS scheme and Zhang-Naini-Susilo IBCS scheme.