One-Round ID-Based Threshold Signature Scheme from Bilinear Pairings

Abstract

In this paper, we propose a new ID-based threshold signature scheme from the bilinear pairings, which is provably secure in the random oracle model under the bilinear Diffie-Hellman assumption. Our scheme adopts the approach that the private key associated with an identity rather than the master key of PKG is shared. Comparing to the-state-of-art work by Baek and Zheng, our scheme has the following advantages. (1) The round-complexity of the threshold signing protocol is optimal. Namely, during the signing procedure, each party broadcasts only one message. (2) The communication channel is optimal. Namely, during the threshold signing procedure, the broadcast channel among signers is enough. No private channel between any two signing parties is needed.(3) Our scheme is much more efficient than the Baek and Zheng scheme in term of computation, since we try our best to avoid using bilinear pairings. Indeed, the private key of an identity is indirectly distributed by sharing a number xID ∈ Z * q , which is much more efficient than directly sharing the element in the bilinear group. And the major computationally expensive operation called distributed key generation protocol based on the bilinear map is avoided. (4) At last, the proactive security can be easily added to our scheme.

Efficient identity-based threshold signature scheme from bilinear pairings in standard model

“…In other words, it is the holder of the ID-based private key rather than PKG that distributes the key shares. Then several IBTHS schemes from bilinear pairings have been proposed [12,13,14,15]. Now we simply review these results.…”

“…Directly applying the Baek and Zheng's methodology to various identity-based signature, a line of works [12,13,14] were proposed. Although the threshold signing protocols of [12,13] avoid the distributed key generation sub-protocol which consumes most of the time for Baek and Zheng's scheme, their robustness is weaker than that of the Baek-Zheng's scheme in some sense as stated in [15,14]. Based on the identity-based signature scheme secure without random oracles [16,17], Sun et al constructed a non-interactive identity-based threshold signature scheme without random oracles [14].…”

“…Since the IBTHS schemes of [11,12,13,14] all heavily depend on the secret sharing tools based on pairings whose computation is very time-consuming [18], their computation efficiency is not very satisfying in practice. To solve this problem, Gao et al [15] proposed a new identity-based signature scheme and then constructed the corresponding IBTHS scheme which enjoys the computation efficiency similar to the non-identity-based threshold signature scheme in [6].…”

“…(5) It is the private key associated with an identity rather than a master key of the Public Key Generator that is shared among signature generation servers. To the best of our knowledge, there is no identity-based threshold signature scheme which enjoys all the above advantages among all the schemes in [11,12,13,14,15].…”

An Improvement of the User Identification and Key Agreement Protocol with User Anonymity

“…In distributed computing environments, it is necessary to maintain the user anonymity (Lee and Chang, 2000;Wu and Hsu, 2004;Yang et al, 2004;Kumar and Rajendra, 2006;Gao et al, 2009;Wang et al, 2009;Wang and Hu, 2010;Liu and Huang, 2010;Sun et al, 2010;Tseng and Wu, 2010;Xiong et al, 2010;Ren et al, 2010). That is, only the server can identify the user, while no other entity can determine any information concerning the user's identity.…”