Adaptively Secure Threshold Signature Scheme in the Standard Model

Article type: Research Article

Authors: Wang, Zecheng^; | Qian, Haifeng | Li, Zhibin

Affiliations: Department of Computer Sci. & Tech., East China Normal University, 200062 Shanghai, China | Department of Computer Sci. & Tech., Anhui University of Finance and Economics, 233041 Bengbu, China, e-mail: [email protected]; {hfqian, lizb}@cs.ecnu.edu.cn

Abstract: We propose a distributed key generation protocol for pairing-based cryptosystems which is adaptively secure in the erasure-free and secure channel model, and at the same time completely avoids the use of interactive zero-knowledge proofs. Utilizing it as the threshold key generation protocol, we present a secure (t,n) threshold signature scheme based on the Waters' signature scheme. We prove that our scheme is unforgeable and robust against any adaptive adversary who can choose players for corruption at any time during the run of the protocols and make adaptive chosen-message attacks. And the security proof of ours is in the standard model (without random oracles). In addition our scheme achieves optimal resilience, that is, the adversary can corrupt any t<n/2 players.

Keywords: threshold signature, distributed key generation, computational Diffie–Hellman problem, adaptively secure, provable security

Journal: Informatica, vol. 20, no. 4, pp. 591-612, 2009