Research And Implementation Of Efficient Structure-Preserving Blind Signature

Combination of structure-preserving(SP) signatures and Groth-Sahai non-interactive zero-knowledge proof system(GS proof system for short) is very important in the module design of the cryptography protocols, especially in the anonymous protocols for privacy protection. Although SP signatures were efficient, it was left as an open problem to find the optimal signature size and determine if there is more efficient schemes. For these problems, we have studied the complexity of SP signatures. Blind signatures based on non-interactive zero-knowledge proof can protect privacy better, but it is still lack of efficient and secure schemes which can be realized. Using the optimal SP signature scheme, we construct an efficient and secure SP blind signature scheme. The main work and achievement of this paper are as follow:(1)We introduce the research and optimization on the complexity of SP signatures based on asymmetric bilinear groups and present the lower bound that any secure SP signature should match. We prove that SP signatures must use at least two pairing-product verification equations and have signatures consisting of at least three group elements drawn from both groups. According to the complexity research, we construct a SP signature scheme that matches the lower bounds of complexity. Then we formally prove the scheme can resist existential forgery in the chosen-message attack model.(2)This paper combines the SP signature scheme and the blind signature in the common reference model, to design a blind signature scheme based on SP signature (Structure-Preserving Blind Signature) using the SXDH (Symmetric External Diffie-Hellman) instantiation of GS proof system. The scheme is fully compatible with the GS proof system, and matches the lower bounds of complexity, at the same time we give the proof and verification in detail. And then this paper gives out the security proof of the scheme presented in the standard model, proving that the scheme matches the basic security demands of blind signatures, blindness and unforgeable. In terms of performance, compared with traditional blind signature schemes, the scheme has optimal two rounds communication interaction, the user does not need to open commitment and the verifier is unable to get the signatures.(3)We use the PBC (Pairing-Based Cryptography) library which is provided by Stanford University to design and implement the SPBS prototype system, which consists of user, signe and verifier.. In the first place, we design the entity classes, including user, signer, verifie class and their own member attributes and functions. And then, we give the implementec process of core functions which consists of the issuing the blind signatures and the non-interactive zero-knowledge proof of the signatures. Finally, we test the functions of the prototype system. Through test, the system can be able to complete the two core function above.