Study On Theory And Application Of Multi-Party Digital Signature

Multi-party signature schemes have been shown to be useful in various applications, such as electronic polling, electronic payment, etc. In this thesis, we focus on construct-ing or improving of signature schemes, security analysis, security proof, and designing of applied protocols. Here we construct some multi-party signature suitable for especial re-quirements based on the quadratic residues and bilinear pairings. Our research works are related to the threshold signature, ring signature, proxy signature, proxy ring signature and electronic auction protocols. The main contributions are as follows.The idea of threshold cryptography is to distribute the secret information and compu-tation among multi parties in order to prevent a single point of failure or abuse. Recently, Paterson and Schuldt proposed an Identity-based (ID-based) signature scheme which is provably secure in the absence of random oracles. We propose an ID-based threshold sig-nature scheme and a certificateless threshold signature based on their signature scheme, respectively. Both of the proposed construction are proved secure in the standard model. To the best of our knowledge, previous related schemes could only be proved secure in the random oracle model.We firstly propose an ID-based ring signature scheme based on quadratic residue. The proposed scheme is proven to be existential unforgeable against adaptive chosen message-and-identity attack under the random oracle model, assuming the hardness of factoring. Because the proposed scheme does not need pairing computation, a powerful but computationally expensive primitive, so it is more efficient than those which are con-structed from bilinear pairing. An efficient sealed-bid electronic auction protocol based on the ring signature and encryption key chain had been proposed. The peculiar charac-teristics of our protocol are non-repudiation of bidders but preserving their anonymity and allowing the auctioneer to determine the wining bid without revealing the losing bid. Our protocol has additional characteristics such as public verifiability, unforgeability, correct-ness and fairness.In order to eliminate the use of certificates in traditional proxy signature and the key-escrow problem in identity-based proxy signature, the notion of certificateless proxy signature was introduced. We first present a security model for certificateless proxy sig- nature schemes, and then propose an efficient construction based on bilinear pairings. The security of the proposed scheme can be proved to be equivalent to the computational Diffie-Hellman problem in the random oracle with a tight reduction. Identity-based (ID-based) proxy ring signature schemes have been shown to be useful in various applications, such as electronic polling, electronic payment, etc. We firstly propose a feasible ID-based proxy ring signature scheme based on bilinear pairings. The proposed scheme is proved to be existential unforgeable against adaptive chosen message-and-identity attack under the random oracle model, assuming the Computational Diffie-Hellman problem is hard to solve. Finally, our scheme turns out to be more efficient than the previously proposed ones.