Threshold Digital Signature Scheme's Research And Its Applications

With rapid development of the computer and Internet technology, the information security requirements have become more sophisticated.As a effective means to protect information's security, digital signature plays an important role in protecting data's integrity and undeniability.And because of its superior characteristics, threshold signature scheme based on secret sharing has become one of the major subjects in the cryptography. It not only enhances the private key's security, improve the system's reliability and availability, but also achieve the rights's dispersion.In this paper, a practical project, a military security solution leads to the concept of threshold signature.The program uses PKI (Public Key Infrastructure) system to issue the public key certificate for an entity to achieve the authentication between each other, and then use SSL protocol for data transmission. However, the root CA's signature key requires a high degree of confidentiality in its generation,storage and use process, so the threshold signature scheme is introduced to solve the problem.As to the threshold signature problem,following studies have been done:(1) Improve the Shamir secret sharing protocol.Most of threshold digital signature scheme have used the Shamir protocol, so threshold digital signature can get benefit from improving the Shamir secret sharing protocol.In this paper, difference, divided difference and other mathematical tools are used, and the complexity of the protocol is reduced from (ntk (log2n)) to O (ntk), in which n is the number of the participants, t is the value of threshold, and k is bits size of the computing field.(2) Improve Gennaro multiplication protocol.Gennaro protocol is a protocol for secure distributed multiplication of two polynomial shared values, which is used in some threshold signature scheme.In this paper, with the divided difference, difference, fast Fourier transform multiplication and other mathematical tools adopted and the idea of online and offline algorithms introducted, a improved scheme is proposed, which reduce the algorithm complexity from O(n klog2n+nk) to O(nklog2k), where n, k, t have the same meanings as (1)above.(3) Propose a threshold signature scheme based on RSA with no secret distributor.Most of threshold signature schemes with no secret distributor are based on discrete logarithm.In this paper, the routine is broken,and a threshold signature scheme based on RSA with no secret distributor is proposed, which has some novelty. Finally, the paper also gives the broad design for a military security solution, and describes the other application of threshold signature.