Research On Dynamic Threshold Digital Signature Schemes Based On HECCC And Their Applications

The emergence of public key cryptography promotes the generation of digital signature technology. Digital signature technology plays an important role in the modern popular electronic trading. The digital signature schemes based on RSA public key cryptography are widely used in network identity authentication.Threshold digital signature schemes are based on the combination of threshold secret sharing and digital signature scheme. Threshold digital signature has the same flexibility as the threshold secret sharing schemes: A small number of missing persons will not affect the generation of digital signature, and at the same time, it distributes the signature key to all the members of the group, which is more secure than the ordinary digital signature. In the practical application, we often need to select the number of members from the group according to the level of information to participate in the threshold digital signature, so dynamic threshold digital signature scheme is formed,which is based on the threshold digital signature.With the development of computing power of modern computers, the RSA public key cryptography, which is based on difficulty of factorizing large integer, needs longer key and the operand of RSA need to be increased. With the rise of quantum computation, the Shor algorithm based on quantum computation will be able to decompose any large integer. Therefore, RSA encryption will no more security in the near future. Elliptic Curve Cryptography(ECC) as a new public key cryptography,which is based on discrete logarithm problem, has attracted great attention of scholars at home and abroad. The research of ECC is also unceasingly thorough, although ECC has been put into application, but its popularity is far less than RSA now.Hyperelliptic Curve Cryptosystems derive from ECC, has a better advantage comparing with ECC: the secure hyperelliptic curve can be found in a small field, andthe operands of HECC is shorter than ECC under the same safety conditions. Since HECC was put forward, it has been greatly developed. A lot of protocols based on RSA is transplanted to HECC by scholars at home and abroad, Various protocols emerge in an endless stream program based on HECC.The main work of this paper is as follows:(1) Research on threshold digital signature schemes. Aiming at problems existing in the current threshold digital signature schemes, a threshold digital signature scheme based on HECC is proposed.(2) Research on dynamic threshold digital signature schemes. According to the problems existing in the current schemes, the new scheme is designed. A new dynamic threshold digital signature scheme based on the multi-threshold multi-secret sharing protocol is proposed, which is based on the hyperelliptic curve cryptosystem(HECC). Then the new scheme is compared with existing schemes.(3) Hyperelliptic curve cryptosystem is implemented by using number theory library(NTL), then the cryptosystem is used to implement the dynamic threshold digital signature scheme which is designed in this paper. Then the correctness and security of the scheme are analyzed. We also compare the efficiency of various scalar multiplications.