The Research Of Blind Signature And Ring Signature Schemes Based On Multivariate Public Key Cryptosystems

The security of the traditionally digital signature scheme is based on the hardness of integer factorization and discrete logarithm problem. In 1994, Shor proposed an algorithm that could be used to solve the problems above in quantum computers. Then it draws plenty of attentions in the cryptography field. We have to give out schemes based on new hard-solving problems and multivariate public key cryptosystem (MPKC) based on MQ problem is one of the candidates. MPKC has some advantages that it occupies a little resource for building signature schemes, which is appropriate to small mobile devices with restricted computing or storing ability. It is so meaningful and useful in our real life. At present, there exist a great many signature schemes, including Rainbow and UOV that are regarded as secure. At the same time, there exists a main direction that brings the ideas of traditional digital signature schemes which are applied to all kinds of scenarios to MPKC schemes, for widening the adaption of MPKC signature schemes. There are many such traditional schemes that can be adopted like ring signature scheme, blind signature scheme and so on. In addition, there also exist some drawbacks of MPKC. On one hand, the security most of the signature schemes based on MPKC are not only based on MQ NP-hard problem, but also on IP NP-hard problem. Although these two problems are NP-hard, their combination on some way brings compromise to security in MPKC. On the other hand, the size of public keys and private keys is a little large, which leads to restriction on its application to some scenarios. According to the analysis in signature schemes based on MPKC in recent years, we mainly focus on the aspect of taking the ideas from traditional signature schemes, including ring signature scheme and blind signature scheme, to MPKCs. And then we build some signature schemes based on MP problem for widening the adaption of MPKCs under quantum computers. We have three main works in this paper. Firstly, we propose a ring signature scheme partially based on MPKC (Partial-MPKC). Its main idea is to reduce the reliability on IP problem in the ring signature scheme, for improving the security. Meanwhile, its security proof is illustrated as well. Secondly, on account of the big size of public and private keys, we use the method of matrix transformation on partial-MPKC to reduce the size of private keys and improve the efficiency of signature generation at the same time. Finally, on the other aspect of the construction of central map in MPKC, we propose a blind signature scheme based on MPKC using the new construction of central map. The blindness property and non-forge ability are both illustrated clearly.