基于量子BCH码的McEliece及Niederreiter公钥密码算法研究

In order to resist the security threat of quantum computing attacks to the traditional cryptosystem, a class of McEliece public-key cryptosystems was designed in this paper, based on the fact that no quantum computing algorithm can attack the McEliece public-key cryptosystem within polynomial time. Three types of algorithms for generating quantum BCH codes were presented. The first one was general quantum BCH code generation algorithm, the second one was special symmetric quantum BCH code generation algorithm, and the third one was special asymmetric quantum BCH code generation algorithm. Based on the asymmetric quantum BCH codes generated in this paper, the quantum McEliece public-key cryptosystem and the quantum Niederreiter public-key cryptosystem were designed, and the encryption and decryption processes of the two public-key systems were given in detail. The proposed cryptosystems not only retained the advantages of the post-quantum computation, but also can encrypt and decrypt in quantum states. The basic field has been extended to the arbitrary finite field. The computational complexity theory, data structure and algorithm model of the two public-key cryptosystems were analyzed. The exponential time and space complexity were obtained, and the results of resisting the attacks of Shor and Grover algorithms were also obtained. Finally, with the structural characteristics of quantum BCH codes, a classical Niederreiter signature system was designed, which has the ability of resisting quantum attacks.