McEliece Password Based On Quasi-cyclic Parity Codes Study

With the vigorous development of Internet technology in recent years,people's material life has been greatly improved.However,in reality,with the development of science and technology,there are many information security problems.For example,Information is stolen and tampered with during the transmission process,which has become a hot issue in the field of communication.At present,the classical public key cryptography algorithm is limited by the defect of high algorithm complexity,and it is difficult to meet the needs of the increasingly complex communication environment.A new generation of anti-quantum computer algorithms has emerged in response to this problem.In order to overcome the problems,such as the large amount of key storage in traditional algorithms,this paper summarizes the current McEliece public key cryptography(PKC)scheme based on linear codes,and combines with the traditional Mc Eliece public key cryptosystem,and proposes a high-security QC-MDPC codes based Mc Eliece public key cryptography scheme.The main research contents of the paper are as follows:(1)Aiming at the problem of high bit error rate of McEliece public key cryptography under the condition of high security level,a new decoding method is proposed based on the traditional bit decoding inversion algorithm.Firstly,while dividing a string of bits into two groups,a parallel decoder is added,which can not only significantly reduce the number of decoding operations,but also improve the decoding rate of the method for QC-MDPC codes;secondly,the alignment loop the decoding error probability of the parity check code is analyzed,and the improved threshold is selected at each iteration;finally,the original bit decoding algorithm and the improved bit decoding algorithm are compared under different security levels.The experimental results show that the method in this paper achieves better results than the traditional method.(2)Aiming at the problem that the classical public key cryptosystem is vulnerable to information set decoding attack,a more secure QC-MDPC-Mc Eliece public key cryptosystem is proposed.In order to better improve the effect of the algorithm,this paper selects three matrices and applies them to the key generation stage,and uses a special structure to scramble the original check matrix,thereby enhancing the density of the check matrix and changing the sparsity of the original public key structure.Confuse the attacker.Experimental results show that the proposed method can resist a series of linear decoding attacks,such as information set decoding attacks.(3)Aiming at the problem that traditional quasi-cyclic parity-check codes are vulnerable to GJS attacks,a Mc Eliece public key cryptography scheme based on the concatenation of RS codes and QC-MDPC codes is designed.Based on the analysis of the GJS attack method proposed by Guo et al.,this paper reduces the threat caused by the error pattern of the special structure by increasing the complexity of the public key and the private key.In the decoding stage,the simulation value of the maximum energy consumption is obtained by using the optimal threshold expression.After analysis,the bit error rate of the concatenated code can be ignored,so it can resist the GJS attack.Compared with the original scheme,although the concatenated code will increase the key amount of the public key system,it improves the security.