A Secure Communication Scheme Based On Error Correcting Codes

Since the general linear block code decoding problem of error correcting codes was proved to be a non-deterministic polynomial complete(NPC)difficult problem,McElicece proposed a public key cryptosystem based on error correction codes.Scholars in the field of cryptography generally believe that quantum computers cannot overcome NPC problems.Therefore,this kind of public key cryptosystem based on error correction codes could counter quantum attacks.However,this kind of cryptosystem has not been widely used due to its disadvantages such as large number of keys,low data transmission rate,and lack of error correction capability.The typical improvement schemes that have emerged since then include Wang Xinmei's M public-key system with error correction capability,and the M-symmetric cryptosystem proposed by Rao.But these improvements are only unilaterally improved on a single shortcoming of the M public-key system,the problems like large number of keys were not solved.For this reason,the author of this thesis participated in a secure communication scheme based on low density parity-check(LDPC)codes,which uses the quasi-cyclic characteristics of quasi-cyclic low density parity-check(QC-LDPC)codes to reduce the key volume and coding complexity while preserving the excellent error correction performance of LDPC.The symmetrical cryptosystem is adopted to make it have a wider range of application scenarios.The communication parties use the linear congruential method to generate pseudo-random sequence to generate a large number of equivalent QC-LDPC codes,and achieve a similarity mechanism with one-time pad security.Although this scheme has made an allround improvement to the M public key system,it still has some disadvantages,like that the code length rate is not flexible enough,and the linear congruential method cannot produce a truly random code matrix.This thesis continues to conduct in-depth research and improvement of that program.The wireless channel is characterized by randomness,short-term reciprocity,fast time-to-decay,and fast vacancies.It uses the completely random key extracted from the characteristics of the wireless channel for encryption to achieve an approximate one-time pad encryption mechanism.This thesis studies related techniques and theories such as channel characteristics extraction,key quantification algorithm and consensus negotiation scheme,and carries out a large number of simulation experiments to design synchronous key extraction scheme with high key entropy and key generation rate.The LDPC codes constructed by the progressive edge-growth(PEG)algorithm has excellent performance and this algorithm could generate LDPC codes with arbitrary code length and code rate.This thesis combines the PEG algorithm with the idea of secure communication,proposes a key based progressive edge-growth(K-PEG)algorithm,which constructs massive LDPC codes controlled by random key sequences.Simulations show that the error correcting performance of the LDPC codes constructed by K-PEG algorithm is obviously better than that of the QC-LDPC code in the original algorithm.The number of equivalent LDPC codes that can be constructed with the same code length is also significantly larger,which means that the communication schemes with this algorithm can obtain a greater key space.Therefore,the K-PEG algorithm can improve the reliability,security,and coding flexibility of the original scheme.Finally,this thesis combines the scheme of key extracting based on wireless channel characteristics with K-PEG algorithm,designs a new secure communication scheme based on LDPC codes.This scheme has the security of approaching one-time-pad encryption mechanism,better error correction capabilities and higher coding flexibility than the original scheme.