Application Of Error Correcting Codes In Secure Communication

With the design and implementation of the Shor algorithm,the security of various cryptosystems based on the exchange algebra structure are facing severe challenges.In order to resist this type of attack,scholars in the cryptography community are looking for sufficiently secure password schemes to replace the current cryptographic schemes.Among them,the cryptosystem based on error correcting codes is an alternative.The scheme first proposes the McEliece public key cryptosystem.On this basis,the M symmetric cryptosystem is proposed,and then the MC block cipher encryption and error correction scheme is proposed.The LDPC code is a type of linear block code proposed by Robert Gallager in 1962.This code is close to the Shannon limit and is a good type of code.The QC-LDPC code has gradually become a research focus of scholars due to its simple structure and small space for key storage.The original keys used in all error-correcting-codes based cryptographic schemes are Goppa codes,which have large Equivalent class code and low information rate,so that it can hinder their application.This paper attempts to use a more flexible and space-consuming code,QC-LDPC code,to replaces the Goppa code into a cryptographic scheme based on error correcting codes.The application schemes of various current encryption cryptosystems based on error correcting codes,such as identity authentication or digital signature,are analyzed.This paper designs a secure key agreement communication scheme.The scheme first performs two-way authentication in using encryption.In the authentication process,the two parties exchange keys for key negotiation,and then a secure symmetric communication can be performed.The security analysis and reliability analysis of the scheme are respectively carried out.The scheme can resist the selective plaintext attack based on error correcting codes.The security is based on the difficulty of decoding and the difficulty of large matrix decomposition.Two decoding methods are used in the scheme,and the improved BF decoding method is applied in the scheme.This paper also designs QC-LDPC codes suitable for secure communication.And analy the requirements the structure and coding and decoding methods of LDPC codes with error correcting codes for secure communication.In this paper,a QC-LDPC code is constructed by using RDF combination design.The designed code can not only have a large number of equivalent class codes but also improve the error correction performance,and the design method is also more flexible.The secure communication scheme can be ensured to be safe and reliable,and not only applicable to the symmetric communication part in the authentication negotiation communication scheme designed herein,but also to the authentication part in the scheme.