A Secure Communication Scheme Based On Code-Based Cryptography

Due to the rapid development of quantum computing technology,the problem of large integer decomposition and discrete logarithms will no longer be difficult to calculate.So algorithms such as RSA will no longer be secure.For this reason,many researchers believe that the security of the new era's anti-quantum cryptography theory needs to be based on some new difficult problems,among which the NPC problem is currently difficult to crack by quantum computers.In error correction codes,the decoding problem of general linear codes is the NPC problem.Therefore,we study cryptographic theory based on error correction codes.In the encryption and decryption system based on error correction codes: McEliece and Niderreiter and others proposed the M system and the N system,However,the error correction code based on these two systems is the Goppa code,which needs big storage space for the public key.Due to the quasi-cyclic nature of the check matrix of QC-LDPC codes,many scholars now build M-system and N-system based on it to reduce the amount of keys.In 2018,Baldi et al.Proposed a variant of the N system based on QC-LDPC codes,and proposed an improved Q decoding algorithm,which has fast decoding speed and high accuracy.In order to apply this decoding algorithm to the M system,we propose a variant of the M system,and due to the introduction of the double public key,the security of the M system is improved.In the digital signature system based on error correction code: Courtois et al.Proposed a digital signature scheme based on the decoding problem,namely the CFS scheme.Although this scheme is secure,the error correction code is based on Goppa code,which has a large amount of key space and low signature efficiency.Due to the problem of signature efficiency,it is difficult to apply in practice,and many scholars rarely study this branch again.But with the increase in computer computing power,this problem may also be solved.In order to reduce the amount of keys,we also proposed a digital signature system based on QC-LDPC codes,and used the Q decoding algorithm.In the identification scheme based on error correction code: stern proposed a zero-knowledge identity authentication scheme based on the error correction code decoding problem,and many scholars have improved it since then,but these schemes are designed to achieve sufficient security The communication parties need to performat least 20 rounds,which is difficult to apply in actual communication.We simulated and implemented the stern scheme based on QC-LDPC codes,and analyzed the number of transmission bits during the identity authentication process.We established the correlation to reduce the number of transmission bits,thus reducing the memory required by the communicating parties during the identity authentication process.Space,and the security strength has not been weakened,but it does not solve the problem of high time complexity due to the need for multiple executions.To this end,we propose a new identity authentication algorithm that is not based on stern.This algorithm uses the improved M system proposed previously and uses the Q decoding algorithm.This algorithm only needs to be executed in one round,which is convenient for practical applications.In applications,it is currently sufficiently secure to withstand existing attacks.Finally,we propose a complete secure communication scheme.After the two parties have successfully authenticated using the above-mentioned identity authentication scheme,two-way authentication is performed,and then symmetrical encrypted communication is performed.And change the key regularly to improve security.