Research On Public Key Cryptography Schemes Based On Quasi-dyadic Codes

The development of quantum computer technology makes the number theory based public key cryptosystem face serious challenges,so the public key cryptosystems with anti-quantum computer attack characteristics have attracted a wide spread attention in the cryptographic circle.The general linear decoding in error correcting code theory is a NPC problem,which is different from the NP problems in number theory such as large integer factorization and discrete logarithm,can resist quantum computer attack.Therefore,it is of great significance to combine the error-correcting code theory with the cryptography to study the post-quantum code based public key cryptosystem.The implementation process of code based public key cryptography is only XOR,which is more efficient than other public key cryptosystems such as RSA and ECC,so it has the basic characteristics used in embedded system with limited resource,and meets with the requirements of lightweight cryptography.However,the original code based public key cryptosystem,identification scheme and digital signature scheme are very difficult to be used in practical application scenarios because of the huge key size.Therefore,the design of secure and efficient error correcting code based public key cryptography is a hotspot and difficult problem of modern cryptography.The main work of this paper is as follows:Firstly,we construct the QD-MDPC code based public key encryption algorithm with small key size.The QD-MDPC code is designed to reduce the key size,and calculate the generation matrix.At the same time,the random non-singular matrix and the permutation matrix are selected to generate the public and secret keys.The random error vector is added in the encryption process to further enhance the security of the cryptography.And the structure attack and the decoding attack analysis are carried out for the cryptographic algorithm,which proves the security of the algorithm.By constructing this QD-MDPC code,the key size of the cryptographic algorithm is greatly reduced and is suitable for embedded devices with limited storage resources.Secondly,two kinds of zero-knowledge identification schemes are constructed by combining the above-mentioned public key encryption algorithm based on QD-MDPC code.These two identification schemes are based on different hard problems in coding theory and have different performance.The former identification protocol reduces commitments needed to be sent by calculating the hash value of one commitment in every round,thereby reducing the communication costs.And this paper analyzes the security properties such as the completeness,soundness and zero knowledge.Then,based on the general decoding problem,a more optimized identification protocol is constructed.The protocol calculates the hash value of two commitments in each round,which further reduces the identification communication overhead.And the performance analysis shows that compared with other schemes,the proposed scheme optimizes the key size and the communication costs,especially the second identification protocol,which permits greater application advantage in devices with limited storage resource and computing ability.Finally,this paper designs an undeniable signature scheme based on quasi-dyadic code.The signature scheme consists of three algorithms: USetup,USign and UVerify.The setup algorithm generates the public and private key and public parameters of the signer.The signature algorithm generates a signature triplet,of which the verifier verifies the validity with the signer through a five-pass zero-knowledge protocol.This paper analyzes the security properties of the completeness,reliability,zero knowledge,unforgeability,invisibility and non-transitivity of the undeniable signature scheme.Performance analysis shows that the signature length and communication costs are better than the compared scheme.