Research On Privacy Protection Of Post-ouantum Blockchain Based On Lattice Cryptography

Blockchain technology can establish a trusted value transmission channel between unfamiliar nodes in an untrusted environment and solve the trust problem of traditional centralized system.It has been widely used in intelligent medical care,electronic voting,sharing economy and other fields.However,while the blockchain is developing rapidly,it faces severe challenges in terms of security and privacy.With the continuous development of quantum computing,the underlying cryptographic mechanisms of blockchain will be threatened by quantum computing attacks,and the security of blockchain system will become fragile.In addition,the relationship between the user information and the transaction address in blockchain transactions is close,the attacker can infer the real identity of users through data mining and other means,and the blockchain ledger is open and transparent to all nodes in the network.The privacy and security of data cannot be guaranteed.Therefore,it is of great significance to study cryptographic algorithms that can resist quantum computing attacks and realize the security protection of user privacy data in blockchain system.In view of the privacy disclosure of user identity and transaction data in the blockchain system,and the inability of the underlying cryptographic mechanism of the blockchain to resist quantum computing attacks,this paper carries out research on the post-quantum blockchain privacy protection scheme based on lattice cryptography.The specific research work of this paper is as follows:(1)A post-quantum blockchain anonymous transaction scheme based on ring signature on lattice is proposed.Aiming at the problem of privacy leakage of user identity in blockchain transactions,a certificateless linkable ring signature algorithm based on the assumption of difficulty in solving small integers on lattice is studied,and a post-quantum blockchain anonymous transaction scheme is constructed.Firstly,combined with the certificateless cryptosystem,a certificateless linkable ring signature algorithm is designed by using the trapdoor generation principle and the preimage sampling technology,which effectively avoids the problems of public key management and key escrow.Secondly,the bimodal Gaussian rejection sampling algorithm is used to generate signature,and the output signature distribution is independent of the signer’s private key,which can better protect the private key information.Compared with the general rejection sampling algorithm,the bimodal Gaussian rejection sampling algorithm reduces the sampling rejection rate and improves the efficiency of the signature algorithm.In addition,a post-quantum blockchain anonymous transaction scheme is constructed based on the ring signature algorithm to achieve user identity anonymity and anti-quantum attack security.Combined with the principle of key mirror image,it can effectively prevent malicious users from double-spending attacks that may occur in transactions.Finally,under the random oracle model,the security of the scheme is analyzed and demonstrated.Compared with other ring signature schemes on lattice in terms of storage cost and time cost,the analysis shows that the public key size and signature size of the scheme are shorter,and the time cost of generating key and signature is smaller,and the calculation efficiency is higher.(2)A post-quantum blockchain privacy protection scheme based on fully homomorphic encryption is designed.In order to solve that problem of transaction data leakage such as transfer amount in blockchain system,a certificateless fully homomorphic encryption algorithm base on the learning with errors difficulty assumption on lattice is studied,and a postquantum blockchain privacy protection scheme is construct.Firstly,the key pair is generated by using fixed-dimensional lattice delegation algorithm and pre-image sampling algorithm to reduce the growth of lattice dimension.Secondly,a fully homomorphic encryption algorithm is designed based on the approximate eigenvector,which eliminates the operation key and improves the efficiency of homomorphic operation.Under the random oracle model,the correctness and security of the algorithm are analyzed and demonstrated.It is proved that the algorithm satisfies the security of indistinguishability under adaptive-identity chosenplaintext attack(IND-ID-CPA).In addition,a post-quantum blockchain privacy protection scheme is constructed based on the blockchain account balance model.Using the proposed certificateless fully homomorphic encryption algorithm,data such as local balance and transfer amount are encrypted and calculated during the transaction process.The whole network node can only verify the ciphertext of the transaction data,which realizes the privacy protection and security calculation of the transaction data,and optimizes the privacy management of blockchain data.Finally,the comparison shows that compared with other homomorphic encryption schemes,this scheme has the security against quantum computing attack,and the size of public key and private key is obviously reduced,and the encryption efficiency is higher.