A Certificateless Homomorphic Encryption Scheme for Protecting Transaction Data Privacy of Post-Quantum Blockchain

Abstract

Blockchain has a profound impact on all areas of society by virtue of its immutability, decentralization and other characteristics. However, blockchain faces the problem of data privacy leakage during the application process, and the rapid development of quantum computing also brings the threat of quantum attack to blockchain. In this paper, we propose a lattice-based certificateless fully homomorphic encryption (LCFHE) algorithm based on approximate eigenvector firstly. And we use the lattice-based delegate algorithm and preimage sampling algorithm to extract part of the private key based on certificateless scheme, which is composed of the private key together with the secret value selected by the user, thus effectively avoiding the problems of certificate management and key escrow. Secondly, we propose a post-quantum blockchain transaction privacy protection scheme based on LCFHE algorithm, which uses the ciphertext calculation characteristic of homomorphic encryption to encrypt the account balance and transaction amount, effectively protecting the transaction privacy of users and having the ability to resist quantum attacks. Finally, we analyze the correctness and security of LCFHE algorithm, and the security of the algorithm reduces to the hardness of learning with errors (LWE) hypothesis.