Biblio

The design of public-key cryptography algorithm based on LWE hard problem is a hot topic in the field of post-quantum cryptography. In this paper, we design a new homomorphic encryption algorithm based on LWE problem. Firstly, to solve the problem that the existing encryption algorithms can only encrypt a single 0 or 1 bit, a new encryption algorithm based on LWE over integer is proposed, and its correctness and security are proved by theoretical analysis. Secondly, an additive homomorphism algorithm is constructed based on the algorithm, and the correctness of the algorithm is proved. The homomorphism algorithm can carry out multi-level homomorphism addition under certain parameters. Finally, the public key cryptography algorithm and homomorphic encryption algorithm are simulated through experiments, which verifies the correctness of the algorithm again, and compares the efficiency of the algorithm with existing algorithms. The experimental data shows that the algorithm has certain efficiency advantages.

Proxy Re-encryption (PRE) is a useful cryptographic structure who enables a semi-trusted proxy to convert a ciphertext for Alice into a ciphertext for Bob without seeing the corresponding plaintext. Although there are many PRE schemes in recent years, few of them are set up based on lattice. Not only this, these lattice-based PRE schemes are all more complicated than the traditional PRE schemes. In this paper, through the study of the common lattice problems such as the Small integer solution (SIS) and the Learning with Errors (LWE), we analyze the feasibility of efficient lattice-based PRE scheme combined with the previous results. Finally, we propose an efficient lattice-based PRE scheme L-PRE without losing the hardness of lattice problems.