Lattice-Based Post-Quantum Cryptography for Homomorphic Encryption

As quantum computing technology continues to advance, the development of post-quantum cryptography (PQC) methods capable of resisting quantum computing attacks has emerged as a key research direction. Existing homomorphic encryption schemes, such as RSA, ElGamal, and Paillier, face potential vulnerabilities to quantum attacks. To address this challenge, this study proposes a lattice-based PQC homomorphic encryption scheme. The approach leverages lattice cryptographic methods to resist quantum attacks while enabling homomorphic encryption for computational applications. This research provides mathematical proofs, computational examples, and a comprehensive security analysis of the proposed lattice-based PQC homomorphic encryption scheme. The findings aim to serve as a reference for developers working on homomorphic encryption applications, such as federated learning.