Paper 2024/991
Leveled Homomorphic Encryption Schemes for Homomorphic Encryption Standard
Abstract
Homomorphic encryption allows for computations on encrypted data without exposing the underlying plaintext, enabling secure and private data processing in various applications such as cloud computing and machine learning. This paper presents a comprehensive mathematical foundation for three prominent homomorphic encryption schemes: Brakerski-Gentry-Vaikuntanathan (BGV), Brakerski-Fan-Vercauteren (BFV), and Cheon-Kim-Kim-Song (CKKS), all based on the Ring Learning with Errors (RLWE) problem. We align our discussion with the functionalities proposed in the recent homomorphic encryption standard, providing detailed algorithms and correctness proofs for each scheme. Additionally, we propose improvements to the current schemes focusing on noise management and optimization of public key encryption and leveled homomorphic computation. Our modifications ensure that the noise bound remains within a fixed function for all levels of computation, guaranteeing correct decryption and maintaining efficiency comparable to existing methods. The proposed enhancements reduce ciphertext expansion and storage requirements, making these schemes more practical for real-world applications.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint.
- Keywords
- Homomorphic EncryptionLearning with ErrorsRing Learning with ErrorsNoise BoundsLattice Attacks
- Contact author(s)
-
sgao @ clemson edu
kjyates @ clemson edu - History
- 2024-06-20: approved
- 2024-06-19: received
- See all versions
- Short URL
- https://ia.cr/2024/991
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2024/991,
author = {Shuhong Gao and Kyle Yates},
title = {Leveled Homomorphic Encryption Schemes for Homomorphic Encryption Standard},
howpublished = {Cryptology ePrint Archive, Paper 2024/991},
year = {2024},
note = {\url{https://eprint.iacr.org/2024/991}},
url = {https://eprint.iacr.org/2024/991}
}
