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Efficient reductions in cyclotomic rings - Application to Ring-LWE based FHE schemes
| Content Provider | Hyper Articles en Ligne (HAL) |
|---|---|
| Author | Bajard, Jean-Claude Eynard, Julien Hasan, Anwar Martins, Paulo Sousa, Leonel Zucca, Vincent |
| Abstract | With Fully Homomorphic Encryption (FHE), it is possible to process encrypted data without access to the private-key. This has a wide range of applications, most notably the offloading of sensitive data processing. Most research on FHE has focused on the improvement of its efficiency, namely by introducing of schemes based on Ring-Learning With Errors (RLWE), and techniques such as batching, which allows for the encryption of multiple messages in the same ciphertext. Much of the related research has focused on RLWE relying on power-of-two cy-clotomic polynomials. While it is possible to achieve efficient arithmetic with such polynomials, one cannot exploit batching. Herein, the efficiency of ring arithmetic underpinned by non-power-of-two cyclomotic polyno-mials is analyzed and improved. Two methods for polynomial reduction are proposed, one based on the Barrett reduction and the other on a Montgomery representation. Speed-ups of up to 2.66 are obtained for the reduction operation using an i7-5960X processor when compared with a straightforward implementation of the Barrett reduction. Moreover, the proposed methods are exploited to enhance homomorphic multiplication of Fan-Vercauteren (FV) and Brakerski-Gentry-Vaikuntantahan (BGV) encryption schemes, producing experimental speed-ups of up to 1.37. |
| File Format | |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Polynomial Reduction Number Theoretic Transform Residue Number Systems Ring-Learning With Errors Homomorphic Encryption info Computer Science [cs] |
| Content Type | Text |
| Resource Type | Article |
