A Full RNS Variant of FV like Somewhat Homomorphic Encryption Schemes

• Main Authors: Bajard, Jean-Claude, Eynard, Julien, Hasan, Anwar, Zucca, Vincent
• Other Authors: Performance et Qualité des Algorithmes Numériques (PEQUAN), Laboratoire d'Informatique de Paris 6 (LIP6), Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Department of Electrical and Computer Engineering Waterloo (ECE), University of Waterloo Waterloo, ANR-15-CE39-0002,ARRAND,Arithmétiques Randomisées(2015)
• Format: Conference Object
• Language: English
• Published: HAL CCSD 2016
• Subjects: Lattice-based Cryptography; Homomorphic Encryption; FV; Residue Number Systems; Software Implementation; [INFO]Computer Science [cs]; Newfoundland
• Online Access: https://hal.sorbonne-universite.fr/hal-01371941; https://hal.sorbonne-universite.fr/hal-01371941/document; https://hal.sorbonne-universite.fr/hal-01371941/file/SAC2016.pdf; https://doi.org/10.1007/978-3-319-69453-5_23

International audience Since Gentry's breakthrough work in 2009, homomorphic cryptography has received a widespread attention. Implementation of a fully homomorphic cryptographic scheme is however still highly expensive. Somewhat Homomorphic Encryption (SHE) schemes, on the other hand, allow only a limited number of arithmetical operations in the encrypted domain, but are more practical. Many SHE schemes have been proposed, among which the most competitive ones rely on (Ring-) Learning With Error (RLWE) and operations occur on high-degree polynomials with large coecients. This work focuses in particular on the Chinese Remainder Theorem representation (a.k.a. Residue Number Systems) applied to large coecients. In SHE schemes like that of Fan and Vercauteren (FV), such a representation remains hardly compatible with procedures involving coecient-wise division and rounding required in decryption and homomorphic multiplication. This paper suggests a way to entirely eliminate the need for multi-precision arithmetic, and presents techniques to enable a full RNS implementation of FV-like schemes. For dimensions between 2 11 and 2 15 , we report speed-ups from 5⇥ to 20⇥ for decryption, and from 2⇥ to 4⇥ for multiplication.