NFLlib: NTT-Based Fast Lattice Library

Aguilar-Melchor, Carlos; Barrier, Joris; Guelton, Serge; Guinet, Adrien; Killijian, Marc-Olivier; Lepoint, Tancrède

doi:10.1007/978-3-319-29485-8_20

Cited by 94 publications

(47 citation statements)

References 29 publications

(65 reference statements)

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“…No parallelism was exploited. In Figure 1, one can find the execution timings of polynomial reduction, using NFL for power-of-two cyclotomics [1]; the unoptimized and optimized Barrett reductions and the Montgomery reduction for non-power-of-two cyclotomics. In order to highlight the gain brought by our algorithms compare to generic ones we also compare with NTL's reduction using preconditioning [16].…”

Section: Resultsmentioning

confidence: 99%

Efficient Reductions in Cyclotomic Rings - Application to Ring-LWE Based FHE Schemes

Bajard

Eynard

Hasan

et al. 2017

Selected Areas in Cryptography – SAC 2017

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Section: Resultsmentioning

confidence: 99%

Efficient Reductions in Cyclotomic Rings - Application to Ring-LWE Based FHE Schemes

Bajard

Eynard

Hasan

et al. 2017

Selected Areas in Cryptography – SAC 2017

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“…So, data in q can stay in this form throughout the computations. The two scalar products in Relin RNS involve k 2 NTT + 2k 2 nIMM + 2kinvNTT, exactly like the relinearization step in MP variant. And finally 2knIMM are needed to manage the Montgomery representation, in q, with respect tom.…”

Section: B3 Some Details About Complexitymentioning

confidence: 99%

“…The C++ NFLlib library [2] was used for arithmetic in R. It provides an e cient NTT-based product in R p for p a product of 30 or 62-bit prime integers, and with degree n as a power of 2, up to 2 15 .…”

Section: Software Implementationmentioning

confidence: 99%

“…Thus, the sum involves k 2 nEM. The reduction modulo q can be performed by using an e cient reduction as described in [2], reducing to around 2 multiplications of k-word integers, that is O(k 1+" )nEM (where " stands for complexity of multi-precision multiplication in radix-base 2 ⌫ ; e.g. " = 1 for the schoolbook multiplication).…”

Section: B3 Some Details About Complexitymentioning

confidence: 99%

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A Full RNS Variant of FV Like Somewhat Homomorphic Encryption Schemes

Bajard

Eynard

Hasan

et al. 2017

Lecture Notes in Computer Science

129

151

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Abstract. 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 coe cients. This work focuses in particular on the Chinese Remainder Theorem representation (a.k.a. Residue Number Systems) applied to large coe cients. In SHE schemes like that of Fan and Vercauteren (FV), such a representation remains hardly compatible with procedures involving coe cient-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.

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“…In [19], an implementation of FV using the multipurpose FLINT library [20] performs an homomorphic multiplication of FV in 148 ms for degree 4096 polynomials with 125 bits coefficients. Then, FV has been implemented to NFLlib [21], an efficient C++ implementation of ideal lattice cryptography. Authors can perform an homomorphic multiplication in 17.2 ms for the same parameters.…”

Section: Introductionmentioning

confidence: 99%

Hardware/Software Co-Design of an Accelerator for FV Homomorphic Encryption Scheme Using Karatsuba Algorithm

Migliore

Real

Lapôtre

et al. 2018

IEEE Trans. Comput.

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Somewhat Homomorphic Encryption (SHE) schemes allow to carry out operations on data in the cipher domain. In a cloud computing scenario, personal information can be processed secretly, inferring a high level of confidentiality. For many years, practical parameters of SHE schemes were overestimated, leading to only consider the FFT algorithm to accelerate SHE in hardware. Nevertheless, recent work demonstrates that parameters can be lowered without compromising the security [1]. Following this trend, this work investigates the benefits of using Karatsuba algorithm instead of FFT for the Fan-Vercauteren (FV) Homomorphic Encryption scheme. The proposed accelerator relies on an hardware/software co-design approach, and is designed to perform fast arithmetic operations on degree 2560 polynomials with 135 bits coefficients, allowing to compute small algorithms homomorphically. Compared to a functionally equivalent design using FFT, our accelerator performs an homomorphic multiplication in 11.9 ms instead of 15.46 ms, and halves the size of logic utilization and registers on the FPGA.

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NFLlib: NTT-Based Fast Lattice Library

Cited by 94 publications

References 29 publications

Efficient Reductions in Cyclotomic Rings - Application to Ring-LWE Based FHE Schemes

Efficient Reductions in Cyclotomic Rings - Application to Ring-LWE Based FHE Schemes

A Full RNS Variant of FV Like Somewhat Homomorphic Encryption Schemes

Hardware/Software Co-Design of an Accelerator for FV Homomorphic Encryption Scheme Using Karatsuba Algorithm

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