# NFLlib: NTT-Based Fast Lattice Library

@inproceedings{Melchor2016NFLlibNF,
title={NFLlib: NTT-Based Fast Lattice Library},
author={Carlos Aguilar Melchor and Joris Barrier and Serge Guelton and Adrien Guinet and Marc-Olivier Killijian and Tancr{\e}de Lepoint},
booktitle={CT-RSA},
year={2016}
}`
• Published in CT-RSA 29 February 2016
• Computer Science, Mathematics
Recent years have witnessed an increased interest in lattice cryptography. Besides its strong security guarantees, its simplicity and versatility make this powerful theoretical tool a promising competitive alternative to classical cryptographic schemes. In this paper, we introduce NFLlib, an efficient and open-source C++ library dedicated to ideal lattice cryptography in the widely-spread polynomial ring $$\mathbb Z_{p}[x]/x^n+1$$ for n a power of 2. The library combines algorithmic…
124 Citations
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## References

SHOWING 1-10 OF 37 REFERENCES
Towards Efficient Arithmetic for Lattice-Based Cryptography on Reconfigurable Hardware
• Computer Science, Mathematics
LATINCRYPT
• 2012
This work makes a first step towards efficient FFT-based arithmetic for lattice-based cryptography and shows that the FFT can be implemented efficiently on reconfigurable hardware.
On the Design of Hardware Building Blocks for Modern Lattice-Based Encryption Schemes
• Computer Science, Mathematics
CHES
• 2012
This work gives a comparison between a matrix and polynomial based variant of the LWE scheme, and examines three different variants for sampling Gaussian distributed integers in hardware, namely rejection sampling, a rounding based approach, and a look-up table based approach.
Implementing Candidate Graded Encoding Schemes from Ideal Lattices
• Computer Science, Mathematics
ASIACRYPT
• 2015
This work provides the first implementation of such approximate multilinear maps based on ideal lattices using GGH-like schemes, and proposes algorithms and implementations for sampling from discrete Gaussians, for inverting in some Cyclotomic number fields and for computing norms of ideals in some Cyclone number rings.
Efficient Identity-Based Encryption over NTRU Lattices
• Computer Science, Mathematics
ASIACRYPT
• 2014
This work presents the first lattice-based IBE scheme with practical parameters and obtains digital signature schemes which are shorter than the previously most-compact ones of Ducas, Durmus, Lepoint, and Lyubashevsky from Crypto 2013.
High Performance Lattice-based CCA-secure Encryption
• Computer Science, Mathematics
IACR Cryptol. ePrint Arch.
• 2015
This paper gives a thorough security analysis as well as an efficient implementation of the CCA1-secure encryption scheme instantiated with the most efficient trapdoor construction and attest that it even outperforms the CPA- secure encryption scheme from Lindner and Peikert presented at CT-RSA 2011.
An Efficient and Parallel Gaussian Sampler for Lattices
To the knowledge, this is the first algorithm and rigorous analysis demonstrating the security of a perturbation-like technique and a new Gaussian sampling algorithm for lattices that is efficient and highly parallelizable.
Faster Gaussian Lattice Sampling Using Lazy Floating-Point Arithmetic
• Computer Science
ASIACRYPT
• 2012
This work introduces a laziness technique that can significantly speed up lattice sampling algorithms, in certain cases such as NTRUSign lattices, laziness can decrease the complexity to O( n2) or even O(n).
Lattice Signatures and Bimodal Gaussians
• Computer Science, Mathematics
IACR Cryptol. ePrint Arch.
• 2013
A construction of a lattice-based digital signature scheme that represents an improvement over today’s most efficient lattice schemes and has shorter signature and public key sizes than all previously proposed lattice signature schemes.
Accelerating NTRU based homomorphic encryption using GPUs
• Computer Science, Mathematics
2014 IEEE High Performance Extreme Computing Conference (HPEC)
• 2014
A large polynomial arithmetic library optimized for Nvidia GPUs to support fully homomorphic encryption schemes and is put to use to evaluate homomorphic evaluation of two block ciphers: Prince and AES.
Lattice Signatures Without Trapdoors
This work provides an alternative method for constructing lattice-based digital signatures which does not use the "hash-and-sign" methodology, and shows that by slightly changing the parameters, one can get even more efficient signatures that are based on the hardness of the Learning With Errors problem.