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Lattice-based Encryption Over Standard Lattices In Hardware

Published: 05 June 2016 Publication History

Abstract

Lattice-based cryptography has gained credence recently as a replacement for current public-key cryptosystems, due to its quantum-resilience, versatility, and relatively low key sizes. To date, encryption based on the learning with errors (LWE) problem has only been investigated from an ideal lattice standpoint, due to its computation and size efficiencies. However, a thorough investigation of standard lattices in practice has yet to be considered. Standard lattices may be preferred to ideal lattices due to their stronger security assumptions and less restrictive parameter selection process.
In this paper, an area-optimised hardware architecture of a standard lattice-based cryptographic scheme is proposed. The design is implemented on a FPGA and it is found that both encryption and decryption fit comfortably on a Spartan-6 FPGA. This is the first hardware architecture for standard lattice-based cryptography reported in the literature to date, and thus is a benchmark for future implementations. Additionally, a revised discrete Gaussian sampler is proposed which is the fastest of its type to date, and also is the first to investigate the cost savings of implementing with λ/2-bits of precision.
Performance results are promising compared to the hardware designs of the equivalent ring-LWE scheme, which in addition to providing stronger security proofs; generate 1272 encryptions per second and 4395 decryptions per second.

References

[1]
M. Ajtai. Generating hard instances of lattice problems (extended abstract). In STOC, pages 99--108, 1996.
[2]
M. Albrecht. Discrete Gaussian samplers over lattices. http://doc.sagemath.org/html/en/reference/\allowbreakstats/sage/stats/distributions/discrete_gaussian_lattice.html, 2014.
[3]
A. Becker and T. Laarhoven. Efficient (ideal) lattice sieving using cross-polytope LSH. IACR Cryptology ePrint Archive, 2015:823, 2015.
[4]
D. J. Bernstein. A subfield-logarithm attack against ideal lattices. http://blog.cr.yp.to/20140213-ideal.html. Feb. 2014. Accessed: 21.10.2015.
[5]
J. W. Bos, M. Naehrig, and J. van de Pol. Sieving for shortest vectors in ideal lattices: a practical perspective. IACR Cryptology ePrint Archive, 2014:880, 2014.
[6]
Z. Brakerski, A. Langlois, C. Peikert, O. Regev, and D. Stehlé. Classical hardness of learning with errors. In STOC, pages 575--584, 2013.
[7]
J. Buchmann, D. Cabarcas, F. Göpfert, A. Hülsing, and P. Weiden. Discrete Ziggurat: A time-memory trade-off for sampling from a Gaussian distribution over the integers. In Selected Areas in Cryptography, pages 402--417, 2013.
[8]
H. Chen, K. Lauter, and K. E. Stange. Attacks on search RLWE. Cryptology ePrint Archive, Report 2015/971, 2015.
[9]
R. Cramer, L. Ducas, C. Peikert, and O. Regev. Recovering short generators of principal ideals in cyclotomic rings. IACR Cryptology ePrint Archive, 2015:313, 2015.
[10]
L. Ducas, A. Durmus, T. Lepoint, and V. Lyubashevsky. Lattice signatures and bimodal Gaussians. In CRYPTO (1), pages 40--56, 2013. Full version: https://eprint.iacr.org/2013/383.pdf.
[11]
K. Eisenträger, S. Hallgren, and K. Lauter. Weak instances of PLWE. In Selected Areas in Cryptography--SAC 2014, pages 183--194. Springer, 2014.
[12]
Y. Elias, K. Lauter, E. Ozman, and K. Stange. Provably weak instances of ring-LWE. In CRYPTO, volume 9215, pages 63--92. 2015.
[13]
C. Gentry, C. Peikert, and V. Vaikuntanathan. Trapdoors for hard lattices and new cryptographic constructions. In STOC, pages 197--206, 2008.
[14]
N. Göttert, T. Feller, M. Schneider, J. Buchmann, and S. A. Huss. On the design of hardware building blocks for modern lattice-based encryption schemes. In CHES, pages 512--529, 2012.
[15]
T. Ishiguro, S. Kiyomoto, Y. Miyake, and T. Takagi. Parallel Gauss sieve algorithm: Solving the SVP challenge over a 128-dimensional ideal lattice. In PKC, pages 411--428, 2014.
[16]
D. E. Knuth and A. C. Yao. The complexity of nonuniform random number generation. Algorithms and complexity: new directions and recent results, pages 357--428, 1976.
[17]
R. Lindner and C. Peikert. Better key sizes (and attacks) for LWE-based encryption. In CT-RSA, pages 319--339, 2011.
[18]
V. Lyubashevsky. Lattice signatures without trapdoors. In EUROCRYPT, pages 738--755, 2012.
[19]
V. Lyubashevsky and D. Micciancio. Generalized compact knapsacks are collision resistant. In Automata, Languages and Programming, pages 144--155. Springer, 2006.
[20]
T. Matsumoto and H. Imai. Public quadratic polynomial-tuples for efficient signature-verification and message-encryption. In EUROCRYPT, pages 419--453. Springer, 1988.
[21]
R. J. McEliece. A public-key cryptosystem based on algebraic coding theory. DSN progress report, 42(44):114--116, 1978.
[22]
R. C. Merkle. A certified digital signature. In CRYPTO, pages 218--238. Springer, 1990.
[23]
R. Overbeck and N. Sendrier. Code-based cryptography. In Post-Quantum Cryptography, pages 95--145. 2009.
[24]
C. Peikert. An efficient and parallel Gaussian sampler for lattices. In CRYPTO, pages 80--97, 2010.
[25]
T. Pöppelmann, L. Ducas, and T. Güneysu. Enhanced lattice-based signatures on reconfigurable hardware. In CHES, pages 353--370, 2014. Full version: https://eprint.iacr.org/2014/254.pdf.
[26]
T. Pöppelmann and T. Güneysu. Towards practical lattice-based public-key encryption on reconfigurable hardware. In Selected Areas in Cryptography, pages 68--85, 2013.
[27]
T. Pöppelmann and T. Güneysu. Area optimization of lightweight lattice-based encryption on reconfigurable hardware. In ISCAS, pages 2796--2799, 2014.
[28]
O. Regev. On lattices, learning with errors, random linear codes, and cryptography. In STOC, pages 84--93, 2005.
[29]
O. Regev. The learning with errors problem. Invited survey in CCC, 2010.
[30]
S. Rich and B. Gellman. NSA seeks to build quantum computer that could crack most types of encryption. The Washington Post, January 2014.
[31]
S. S. Roy, O. Reparaz, F. Vercauteren, and I. Verbauwhede. Compact and side channel secure discrete Gaussian sampling. IACR Cryptology ePrint Archive, 2014:591, 2014.
[32]
S. S. Roy, F. Vercauteren, N. Mentens, D. D. Chen, and I. Verbauwhede. Compact ring-LWE cryptoprocessor. In CHES, pages 371--391. Springer, 2014.
[33]
S. S. Roy, F. Vercauteren, and I. Verbauwhede. High Precision Discrete Gaussian Sampling on FPGAs. In Selected Areas in Cryptography, pages 1--39, 2013.
[34]
M.-J. O. Saarinen. Gaussian sampling precision and information leakage in lattice cryptography. Cryptology ePrint Archive, Report 2015/953, 2015.
[35]
M. Schneider. Sieving for shortest vectors in ideal lattices. In AFRICACRYPT, pages 375--391, 2013.
[36]
P. W. Shor. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput., 26(5):1484--1509, Oct. 1997.

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  1. Lattice-based Encryption Over Standard Lattices In Hardware

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    cover image ACM Other conferences
    DAC '16: Proceedings of the 53rd Annual Design Automation Conference
    June 2016
    1048 pages
    ISBN:9781450342360
    DOI:10.1145/2897937
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    Published: 05 June 2016

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    • (2024)Multi-LFSR Architectures for BRLWE-Based Post Quantum CryptographyIEEE Access10.1109/ACCESS.2024.342699012(96258-96272)Online publication date: 2024
    • (2024)Near Threshold Computation of Partitioned Ring Learning With Error (RLWE) Hardware Accelerator on Reconfigurable ArchitectureIEEE Access10.1109/ACCESS.2024.340123512(68814-68827)Online publication date: 2024
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