Parallel Implementation of BDD Enumeration for LWE

Kirshanova, Elena; May, Alexander; Wiemer, Friedrich

doi:10.1007/978-3-319-39555-5_31

Cited by 9 publications

(12 citation statements)

References 19 publications

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“…We remark that solving BDD is one of the approaches to solve the learning with errors (LWE) problem. As such, various experiments had been performed on LWE instances via the BDD approach [29,23]. A good discussion of the various approaches to solve CVP/BDD can be found in [2].…”

Section: Background On Latticesmentioning

confidence: 99%

On the Bounded Distance Decoding Problem for Lattices Constructed and Their Cryptographic Applications

Ling

Xing

et al. 2020

IEEE Trans. Inform. Theory

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In this paper, we propose new classes of trapdoor functions to solve the closest vector problem in lattices. Specifically, we construct lattices based on properties of polynomials for which the closest vector problem is hard to solve unless some trapdoor information is revealed. We thoroughly analyze the security of our proposed functions using state-of-theart attacks and results on lattice reductions. Finally, we describe how our functions can be used to design quantum-safe encryption schemes with reasonable public key sizes. In particular, our scheme can offer around 106 bits of security with a public key size of around 6.4 KB. Our encryption schemes are efficient with respect to key generation, encryption and decryption.

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Section: Background On Latticesmentioning

confidence: 99%

On the Bounded Distance Decoding Problem for Lattices Constructed and Their Cryptographic Applications

Ling

Xing

et al. 2020

IEEE Trans. Inform. Theory

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“…The branches of a weighted tree are independents, so the parallelism can be widely investigated through running the code on the branches of the tree in parallel. There are few papers introduced implementations of parallelism on the LWE problem using multi-cores [1], [25], [26]. But to the best of my knowledge, up to now there is no investigation of GPU (Graphics Processing Unit) computation on the LWE problem.…”

Section: Introductionmentioning

confidence: 99%

“…The retrieved solution in Lindner-Peikert's implementation is an approximation to a closest vector, while in prunedenumeration implementation is a closest vector. In order to show a wide rate of improvement and scalability of our implementation, a comparison has been conducted between the sequential implementation provided by Kirshanova et al [1] and our implementation using a single GPU and two GPUs. In Lindner-Peikert's implementation, the speedups achieved by a single GPU and two GPUs are in average 6 and 13 times respectively.…”

Section: Introductionmentioning

confidence: 99%

Improving BDD Enumeration for LWE Problem Using GPU

2020

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In this paper, we present a GPU-based parallel algorithm for the Learning With Errors (LWE) problem using a lattice-based Bounded Distance Decoding (BDD) approach. To the best of our knowledge, this is the first GPU-based implementation for the LWE problem. Compared to the sequential BDD implementation of Lindner-Peikert and pruned-enumeration strategies by Kirshanova [1], our GPU-based implementation is almost faster by a factor 6 and 9 respectively. The used GPU is NVIDIA GeForce GTX 1060 6G. We also provided a parallel implementation using two GPUs. The results showed that our algorithm is scalable and faster than the sequential version (Lindner-Peikert and pruned-enumeration) by a factor of almost 13 and 16 respectively. Moreover, the results showed that our parallel implementation using two GPUs is more efficient than Kirshanova et al.'s parallel implementation using 20 CPU-cores. INDEX TERMS Learning with error, lattice-based cryptography, LLL algorithm, shortest vector problem, closest vector problem, bounded distance decoding, GPU, cryptanalysis. NOMENCLATURE , Inner product |S| Number of elements of a set S Euclidean norm Z p Set of nonnegative integers less than p O(f) Soft O notation v Row vector (usually in Z m) a mod q Remainder after division of a by q poly(n) Polynomial function of degree n span{b 1 ,. .. , b n } Span of a set of vectors over Z

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“…On the other hand, we do not have provable security on our particular structure, but neither does NTRU; although NTRU has been researched intensively for quite some time now. Another motivation to follow an alternative path of study from LWE-based cryptosystems (and q-ary lattices) is the recent progress of attacks on such cryptosystems [3,5,13,38,39,41] and the recent talk given by Lyubashevsky at PKC'16 in which he also qualifies LWE-based problems as particular instances of "basic" lattice problems and advised "to understand the underlying knapsack problems" to build practical schemes [47].…”

Section: Introductionmentioning

confidence: 99%

Enhancing Goldreich, Goldwasser and Halevi’s scheme with intersecting lattices

Sipasseuth

Plantard

Susilo

2019

Journal of Mathematical Cryptology

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We present a technique to enhance the security of the Goldreich, Goldwasser and Halevi (GGH) scheme. The security of GGH has practically been broken by lattice reduction techniques. Those attacks are successful due to the structure of the basis used in the secret key. In this work, we aim to present a new technique to alleviate this problem by modifying the public key which hides the structure of the corresponding private key. We intersect the initial lattice with a random one while keeping the initial lattice as our secret key and use the corresponding result of the intersection as the public key. We show sufficient evidence that this technique will make GGH implementations secure against the aforementioned attacks.

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Parallel Implementation of BDD Enumeration for LWE

Cited by 9 publications

References 19 publications

On the Bounded Distance Decoding Problem for Lattices Constructed and Their Cryptographic Applications

On the Bounded Distance Decoding Problem for Lattices Constructed and Their Cryptographic Applications

Improving BDD Enumeration for LWE Problem Using GPU

Enhancing Goldreich, Goldwasser and Halevi’s scheme with intersecting lattices

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