Lattice Enumeration Using Extreme Pruning

Gama, Nicolas; Nguyêñ, Phong Q.; Regev, Oded

doi:10.1007/978-3-642-13190-5_13

Cited by 204 publications

(334 citation statements)

References 33 publications

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“…Indeed, Gama et al [7] show, with respect to enumeration-based SVP algorithms, a theoretical exponential speedup if the input basis is rerandomized, reduced and the enumeration search tree for each reduced basis is pruned extremely. Experiments confirm this huge speedup in practice [13].…”

Section: Using Multiple Randomized Basesmentioning

confidence: 99%

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Tuning GaussSieve for Speed

Fitzpatrick

Bischof

Buchmann

et al. 2015

Progress in Cryptology - LATINCRYPT 2014

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Abstract. The area of lattice-based cryptography is growing ever-more prominent as a paradigm for quantum-resistant cryptography. One of the most important hard problem underpinning the security of latticebased cryptosystems is the shortest vector problem (SVP). At present, two approaches dominate methods for solving instances of this problem in practice: enumeration and sieving. In 2010, Micciancio and Voulgaris presented a heuristic member of the sieving family, known as GaussSieve, demonstrating it to be comparable to enumeration methods in practice. With contemporary lattice-based cryptographic proposals relying largely on the hardness of solving the shortest and closest vector problems in ideal lattices, examining possible improvements to sieving algorithms becomes highly pertinent since, at present, only sieving algorithms have been successfully adapted to solve such instances more efficiently than in the random lattice case. In this paper, we propose a number of heuristic improvements to GaussSieve, which can also be applied to other sieving algorithms for SVP.

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Section: Using Multiple Randomized Basesmentioning

confidence: 99%

“…The original algorithm [11] solves SVP (deterministically) with time complexity n n 2 +o(n) (n being the lattice dimension). More recent works (such as [7]) allow probabilistic SVP solution, sacrificing guaranteed solution for runtime improvements.…”

Section: Introductionmentioning

confidence: 99%

Tuning GaussSieve for Speed

Fitzpatrick

Bischof

Buchmann

et al. 2015

Progress in Cryptology - LATINCRYPT 2014

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show abstract

“…A small vector is obtained in the projection of this lattice, and the resulting vector is inserted into the main lattice basis at the ith position. The search for the small vector in the projected lattice is performed by an enumeration method using a heuristic called extreme pruning [6].…”

Section: Estimating Bkzmentioning

confidence: 99%

“…Gama, Nguyen and Regev in 2010 [6] proposed improved heuristics for solving SVP using enumeration via a technique called extreme pruning. Potentially, this technique could be used with the enumeration of the β dimensional projected lattices within the BKZ algorithm.…”

Section: Estimating Bkzmentioning

confidence: 99%

Estimating Key Sizes for High Dimensional Lattice-Based Systems

Pol

Smart

2013

Cryptography and Coding

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Abstract. We revisit the estimation of parameters for use in applications of the BGV homomorphic encryption system, which generally require high dimensional lattices. In particular, we utilize the BKZ-2.0 simulator of Chen and Nguyen to identify the best lattice attack that can be mounted using BKZ in a given dimension at a given security level. Using this technique, we show that it should be possible to work with lattices of smaller dimensions than previous methods have recommended, while still maintaining reasonable levels of security. As example applications we look at the evaluation of AES via FHE operations presented at Crypto 2012, and the parameters for the SHE variant of BGV used in the SPDZ protocol from Crypto 2012.

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“…Schnorr and Euchner [26] presented a zig-zag strategy for enumerating the lattice vectors to make the algorithm have a better performance in practice. In 2010, Gama, Nguyen and Regev [9] introduced an extreme pruning technique and improved the running time in both theory and practice. All enumeration algorithms above require a polynomial space complexity.…”

Section: Introductionmentioning

confidence: 99%

A Three-Level Sieve Algorithm for the Shortest Vector Problem

Zhang

Pan

2014

Lecture Notes in Computer Science

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Abstract. In AsiaCCS 2011, Wang et al. proposed a two-level heuristic sieve algorithm for the shortest vector problem in lattices, which improves the Nguyen-Vidick sieve algorithm. Inspired by their idea, we present a three-level sieve algorithm in this paper, which is shown to have better time complexity. More precisely, the time complexity of our algorithm is 2 0.3778n+o(n) polynomial-time operations and the corresponding space complexity is 2 0.2833n+o(n) polynomially many bits.

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Lattice Enumeration Using Extreme Pruning

Cited by 204 publications

References 33 publications

Tuning GaussSieve for Speed

Tuning GaussSieve for Speed

Estimating Key Sizes for High Dimensional Lattice-Based Systems

A Three-Level Sieve Algorithm for the Shortest Vector Problem

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