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Lattice basis reduction: Improved practical algorithms and solving subset sum problems
[chapter]

1991
*
Lecture Notes in Computer Science
*

We report on

doi:10.1007/3-540-54458-5_51
fatcat:wifd5jgwqfd3vgcasvswameqha
*improved**practical**algorithms*for*lattice**basis**reduction*. We propose a*practical*floating point version of the L 3 -*algorithm*of Lenstra, Lenstra, Lovász (1982) . ... Empirical tests show that the strongest of these*algorithms**solves*almost all*subset**sum**problems*with up to 66 random weights of arbitrary bit length within at most a few hours on a UNISYS 6000/70 or ... The new*lattice**basis*(1)*and*the stronger*reduction**algorithms*lead to a substantially*improved*success rate of*subset**sum**algorithms*. ...##
###
Lattice basis reduction: Improved practical algorithms and solving subset sum problems

1994
*
Mathematical programming
*

We report on

doi:10.1007/bf01581144
fatcat:dizrkbtgkneurecbwqgsa7dx2y
*improved**practical**algorithms*for*lattice**basis**reduction*. We propose a*practical*floating point version of the L 3 -*algorithm*of Lenstra, Lenstra, Lovász (1982) . ... Empirical tests show that the strongest of these*algorithms**solves*almost all*subset**sum**problems*with up to 66 random weights of arbitrary bit length within at most a few hours on a UNISYS 6000/70 or ... The new*lattice**basis*(1)*and*the stronger*reduction**algorithms*lead to a substantially*improved*success rate of*subset**sum**algorithms*. ...##
###
Lattice Basis Reduction with Dynamic Approximation
[chapter]

2001
*
Lecture Notes in Computer Science
*

In this paper we present a heuristic based on dynamic approximations for

doi:10.1007/3-540-44691-5_6
fatcat:xlbcfqheszexnolq6jxj7lztke
*improving*the well-known Schnorr-Euchner*lattice**basis**reduction**algorithm*. ... In particular, the new heuristic is more efficient in reducing large*problem*instances*and*extends the applicability of the Schnorr-Euchner*algorithm*such that*problem*instances that the stateof-the-art ... . , a n (the weights)*and*S ∈ IN (the*sum*) find variables x 1 , . . . , x n ∈ {0, 1} such that S = n i=1 x i a i . (6) In [8] , the*problem*of*solving*the*subset**sum**problem*is reduced to the*problem*...##
###
Practical, Predictable Lattice Basis Reduction
[chapter]

2016
*
Lecture Notes in Computer Science
*

*Lattice*

*reduction*

*algorithms*are notoriously hard to predict, both in terms of running time

*and*output quality, which poses a major

*problem*for cryptanalysis. ... One key technique to achieving this goal is a novel

*algorithm*to

*solve*the Shortest Vector

*Problem*(SVP) in the dual without computing the dual

*basis*. ... We also thank Florian Göpfert for helpful discussions in the early stages of the development of the dual enumeration

*algorithm*. ...

##
###
Cryptanalysis of a Public-key Cryptosystem Using Lattice Basis Reduction Algorithm
[article]

2012
*
arXiv
*
pre-print

s cryptosystem based on

arXiv:1210.7417v1
fatcat:leoc6jp6xza5faz6obazian67y
*Lattice**basis**reduction**algorithms*. By computing complexity of propose attack, we show that unlike Aboud's cryptanalysis, our cryptanalysis is more efficient*and**practicable*. ... This cryptosystem uses a super-increasing sequence as private key*and*the authors investigate a new*algorithm*called permutation combination*algorithm*to enhance density of knapsack to avoid the low-density ... This cryptosystem is vulnerable to LLL-*lattice**basis**reduction**algorithm*, since it uses a super-increasing sequence as a private key*and*attempt to hide this sequence with modular multiplication for constructing ...##
###
Flags and Lattice Basis Reduction
[chapter]

2001
*
European Congress of Mathematics
*

In our reformulation,

doi:10.1007/978-3-0348-8268-2_3
fatcat:5brsyodrt5drleatdm2eyqvlcq
*lattice**basis**reduction**algorithms*are more appropriately called "flag*reduction*"*algorithms*. ... We reinterpret a large class of*lattice**basis**reduction**algorithms*by using the concept of a "flag". ... Aardal*and*C. A. J. Hurkens for their comments. He was supported by the National Science Foundation under grant number DMS 9224205. ...##
###
Lattice Basis Reduction Attack against Physically Unclonable Functions

2015
*
Proceedings of the 22nd ACM SIGSAC Conference on Computer and Communications Security - CCS '15
*

*basis*

*reduction*attack

*and*a photonic side channel analysis. ... Finally, by conducting an exhaustive discussion on our experimental results, the

*practical*feasibility of our attack scenario is proved as well. ... ACKNOWLEDGEMENTS The authors would like to acknowledge the support of the German Federal Ministry of Education

*and*Research in the project Photon FX2

*and*the Helmholtz Research School on Security Technologies ...

##
###
Communication Over MIMO Broadcast Channels Using Lattice-Basis Reduction

2007
*
IEEE Transactions on Information Theory
*

*Lattice*

*basis*

*reduction*helps us to reduce the average transmitted energy by modifying the region which includes the constellation points. ... A simple scheme for communication over MIMO broadcast channels is introduced which adopts the

*lattice*

*reduction*technique to

*improve*the naive channel inversion method. ... Minkowski

*reduction*can be seen as a greedy solution for the

*lattice*-

*basis*

*reduction*

*problem*. ...

##
###
A Relax-and-Round Approach to Complex Lattice Basis Reduction
[article]

2018
*
arXiv
*
pre-print

We propose a relax-

arXiv:1808.04841v1
fatcat:b3aab4e4jvbcrigcumdhckwa2e
*and*-round approach combined with a greedy search strategy for performing complex*lattice**basis**reduction*. ... We show that, for*lattice**basis**reduction*, such a family of solutions to the relaxed*problem*is the set of unitary matrices multiplied by a real, positive constant*and*propose a search strategy based on ... Section II presents the system model*and*the*lattice**basis**reduction**problem*. ...##
###
A Lattice Basis Reduction Approach for the Design of Finite Wordlength FIR Filters

2018
*
IEEE Transactions on Signal Processing
*

We introduce a fast

doi:10.1109/tsp.2018.2812739
fatcat:sb6jsfhxkvgfrm5vpry6om3phu
*and*efficient method, based on the computation of good nodes for polynomial interpolation*and*Euclidean*lattice**basis**reduction*. ... Such requirements increase the complexity of determining optimal designs for the*problem*at hand. ...*Lattice**basis**reduction**algorithms*allow one to move from a bad*basis*to a good one, an important preconditioning step in*solving**lattice**problems*. ...##
###
Fast Lattice Basis Reduction Suitable for Massive Parallelization and Its Application to the Shortest Vector Problem
[chapter]

2018
*
Lecture Notes in Computer Science
*

In our

doi:10.1007/978-3-319-76578-5_15
fatcat:gmoy7fowdnej5lcppzr4ou74by
*algorithm*, given a*lattice**basis*as input, variants of the*lattice**basis*are generated,*and*then each process reduces its*lattice**basis*; at this time, the processes cooperate*and*share auxiliary ... We*solved*a 150-dimension*problem*instance in about 394 days by using large clusters,*and*we also*solved**problem*instances of dimensions 134, 138, 140, 142, 144, 146,*and*148. ... Conclusion We proposed an*algorithm*suitable for parallel computing environments to reduce the*lattice**basis**and*presented its results in the SVP Challenge. ...##
###
Parallel Lattice Basis Reduction Using a Multi-threaded Schnorr-Euchner LLL Algorithm
[chapter]

2009
*
Lecture Notes in Computer Science
*

Experiments with sparse

doi:10.1007/978-3-642-03869-3_88
fatcat:jpv4qzj3hnbqhczpjhfppnaloa
*and*dense*lattice*bases show a speed-up factor of about 1.8 for the 2-thread*and*about factor 3.2 for the 4-thread version of our new parallel*lattice**basis**reduction**algorithm*... In this paper, we introduce a new parallel variant of the LLL*lattice**basis**reduction**algorithm*. ... Knapsack*lattices*(see Figure 2 ) have been developed in the context of*solving*the*subset**sum**problems*[19, 9, 8, 28] . For our experiments we have defined W = √ n + 1. The weights a 1 ,... ...##
###
Lattice Reduction for Modular Knapsack
[chapter]

2013
*
Lecture Notes in Computer Science
*

The complexity of

doi:10.1007/978-3-642-35999-6_18
fatcat:lo5wyuulsbd5tjxgebx63fhapq
*lattice**reduction**algorithms*to*solve*those*problems*is upper-bounded in the function of the*lattice*dimension*and*the maximum norm of the input*basis*. ... The complexity of*lattice**reduction**algorithms*to*solve*those*problems*is upper-bounded in the function of the*lattice*dimension*and*the maximum norm of the input*basis*. ... The knapsack*problem*is also known as the*subset**sum**problem*[12] . When s i d, it becomes a sparse*subset**sum**problem*(SSSP). The decisional version of the knapsack*problem*is NP-complete [9] . ...##
###
Lattice Reduction by Random Sampling and Birthday Methods
[chapter]

2003
*
Lecture Notes in Computer Science
*

We present a novel

doi:10.1007/3-540-36494-3_14
fatcat:akmrdilf6zaprhaoehhx64k76e
*practical**algorithm*that given a*lattice**basis*b1, ..., bn finds in O(n 2 ( k 6 ) k/4 ) average time a shorter vector than b1 provided that b 1 is ( k 6 ) n/(2k) times longer than the ... We assume that the given*basis*b1, ..., bn has an orthogonal*basis*that is typical for worst case*lattice*bases. ... Tobias for carrying out the*practical*experiments reported in this paper*and*for providing Figure 1 . ...##
###
On the KZ Reduction
[article]

2018
*
arXiv
*
pre-print

Finally, we propose a new KZ

arXiv:1702.08152v2
fatcat:xjnddy3efbfljbgakascy24qxa
*reduction**algorithm*by modifying the commonly used Schnorr-Euchner search strategy for*solving*SVPs*and*the*basis*expansion method proposed by Zhang et al. ... Simulation results show that the new KZ*reduction**algorithm*is much faster*and*more numerically reliable than the KZ*reduction**algorithm*proposed by Zhang et al., especially when the*basis*matrix is ill ... In addition to the above application, the KZ*reduction*has applications in*solving**subset**sum**problems*[16] . ...
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