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Lattice basis reduction: Improved practical algorithms and solving subset sum problems
[chapter]
1991
Lecture Notes in Computer Science
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We report on 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. ...
doi:10.1007/3-540-54458-5_51
fatcat:wifd5jgwqfd3vgcasvswameqha
Lattice basis reduction: Improved practical algorithms and solving subset sum problems
1994
Mathematical programming
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We report on 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. ...
doi:10.1007/bf01581144
fatcat:dizrkbtgkneurecbwqgsa7dx2y
Lattice Basis Reduction with Dynamic Approximation
[chapter]
2001
Lecture Notes in Computer Science
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In this paper we present a heuristic based on dynamic approximations for 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 ...
doi:10.1007/3-540-44691-5_6
fatcat:xlbcfqheszexnolq6jxj7lztke
Practical, Predictable Lattice Basis Reduction
[chapter]
2016
Lecture Notes in Computer Science
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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. ...
doi:10.1007/978-3-662-49890-3_31
fatcat:vtn2z4kbqjc6fmbirzw5rdfavm
Cryptanalysis of a Public-key Cryptosystem Using Lattice Basis Reduction Algorithm
[article]
2012
arXiv
pre-print
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s cryptosystem based on 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 ...
arXiv:1210.7417v1
fatcat:leoc6jp6xza5faz6obazian67y
Flags and Lattice Basis Reduction
[chapter]
2001
European Congress of Mathematics
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In our reformulation, 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. ...
doi:10.1007/978-3-0348-8268-2_3
fatcat:5brsyodrt5drleatdm2eyqvlcq
Lattice Basis Reduction Attack against Physically Unclonable Functions
2015
Proceedings of the 22nd ACM SIGSAC Conference on Computer and Communications Security - CCS '15
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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 ...
doi:10.1145/2810103.2813723
dblp:conf/ccs/GanjiKST15
fatcat:td3dtooa3ngq3pqis3ud6s4t4q
Communication Over MIMO Broadcast Channels Using Lattice-Basis Reduction
2007
IEEE Transactions on Information Theory
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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. ...
doi:10.1109/tit.2007.909095
fatcat:syi7eeu7jzf7lnpqc3bzvuadhi
A Relax-and-Round Approach to Complex Lattice Basis Reduction
[article]
2018
arXiv
pre-print
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We propose a relax-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. ...
arXiv:1808.04841v1
fatcat:b3aab4e4jvbcrigcumdhckwa2e
A Lattice Basis Reduction Approach for the Design of Finite Wordlength FIR Filters
2018
IEEE Transactions on Signal Processing
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We introduce a fast 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. ...
doi:10.1109/tsp.2018.2812739
fatcat:sb6jsfhxkvgfrm5vpry6om3phu
Fast Lattice Basis Reduction Suitable for Massive Parallelization and Its Application to the Shortest Vector Problem
[chapter]
2018
Lecture Notes in Computer Science
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In our 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. ...
doi:10.1007/978-3-319-76578-5_15
fatcat:gmoy7fowdnej5lcppzr4ou74by
Parallel Lattice Basis Reduction Using a Multi-threaded Schnorr-Euchner LLL Algorithm
[chapter]
2009
Lecture Notes in Computer Science
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Experiments with sparse 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 ,... ...
doi:10.1007/978-3-642-03869-3_88
fatcat:jpv4qzj3hnbqhczpjhfppnaloa
Lattice Reduction for Modular Knapsack
[chapter]
2013
Lecture Notes in Computer Science
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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 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] . ...
doi:10.1007/978-3-642-35999-6_18
fatcat:lo5wyuulsbd5tjxgebx63fhapq
Lattice Reduction by Random Sampling and Birthday Methods
[chapter]
2003
Lecture Notes in Computer Science
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We present a novel 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 . ...
doi:10.1007/3-540-36494-3_14
fatcat:akmrdilf6zaprhaoehhx64k76e
On the KZ Reduction
[article]
2018
arXiv
pre-print
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Finally, we propose a new KZ 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] . ...
arXiv:1702.08152v2
fatcat:xjnddy3efbfljbgakascy24qxa
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