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

C. P. Schnorr, M. Euchner
1991 Lecture Notes in Computer Science  
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

C. P. Schnorr, M. Euchner
1994 Mathematical programming  
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]

Werner Backes, Susanne Wetzel
2001 Lecture Notes in Computer Science  
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]

Daniele Micciancio, Michael Walter
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.  ... 
doi:10.1007/978-3-662-49890-3_31 fatcat:vtn2z4kbqjc6fmbirzw5rdfavm

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

Roohallah Rastaghi, Hamid R. Dalili Oskouei
2012 arXiv   pre-print
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]

Hendrik W. Lenstra
2001 European Congress of Mathematics  
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

Fatemeh Ganji, Juliane Krämer, Jean-Pierre Seifert, Shahin Tajik
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  ... 
doi:10.1145/2810103.2813723 dblp:conf/ccs/GanjiKST15 fatcat:td3dtooa3ngq3pqis3ud6s4t4q

Communication Over MIMO Broadcast Channels Using Lattice-Basis Reduction

Mahmoud Taherzadeh, Amin Mobasher, Amir K. Khandani
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.  ... 
doi:10.1109/tit.2007.909095 fatcat:syi7eeu7jzf7lnpqc3bzvuadhi

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

Marius Arvinte, Ahmed H. Tewfik
2018 arXiv   pre-print
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

Nicolas Brisebarre, Silviu-Ioan Filip, Guillaume Hanrot
2018 IEEE Transactions on Signal Processing  
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]

Tadanori Teruya, Kenji Kashiwabara, Goichiro Hanaoka
2018 Lecture Notes in Computer Science  
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]

Werner Backes, Susanne Wetzel
2009 Lecture Notes in Computer Science  
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]

Thomas Plantard, Willy Susilo, Zhenfei Zhang
2013 Lecture Notes in Computer Science  
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]

Claus Peter Schnorr
2003 Lecture Notes in Computer Science  
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]

Jinming Wen, Xiao-Wen Chang
2018 arXiv   pre-print
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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