## Search Results for the-lll-algorithm

*This book provides an introduction to the theory and applications of lattice basis reduction and the LLL algorithm.*

**Author**: Murray R. Bremner

**Publisher:** CRC Press

**ISBN:** 9781439807026

**Category:** Computers

**Page:** 332

**View:** 392

*The first book to offer a comprehensive view of the LLL algorithm, this text surveys computational aspects of Euclidean lattices and their main applications. It includes many detailed motivations, explanations and examples.*

**Author**: Phong Q. Nguyen

**Publisher:** Springer Science & Business Media

**ISBN:** 9783642022951

**Category:** Computers

**Page:** 496

**View:** 272

*Solving the shortest vector problem algorithmically gained a boom with the publication of the LLL algorithm in 1982.*

**Author**: Gerwin Pineda

**Publisher:**

**ISBN:** OCLC:1124768789

**Category:** Algorithms

**Page:** 56

**View:** 950

*Then we propose three modified algorithms to improve the computational efficiency, while the reduced matrices satisfy the LLL-reduced criteria. The first modified algorithm, to be referred to as MLLLPIVOT, uses a block pivoting strategy.*

**Author**: Tianyang Zhou

**Publisher:**

**ISBN:** OCLC:253795976

**Category:**

**Page:** 83

**View:** 208

*A flowchart of the algorithm can be found in [ 57 , Ch . 2 , Algorithm 2.6.7 ] . The last modification of the LLL algorithm we mention here is Pohst's MLLL algorithm . It works with vectors bı , ... , bn E R spanning the set A = Zbı + .*

**Author**: Oleg Nikolaevich Vasilenko

**Publisher:** American Mathematical Soc.

**ISBN:** 0821840908

**Category:** Mathematics

**Page:** 243

**View:** 472

*Note that this algorithm is essentially a reformulation of the GramSchmidt orthogonalization procedure in the case where ... [LLL reduction] Apply the LLL algorithm to the n vectors formed by the rows of R", thus obtaining a unimodular ...*

**Author**: Henri Cohen

**Publisher:** Springer Science & Business Media

**ISBN:** 9783662029459

**Category:** Mathematics

**Page:** 536

**View:** 819

*Table 13.1 Comparison of indicators between LLL and improved LLL algorithm Decorrelation algorithms Spectral condition number (Log10) Average correlation coefficient Reduction time (s) Original 10.82 0.60 LLL algorithm 5.71 0.22 0.04 ...*

**Author**: Jiadong Sun

**Publisher:** Springer Science & Business

**ISBN:** 9783642547409

**Category:** Technology & Engineering

**Page:** 733

**View:** 962

*There is already a wide number of variations around the LLL algorithm (due for instance to Kannan or Schnorr [6,13]) whose goal is to find lattice bases with sharper Euclidean properties than the original LLL algorithm.*

**Author**: Esa 9

**Publisher:** Springer Science & Business Media

**ISBN:** 9783540662518

**Category:** Computers

**Page:** 552

**View:** 768

*Seysen's technique, used in combination with the LLL algorithm, and other heuristics, enables us to solve a much larger class of subset sum problems than was previously possible.*

**Author**: Brian Andrew LaMacchia

**Publisher:**

**ISBN:** OCLC:25053550

**Category:** Cryptography

**Page:** 98

**View:** 265

*Furthermore, none of these studies is dedicated to the fine understanding of the internal structure of the algorithm. The LLL algorithm is a multidimensional extension, in dimension n, of the Euclid algorithm (obtained for n = 1) or the ...*

**Author**: Alejandro López-Ortiz

**Publisher:** Springer

**ISBN:** 9783642122002

**Category:** Computers

**Page:** 706

**View:** 459

*Before describing the technicalities of the LLL algorithm, we make some brief remarks indicating the general underlying idea. Given a basis {v1 ,v 2 ,...,v n}, it is easy to form a new basis that satisfies the Size Condition.*

**Author**: Jeffrey Hoffstein

**Publisher:** Springer

**ISBN:** 9781493917112

**Category:** Mathematics

**Page:** 538

**View:** 895

*Lattices are geometric objects that can be pictorially described as the set of intersection points of an infinite, regular n-dimensional grid.*

**Author**: Daniele Micciancio

**Publisher:** Springer Science & Business Media

**ISBN:** 9781461508977

**Category:** Computers

**Page:** 220

**View:** 810

*This implies that the LLL-algorithm has polynomial complexity. Theorem 3 (Lenstra, Lenstra and Lovász). Let A ∈ Zn×n be a lattice basis and let A0 be the number A0 = max{aj | j = 1,... ,n}. The LLL-algorithm performs O(n4 logA 0) ...*

**Author**: Giuseppe Di Battista

**Publisher:** Springer Science & Business Media

**ISBN:** 9783540200642

**Category:** Computers

**Page:** 790

**View:** 324

*We denote the checks whether some fixed value column-wise any and column bQnC1;j of LLL D BQLO reduced has the form matrix of bQ of i;j BLO by BQLO. The algorithm 2 f0; g, i D 1;2;:::;n, for repeats bQi;j with b replaced by 2 f0; g, ...*

**Author**: Tsan-Ming Choi

**Publisher:** Springer

**ISBN:** 9783319535180

**Category:** Business & Economics

**Page:** 280

**View:** 904

*of the GPS world, which will simply be called the LLL algorithm in the rest of this paper. The basic idea of the LLL method is to reach the goal of decorrelation by integer Gram-Schmidt orthogonalization. Because the LLL algorithm was ...*

**Author**: Erik Grafarend

**Publisher:** Springer Science & Business Media

**ISBN:** 9783662052969

**Category:** Science

**Page:** 474

**View:** 637

*A Formalization of the LLL Basis Reduction Algorithm Jose Divasón1, Sebastiaan Joosten2, René Thiemann3(B), and Akihisa Yamada4 1 University of La Rioja, Logro ̃no, Spain 2 University of Twente, Enschede, The Netherlands 3 University of ...*

**Author**: Jeremy Avigad

**Publisher:** Springer

**ISBN:** 9783319948218

**Category:** Mathematics

**Page:** 642

**View:** 826

**the LLL algorithm** is relatively simple to prove, but the complexity analysis is significantly more involved. We refer the interested reader to [382]. **The LLL algorithm** has been extensively studied since its invention [324, 544, 576, ...

**Author**: Jean-Michel Muller

**Publisher:** Birkhäuser

**ISBN:** 9783319765266

**Category:** Mathematics

**Page:** 627

**View:** 683

*17.6 Variants of the LLL algorithm There are many refinements of the LLL algorithm that are beyond the scope of the brief summary in this book. We list some of these now. r As mentioned earlier, it is necessary to use floating-point ...*

**Author**: Steven D. Galbraith

**Publisher:** Cambridge University Press

**ISBN:** 9781107013926

**Category:** Computers

**Page:** 615

**View:** 416

*To explain the reduction procedure mentioned in Section A.2 we have to introduce the LLL-algorithm which, among other things, is very useful in solving numerical diophantine approximation problems. It was designed by Lenstra, ...*

**Author**: Susanne Schmitt

**Publisher:** Walter de Gruyter

**ISBN:** 9783110168082

**Category:** Mathematics

**Page:** 367

**View:** 689

*Experimental parameters Input parameters of Algorithm 1 Selection of lattice Key dimension n bit length t frequency l reduction in Step 4 ... Similarly to the LLL algorithm, there are a number of variants for the BKZ algorithm.*

**Author**: Sabrina De Capitani di Vimercati

**Publisher:** Springer

**ISBN:** 9783642400124

**Category:** Computers

**Page:** 195

**View:** 300

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