Ionica Smeets, Arjen Lenstra, Hendrik Lenstra, László Lovász (auth.), Phong Q. Nguyen, Brigitte Vallée (eds.)3642022944, 978-3-642-02294-4, 978-3-642-02295-1
From the reviews:
“Tells the history of the LLL algorithm and paper. … this helpful and useful volume is a welcome reference book that covers nearly all applications of lattice reduction.”
[Samuel S. Wagstaff, Jr., Mathematical Reviews, Issue 2011 m]
“This book is a compilation of survey-cum-expository articles contributed by leading experts … The LLL algorithm embodies the power of lattice reduction on a wide range of problems in pure and applied fields [… and] the success of LLL attests to the triumph of theory in computer science. This book provides a broad survey of the developments in various fields of mathematics and computer science emanating from the LLL algorithm. As well-known researchers in their areas, the authors present an invaluable perspective on the topics by sharing their insights and understanding. The book is an exemplar of the unity of computer science in bringing a broad array of concepts, tools and techniques to the study of lattice problems. The many open problems and questions stated in every chapter of the book will inspire researchers to explore the LLL algorithm and its variants further. Graduate students in computer science and mathematics and researchers in theoretical computer science will find this book very useful. Finally, it is simply a pleasure to read this lovely book.”
[Krishnan Narayanan, SIGACT News Book Review Column 45(4) 2014]
Table of contents :
Front Matter….Pages I-XIV
The History of the LLL-Algorithm….Pages 1-17
Hermite’s Constant and Lattice Algorithms….Pages 19-69
Probabilistic Analyses of Lattice Reduction Algorithms….Pages 71-143
Progress on LLL and Lattice Reduction….Pages 145-178
Floating-Point LLL: Theoretical and Practical Aspects….Pages 179-213
LLL: A Tool for Effective Diophantine Approximation….Pages 215-263
Selected Applications of LLL in Number Theory….Pages 265-282
The van Hoeij Algorithm for Factoring Polynomials….Pages 283-291
The LLL Algorithm and Integer Programming….Pages 293-314
Using LLL-Reduction for Solving RSA and Factorization Problems….Pages 315-348
Practical Lattice-Based Cryptography: NTRUEncrypt and NTRUSign….Pages 349-390
The Geometry of Provable Security: Some Proofs of Security in Which Lattices Make a Surprise Appearance….Pages 391-426
Cryptographic Functions from Worst-Case Complexity Assumptions….Pages 427-452
Inapproximability Results for Computational Problems on Lattices….Pages 453-473
On the Complexity of Lattice Problems with Polynomial Approximation Factors….Pages 475-496
Back Matter….Pages 1-1
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