Ebook: The LLL Algorithm: Survey and Applications
- Genre: Computers // Algorithms and Data Structures
- Tags: Data Structures Cryptology and Information Theory, Algorithms, Algorithm Analysis and Problem Complexity, Discrete Mathematics in Computer Science, Number Theory, Optimization
- Series: Information Security and Cryptography
- Year: 2010
- Publisher: Springer-Verlag Berlin Heidelberg
- City: New York
- Edition: 1
- Language: English
- pdf
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]
The LLL algorithm is a polynomial-time lattice reduction algorithm, named after its inventors, Arjen Lenstra, Hendrik Lenstra and László Lovász. The algorithm has revolutionized computational aspects of the geometry of numbers since its introduction in 1982, leading to breakthroughs in fields as diverse as computer algebra, cryptology and algorithmic number theory.This book consists of 15 survey chapters on computational aspects of Euclidean lattices and their main applications. Topics covered include polynomial factorization, lattice reduction algorithms, applications in number theory, integer programming, provable security, lattice-based cryptography and complexity.The authors include many detailed motivations, explanations and examples, and the contributions are largely self-contained. The book will be of value to a wide range of researchers and graduate students working in related fields of theoretical computer science and mathematics.