Lattice Basis Reduction: An Introduction to the LLL Algorithm and Its Applications
Author:   Murray R. Bremner
Publisher:   Taylor & Francis Ltd
ISBN:  

9781032921822


Pages:   334
Publication Date:   14 October 2024
Format:   Paperback
Availability:   In Print   Availability explained
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Lattice Basis Reduction: An Introduction to the LLL Algorithm and Its Applications


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Author:   Murray R. Bremner
Publisher:   Taylor & Francis Ltd
Imprint:   CRC Press
Weight:   0.616kg
ISBN:  

9781032921822


ISBN 10:   103292182
Pages:   334
Publication Date:   14 October 2024
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

Introduction to Lattices. Two-Dimensional Lattices. Gram-Schmidt Orthogonalization. The LLL Algorithm. Deep Insertions. Linearly Dependent Vectors. The Knapsack Problem. Coppersmith’s Algorithm. Diophantine Approximation. The Fincke-Pohst Algorithm. Kannan’s Algorithm. Schnorr’s Algorithm. NP-Completeness. The Hermite Normal Form. Polynomial Factorization.

Reviews

the book succeeds in making accessible to nonspecialists the area of lattice algorithms, which is remarkable because some of the most important results in the field are fairly recent. —M. Zimand, Computing Reviews, March 2012 This text is meant as a survey of lattice basis reduction at a level suitable for students and interested researchers with a solid background in undergraduate linear algebra. … The writing is clear and quite concise. —Zentralblatt MATH 1237


Author Information

Murray R. Bremner received a Bachelor of Science from the University of Saskatchewan in 1981, a Master of Computer Science from Concordia University in Montreal in 1984, and a Doctorate in Mathematics from Yale University in 1989. He spent one year as a Postdoctoral Fellow at the Mathematical Sciences Research Institute in Berkeley, and three years as an Assistant Professor in the Department of Mathematics at the University of Toronto. He returned to the Department of Mathematics and Statistics at the University of Saskatchewan in 1993 and was promoted to Professor in 2002. His research interests focus on the application of computational methods to problems in the theory of linear nonassociative algebras, and he has had more than 50 papers published or accepted by refereed journals in this area.

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