| Description |
1 online resource (xvii, 316 pages) : illustrations |
| Series |
Pure and applied mathematics
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Monographs and textbooks in pure and applied mathematics |
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Monographs and textbooks in pure and applied mathematics.
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| Bibliography |
Includes bibliographical references and index. |
| Contents |
1. Introduction to lattices -- 2. Two-dimensional lattices -- 3. Gram-Schmidt orthogonalization -- 4. The LLL algorithm -- 5. Deep insertions -- 6. Linearly dependent vectors -- 7. The knapsack problem -- 8. Coppersmith's algorithm -- 9. Diophantine approximation -- 10. The Fincke-Pohst algorithm -- 11. Kannan's algorithm -- 12. Schnorr's algorithm -- 13. NP-completeness -- 14. The hermite normal form -- 15. Polynomial factorization. |
| Summary |
First developed in the early 1980s by Lenstra, Lenstra, and Lovász, the LLL algorithm was originally used to provide a polynomial-time algorithm for factoring polynomials with rational coefficients. It very quickly became an essential tool in integer linear programming problems and was later adapted for use in cryptanalysis. This book provides an introduction to the theory and applications of lattice basis reduction and the LLL algorithm. With numerous examples and suggested exercises, the text discusses various applications of lattice basis reduction to cryptography, number theory, polynomial. |
| Subject |
Lattice theory -- Textbooks.
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Data reduction -- Textbooks.
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Data reduction |
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Lattice theory |
| Genre |
Electronic books.
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Textbooks
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| Other Form: |
Print version: Bremner, Murray R. Lattice basis reduction. Boca Raton, FL : CRC Press, ©2012 9781439807026 (DLC) 2011032872 (OCoLC)587104256 |
| ISBN |
9781439807040 (electronic bk.) |
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1439807043 (electronic bk.) |
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(hardcover ; alk. paper) |
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(hardcover ; alk. paper) |
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