Lattice basis reduction : an introduction to the LLL algorithm and its applications
著者
書誌事項
Lattice basis reduction : an introduction to the LLL algorithm and its applications
（Monographs and textbooks in pure and applied mathematics, 300）
Chapman & Hall/CRC, c2012
- : hardback
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注記
Includes bibliographical references (p. 299-309) and index
内容説明・目次
内容説明
First developed in the early 1980s by Lenstra, Lenstra, and Lovasz, 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 factorization, and matrix canonical forms.
目次
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.
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