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The LLL Algorithm

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Cover of 'The LLL Algorithm'

Table of Contents

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    Book Overview
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    Chapter 1 The History of the LLL-Algorithm
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    Chapter 2 Hermite’s Constant and Lattice Algorithms
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    Chapter 3 Probabilistic Analyses of Lattice Reduction Algorithms
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    Chapter 4 Progress on LLL and Lattice Reduction
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    Chapter 5 Floating-Point LLL: Theoretical and Practical Aspects
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    Chapter 6 LLL: A Tool for Effective Diophantine Approximation
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    Chapter 7 Selected Applications of LLL in Number Theory
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    Chapter 8 The van Hoeij Algorithm for Factoring Polynomials
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    Chapter 9 The LLL Algorithm and Integer Programming
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    Chapter 10 Using LLL-Reduction for Solving RSA and Factorization Problems
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    Chapter 11 Practical Lattice-Based Cryptography: NTRUEncrypt and NTRUSign
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    Chapter 12 The Geometry of Provable Security: Some Proofs of Security in Which Lattices Make a Surprise Appearance
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    Chapter 13 Cryptographic Functions from Worst-Case Complexity Assumptions
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    Chapter 14 Inapproximability Results for Computational Problems on Lattices
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    Chapter 15 On the Complexity of Lattice Problems with Polynomial Approximation Factors
Attention for Chapter 4: Progress on LLL and Lattice Reduction
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