The LLL Algorithm

1. The History of the LLL-Algorithm
Ionica Smeets, Arjen Lenstra, Hendrik Lenstra, László Lovász, Peter Emde Boas

2. Hermite’s Constant and Lattice Algorithms
Phong Q. Nguyen

3. Probabilistic Analyses of Lattice Reduction Algorithms
Brigitte Vallée, Antonio Vera

4. Progress on LLL and Lattice Reduction
Claus Peter Schnorr

5. Floating-Point LLL: Theoretical and Practical Aspects
Damien Stehlé

6. LLL: A Tool for Effective Diophantine Approximation
Guillaume Hanrot

7. Selected Applications of LLL in Number Theory
Denis Simon

8. The van Hoeij Algorithm for Factoring Polynomials
Jürgen Klüners

9. The LLL Algorithm and Integer Programming
Karen Aardal, Friedrich Eisenbrand

10. Using LLL-Reduction for Solving RSA and Factorization Problems
Alexander May

11. Practical Lattice-Based Cryptography: NTRUEncrypt and NTRUSign
Jeff Hoffstein, Nick Howgrave-Graham, Jill Pipher, William Whyte

12. The Geometry of Provable Security: Some Proofs of Security in Which Lattices Make a Surprise Appearance
Craig Gentry

13. Cryptographic Functions from Worst-Case Complexity Assumptions
Daniele Micciancio

14. Inapproximability Results for Computational Problems on Lattices
Subhash Khot

15. On the Complexity of Lattice Problems with Polynomial Approximation Factors
Oded Regev

Avainsanat: Computer Science, Data Structures, Cryptology and Information Theory, Algorithms, Algorithm Analysis and Problem Complexity, Discrete Mathematics in Computer Science, Number Theory, Optimization