The LLL Algorithm

Survey and Applications


ISBN: 978-3-642-02294-4 (Print) 978-3-642-02295-1 (Online)

Table of contents (15 chapters)

  1. Front Matter

    Pages I-XIV

  2. Chapter

    Pages 1-17

    The History of the LLL-Algorithm

  3. Chapter

    Pages 19-69

    Hermite’s Constant and Lattice Algorithms

  4. Chapter

    Pages 71-143

    Probabilistic Analyses of Lattice Reduction Algorithms

  5. Chapter

    Pages 145-178

    Progress on LLL and Lattice Reduction

  6. Chapter

    Pages 179-213

    Floating-Point LLL: Theoretical and Practical Aspects

  7. Chapter

    Pages 215-263

    LLL: A Tool for Effective Diophantine Approximation

  8. Chapter

    Pages 265-282

    Selected Applications of LLL in Number Theory

  9. Chapter

    Pages 283-291

    The van Hoeij Algorithm for Factoring Polynomials

  10. Chapter

    Pages 293-314

    The LLL Algorithm and Integer Programming

  11. Chapter

    Pages 315-348

    Using LLL-Reduction for Solving RSA and Factorization Problems

  12. Chapter

    Pages 349-390

    Practical Lattice-Based Cryptography: NTRUEncrypt and NTRUSign

  13. Chapter

    Pages 391-426

    The Geometry of Provable Security: Some Proofs of Security in Which Lattices Make a Surprise Appearance

  14. Chapter

    Pages 427-452

    Cryptographic Functions from Worst-Case Complexity Assumptions

  15. Chapter

    Pages 453-473

    Inapproximability Results for Computational Problems on Lattices

  16. Chapter

    Pages 475-496

    On the Complexity of Lattice Problems with Polynomial Approximation Factors

  17. Back Matter

    Pages 1-1