Lattice Basis Reduction

Lattice Basis Reduction

by Murray R. Bremner
Released August 2011
Publisher(s): CRC Press
ISBN: 9781439807040

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Book description

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 i

Table of contents

  1. Front Cover (1/2)
  2. Front Cover (2/2)
  3. Contents
  4. List of Figures
  5. Preface
  6. About the Author
  7. 1. Introduction to Lattices (1/4)
  8. 1. Introduction to Lattices (2/4)
  9. 1. Introduction to Lattices (3/4)
  10. 1. Introduction to Lattices (4/4)
  11. 2. Two-Dimensional Lattices (1/4)
  12. 2. Two-Dimensional Lattices (2/4)
  13. 2. Two-Dimensional Lattices (3/4)
  14. 2. Two-Dimensional Lattices (4/4)
  15. 3. Gram-Schmidt Orthogonalization (1/3)
  16. 3. Gram-Schmidt Orthogonalization (2/3)
  17. 3. Gram-Schmidt Orthogonalization (3/3)
  18. 4. The LLL Algorithm (1/7)
  19. 4. The LLL Algorithm (2/7)
  20. 4. The LLL Algorithm (3/7)
  21. 4. The LLL Algorithm (4/7)
  22. 4. The LLL Algorithm (5/7)
  23. 4. The LLL Algorithm (6/7)
  24. 4. The LLL Algorithm (7/7)
  25. 5. Deep Insertions (1/4)
  26. 5. Deep Insertions (2/4)
  27. 5. Deep Insertions (3/4)
  28. 5. Deep Insertions (4/4)
  29. 6. Linearly Dependent Vectors (1/3)
  30. 6. Linearly Dependent Vectors (2/3)
  31. 6. Linearly Dependent Vectors (3/3)
  32. 7. The Knapsack Problem (1/4)
  33. 7. The Knapsack Problem (2/4)
  34. 7. The Knapsack Problem (3/4)
  35. 7. The Knapsack Problem (4/4)
  36. 8. Coppersmith's Algorithm (1/3)
  37. 8. Coppersmith's Algorithm (2/3)
  38. 8. Coppersmith's Algorithm (3/3)
  39. 9. Diophantine Approximation (1/2)
  40. 9. Diophantine Approximation (2/2)
  41. 10. The Fincke-Pohst Algorithm (1/5)
  42. 10. The Fincke-Pohst Algorithm (2/5)
  43. 10. The Fincke-Pohst Algorithm (3/5)
  44. 10. The Fincke-Pohst Algorithm (4/5)
  45. 10. The Fincke-Pohst Algorithm (5/5)
  46. 11. Kannan's Algorithm (1/4)
  47. 11. Kannan's Algorithm (2/4)
  48. 11. Kannan's Algorithm (3/4)
  49. 11. Kannan's Algorithm (4/4)
  50. 12. Schnorr's Algorithm (1/3)
  51. 12. Schnorr's Algorithm (2/3)
  52. 12. Schnorr's Algorithm (3/3)
  53. 13. NP-Completeness (1/3)
  54. 13. NP-Completeness (2/3)
  55. 13. NP-Completeness (3/3)
  56. 14. The Hermite Normal Form (1/8)
  57. 14. The Hermite Normal Form (2/8)
  58. 14. The Hermite Normal Form (3/8)
  59. 14. The Hermite Normal Form (4/8)
  60. 14. The Hermite Normal Form (5/8)
  61. 14. The Hermite Normal Form (6/8)
  62. 14. The Hermite Normal Form (7/8)
  63. 14. The Hermite Normal Form (8/8)
  64. 15. Polynomial Factorization (1/8)
  65. 15. Polynomial Factorization (2/8)
  66. 15. Polynomial Factorization (3/8)
  67. 15. Polynomial Factorization (4/8)
  68. 15. Polynomial Factorization (5/8)
  69. 15. Polynomial Factorization (6/8)
  70. 15. Polynomial Factorization (7/8)
  71. 15. Polynomial Factorization (8/8)
  72. Bibliography (1/3)
  73. Bibliography (2/3)
  74. Bibliography (3/3)

Product information

  • Title: Lattice Basis Reduction
  • Author(s): Murray R. Bremner
  • Release date: August 2011
  • Publisher(s): CRC Press
  • ISBN: 9781439807040