Elliptic Curves, 2nd Edition

Elliptic Curves, 2nd Edition

by Lawrence C. Washington
Released April 2008
Publisher(s): Chapman and Hall/CRC
ISBN: 9781420071474

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Book description

Like its bestselling predecessor, this second edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. It now includes new chapters on isogenies and hyperelliptic curves, a more complete treatment of the Tate-Lichtenbaum pairing, alternative coordinate systems and related computational issues, and Doud's analytic method for computing torsion on elliptic curves over Q. This edition also discusses how to perform computations with elliptic curves in several popular computer algebra systems. Basic exercises appear at the end of each chapter.

Table of contents

  1. Cover
  2. Title
  3. Copyright
  4. Preface
  5. Preface to the Second Edition
  6. Suggestions to the Reader
  7. Contents
  8. Chapter 1: Introduction (1/2)
  9. Chapter 1: Introduction (2/2)
  10. Chapter 2: The Basic Theory (1/14)
  11. Chapter 2: The Basic Theory (2/14)
  12. Chapter 2: The Basic Theory (3/14)
  13. Chapter 2: The Basic Theory (4/14)
  14. Chapter 2: The Basic Theory (5/14)
  15. Chapter 2: The Basic Theory (6/14)
  16. Chapter 2: The Basic Theory (7/14)
  17. Chapter 2: The Basic Theory (8/14)
  18. Chapter 2: The Basic Theory (9/14)
  19. Chapter 2: The Basic Theory (10/14)
  20. Chapter 2: The Basic Theory (11/14)
  21. Chapter 2: The Basic Theory (12/14)
  22. Chapter 2: The Basic Theory (13/14)
  23. Chapter 2: The Basic Theory (14/14)
  24. Chapter 3: Torsion Points (1/4)
  25. Chapter 3: Torsion Points (2/4)
  26. Chapter 3: Torsion Points (3/4)
  27. Chapter 3: Torsion Points (4/4)
  28. Chapter 4: Elliptic Curves over Finite Fields (1/10)
  29. Chapter 4: Elliptic Curves over Finite Fields (2/10)
  30. Chapter 4: Elliptic Curves over Finite Fields (3/10)
  31. Chapter 4: Elliptic Curves over Finite Fields (4/10)
  32. Chapter 4: Elliptic Curves over Finite Fields (5/10)
  33. Chapter 4: Elliptic Curves over Finite Fields (6/10)
  34. Chapter 4: Elliptic Curves over Finite Fields (7/10)
  35. Chapter 4: Elliptic Curves over Finite Fields (8/10)
  36. Chapter 4: Elliptic Curves over Finite Fields (9/10)
  37. Chapter 4: Elliptic Curves over Finite Fields (10/10)
  38. Chapter 5: The Discrete Logarithm Problem (1/6)
  39. Chapter 5: The Discrete Logarithm Problem (2/6)
  40. Chapter 5: The Discrete Logarithm Problem (3/6)
  41. Chapter 5: The Discrete Logarithm Problem (4/6)
  42. Chapter 5: The Discrete Logarithm Problem (5/6)
  43. Chapter 5: The Discrete Logarithm Problem (6/6)
  44. Chapter 6: Elliptic Curve Cryptography (1/4)
  45. Chapter 6: Elliptic Curve Cryptography (2/4)
  46. Chapter 6: Elliptic Curve Cryptography (3/4)
  47. Chapter 6: Elliptic Curve Cryptography (4/4)
  48. Chapter 7: Other Applications (1/2)
  49. Chapter 7: Other Applications (2/2)
  50. Chapter 8: Elliptic Curves over Q (1/12)
  51. Chapter 8: Elliptic Curves over Q (2/12)
  52. Chapter 8: Elliptic Curves over Q (3/12)
  53. Chapter 8: Elliptic Curves over Q (4/12)
  54. Chapter 8: Elliptic Curves over Q (5/12)
  55. Chapter 8: Elliptic Curves over Q (6/12)
  56. Chapter 8: Elliptic Curves over Q (7/12)
  57. Chapter 8: Elliptic Curves over Q (8/12)
  58. Chapter 8: Elliptic Curves over Q (9/12)
  59. Chapter 8: Elliptic Curves over Q (10/12)
  60. Chapter 8: Elliptic Curves over Q (11/12)
  61. Chapter 8: Elliptic Curves over Q (12/12)
  62. Chapter 9: Elliptic Curves over C (1/11)
  63. Chapter 9: Elliptic Curves over C (2/11)
  64. Chapter 9: Elliptic Curves over C (3/11)
  65. Chapter 9: Elliptic Curves over C (4/11)
  66. Chapter 9: Elliptic Curves over C (5/11)
  67. Chapter 9: Elliptic Curves over C (6/11)
  68. Chapter 9: Elliptic Curves over C (7/11)
  69. Chapter 9: Elliptic Curves over C (8/11)
  70. Chapter 9: Elliptic Curves over C (9/11)
  71. Chapter 9: Elliptic Curves over C (10/11)
  72. Chapter 9: Elliptic Curves over C (11/11)
  73. Chapter 10: Complex Multiplication (1/6)
  74. Chapter 10: Complex Multiplication (2/6)
  75. Chapter 10: Complex Multiplication (3/6)
  76. Chapter 10: Complex Multiplication (4/6)
  77. Chapter 10: Complex Multiplication (5/6)
  78. Chapter 10: Complex Multiplication (6/6)
  79. Chapter 11: Divisors (1/9)
  80. Chapter 11: Divisors (2/9)
  81. Chapter 11: Divisors (3/9)
  82. Chapter 11: Divisors (4/9)
  83. Chapter 11: Divisors (5/9)
  84. Chapter 11: Divisors (6/9)
  85. Chapter 11: Divisors (7/9)
  86. Chapter 11: Divisors (8/9)
  87. Chapter 11: Divisors (9/9)
  88. Chapter 12: Isogenies (1/6)
  89. Chapter 12: Isogenies (2/6)
  90. Chapter 12: Isogenies (3/6)
  91. Chapter 12: Isogenies (4/6)
  92. Chapter 12: Isogenies (5/6)
  93. Chapter 12: Isogenies (6/6)
  94. Chapter 13: Hyperelliptic Curves (1/5)
  95. Chapter 13: Hyperelliptic Curves (2/5)
  96. Chapter 13: Hyperelliptic Curves (3/5)
  97. Chapter 13: Hyperelliptic Curves (4/5)
  98. Chapter 13: Hyperelliptic Curves (5/5)
  99. Chapter 14: Zeta Functions (1/4)
  100. Chapter 14: Zeta Functions (2/4)
  101. Chapter 14: Zeta Functions (3/4)
  102. Chapter 14: Zeta Functions (4/4)
  103. Chapter 15: Fermat’s Last Theorem (1/6)
  104. Chapter 15: Fermat’s Last Theorem (2/6)
  105. Chapter 15: Fermat’s Last Theorem (3/6)
  106. Chapter 15: Fermat’s Last Theorem (4/6)
  107. Chapter 15: Fermat’s Last Theorem (5/6)
  108. Chapter 15: Fermat’s Last Theorem (6/6)
  109. Appendix A: Number Theory (1/2)
  110. Appendix A: Number Theory (2/2)
  111. Appendix B: Groups
  112. Appendix C: Fields (1/2)
  113. Appendix C: Fields (2/2)
  114. Appendix D: Computer Packages (1/2)
  115. Appendix D: Computer Packages (2/2)
  116. References (1/2)
  117. References (2/2)
  118. Index (1/2)
  119. Index (2/2)

Product information

  • Title: Elliptic Curves, 2nd Edition
  • Author(s): Lawrence C. Washington
  • Release date: April 2008
  • Publisher(s): Chapman and Hall/CRC
  • ISBN: 9781420071474