Handbook of elliptic and hyperelliptic curve cryptography

Handbook of elliptic and hyperelliptic curve cryptography

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Détails bibliographiques
Auteurs principaux : Avanzi Roberto (Auteur), Doche Christophe (Auteur), Lange Tanja (Auteur), Nguyen Kim (Auteur), Vercauteren Frederik (Auteur)
Autres auteurs : Cohen Henri (Éditeur scientifique), Frey Gerhard (Éditeur scientifique)
Format : Manuel
Langue : anglais
Titre complet : Handbook of elliptic and hyperelliptic curve cryptography / Roberto Avanzi, Christophe Doche, Tanja Lange, Kim Nguyen, and Frederik Vercauteren; Henri Cohen, Gerhard Frey [scientific editors]
Publié : Boca Raton (Fla.) [etc.] : Chapman & Hall/CRC , cop. 2006
Description matérielle : 1 vol. (XXXIV-808 p.)
Collection : Discrete mathematics and its applications (Boca Raton. Print)
Sujets :
Courbes elliptiques > Guides pratiques
Cryptographie > Mathématiques > Guides pratiques
Automates mathématiques, Théorie des > Guides pratiques
  • 1. Introduction to public-key cryptography
  • I. Mathematical background
  • 2. Algebraic background
  • 3. Background on p-adic numbers
  • 4. Background on curves and jacobians
  • 5. Varieties over special fields
  • 6. Background on pairings
  • 7. Background on weil descent
  • 8. Cohomological background on point counting
  • II. Elementary arithmetic
  • 9. Exponentiation
  • 10. Integer arithmetic
  • 11. Finite field arithmetic
  • 12. Arithmetic of p-adic numbers
  • III. Arithmetic of curves
  • 13. Arithmetic of elliptic curves
  • 14. Arithmetic of hyperelliptic curves
  • 15. Arithmetic of special curves
  • 16. Implementation of pairings
  • IV. Point counting
  • 17. Point counting on elliptic and hyperelliptic curves
  • 18. Complex multiplication
  • V. Computation of discrete logarithms
  • 19. Generic algorithms for computing discrete logarithms
  • 20. Index calculus
  • 21. Index calculus for hyperelliptic curves
  • 22. Transfer of discrete logarithms
  • VI. Applications
  • 23. Algebraic realizations of DL systems
  • 24. Pairing-based cryptography
  • 25. Compositeness and primality testing - factoring
  • VII. Realization of discrete logarithm systems
  • 26. Fast arithmetic in hardware
  • 27 Smart cards
  • 28. Practical attacks on smart cards
  • 29. Mathematical countermeasures against side-channel attacks
  • 30. Random numbers - Generation and testing