Handbook of elliptic and hyperelliptic curve cryptography
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Main Authors : | , , , , |
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Other Authors : | , |
Format : | Textbook |
Language : | anglais |
Title statement : | Handbook of elliptic and hyperelliptic curve cryptography / Roberto Avanzi, Christophe Doche, Tanja Lange, Kim Nguyen, and Frederik Vercauteren; Henri Cohen, Gerhard Frey [scientific editors] |
Published : |
Boca Raton (Fla.) [etc.] :
Chapman & Hall/CRC
, cop. 2006 |
Physical Description : | 1 vol. (XXXIV-808 p.) |
Series : | Discrete mathematics and its applications (Boca Raton. Print) |
Subjects : |
- 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