Efficient point multiplication for elliptic curves over special optimal extension fields

Kapitel in diesem Buch

1. I-VI I
2. Preface VII
3. Mathematics, cryptology, and technology IX
4. Table of contents XI
5. A survey on IQ cryptography 1
6. Algebraic groups and discrete logarithm 17
7. Fermat numbers, Wieferich and Wilson primes: computations and generalizations 29
8. How to distinguish hyperelliptic curves in even characteristic 49
9. Limitations of constructive Weil descent 59
10. On the security of a public-key cryptosystem 71
11. Optimizations for NTRU 77
12. The efficiency and security of a real quadratic field based key exchange protocol 89
13. Extending the binary gcd algorithms 113
14. Stochastic kleptography detection 137
15. An overview of the XTR public key system 151
16. A survey of IND-CCA secure public-key encryption schemes relative to factoring 181
17. Efficient point multiplication for elliptic curves over special optimal extension fields 197
18. Error-correcting codes and cryptography 209
19. Secret public key schemes 221
20. Index form surfaces and construction of elliptic curves over large finite fields 239
21. On the size of solutions of the inequality φ(ax + b) < φ(ax) 249
22. Security of DL-encryption and signatures against generic attacks—a survey 257
23. Square-root algorithms for the discrete logarithm problem (a survey) 283
24. Height functions on elliptic curves 303
25. List of participants 323
26. List of contributors 329