Efficient Arithmetic on Koblitz Curves

Designs, Codes, and Cryptography

Volumn 19, Issue 2-3, 2000, Pages 195-249

  Solinas, Jerome A ^a,b  

^a NATIONAL SECURITY AGENCY   (United States)

^b UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Elliptic curves; Exponentiation; Public key cryptography

Indexed keywords

EID: 0010029876     PISSN: 09251022     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008306223194     Document Type: Article

References (24)

1. D. W. Ash, I. F. Blake, and S. Vanstone, Low complexity normal bases, Discrete Applied Math., Vol. 25 (1989) pp. 191-210.
2. E. Berlekamp, Algebraic Coding Theory, Aegean Park Press (1984).
3. R. Gallant, R. Lambert, and S. Vanstone, Improving the parallelized Pollard lambda search on binary anomalous curves, Math. Comp., posted on May 19, 1999, PII: S-0025-5718(99)01119-9 (to appear in print).
4. D. Gordon, A survey of fast exponentiation methods, J. Algs., Vol. 27 (1998) pp. 129-146.
5. C. Günther and A. Stein (to appear).
6. Institute of Electrical and Electronics Engineers, IEEE P1363: Standard Specifications for Public-Key Cryptography, Draft 10 (1999).
7. t), J. Soc. Electron. Comm. (Japan), Vol. 44 (1986) pp. 31-36.
8. D. Johnson and A. Menezes, The Elliptic Curve Digital Signature Algorithm (ECDSA), Univ. of Waterloo (1999) http://cacr.math.waterloo.ca
9. D. E. Knuth, Seminumerical Algorithms, Addison-Wesley (1981).
10. N. Koblitz. CM curves with good cryptographic properties, Proc. Crypto '91, Springer-Verlag(1992)pp.279-287.
11. N. Koblitz, A Course of Number Theory and Cryptography, 2nd ed., Springer-Verlag (1994).
12. N. Koblitz, An elliptic curve implementation of the Finite Field Digital Signature Algorithm, Proc. Crypto '98, Springer-Verlag (1998) pp. 327-337.
13. K. Koyama and Y. Tsuruoka, Speeding up elliptic cryptosystems by using a signed binary window method, Proc. Crypto '92, Springer-Verlag (1993) pp. 345-357.
14. m) without precomputation (preprint).
15. F. Morain and J. Olivos, Speeding up the computations on an elliptic curve using addition-subtraction chains, Inform. Theor. Appl., Vol. 24 (1990) pp. 531-543.
16. A. Menezes, T. Okamoto and S. Vanstone, Reducing elliptic curve logarithms to logarithms in a finite field, IEEE Transactions on Information Theory, Vol. 39 (1993) pp. 1639-1646.
17. A. Menezes, P. van Oorschot, and S. Vanstone, Handbook of Applied Cryptography, CRC Press (1997).
18. W. Meier and O. Staffelbach, Efficient multiplication on certain non-supersingular elliptic curves, Proc. Crypto '92, Springer-Verlag (1993) pp. 333-344.
19. V Müller, Fast multiplication on elliptic curves over small fields of characteristic two, J. Crypt., Vol. 11 (1998) pp. 219-234.
20. P. van Oorschot and M. Weiner, Parallel collision search with cryptanalytic applications, J. Crypt., Vol. 12 (1999) pp. 1-28.
21. n), http://grouper.ieee.org/ groups/1363/contributions/hp.ps
22. J. Silverman, The Arithmetic of Elliptic Curves, Springer-Verlag (1986).
23. I. Stewart and D. Tall, Algebraic Number Theory, 2nd. ed., Chapman and Hall (1987).
24. M. Weiner and R. Zuccherato, Faster attacks on elliptic curve cryptosystems, Selected Areas in Cryptography, Springer-Verlag (1999) pp. 190-200.