Use of Elliptic Curves in Cryptography

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 218 LNCS, Issue , 1986, Pages 417-426

  Miller, Victor S ^a  

^a IBM RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GEOMETRY;

COMPUTATIONAL POWER; ELLIPTIC CURVE; KEY EXCHANGE PROTOCOLS;

CRYPTOGRAPHY;

EID: 85015402934     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-39799-X_31     Document Type: Conference Paper

References (21)

1. Lang, Serge Elliptic Curves: Diophantine Analysis. Springer-Verlag New York, 1978.
2. Lenstra, H. W., Letter to A. M. Odlyzko.
3. Diffie, W. and Heilman M., New Directions in Cryptography. IEEE Trans. Inform. Theory. IT-22 (1976), 644-054.
4. Western, A. E. and Miller, J. C. P., Table of Indices and Primitive Roots, Royal Society Mathematical Tables, vol. 9, Cambridge Univ. Press, 1968.
5. Adleman, L. A subexponentiai algorithm for the discrete logarithm problem with applications to cryptography. Proc. 20th IEEE Found. Comp. Sc. Symp. (1979), 55-60.
6. Odlyzko, A. M., Discrete logarithms in finite fields and their cryptographic significance, preprint.
7. Silverman, J. Lower bound for the canonical height on elliptic curves. Duke Math. J. 48, 633-648 (1981).
8. Laurent, M., Minoration de la hauteur de Neron-Tate. Seminaire de Theorie does Noinbres, Paris 1981-82, 137-151, Birkhauser (1983).
9. Birch, B. J., Swinnerton-Dyer H. P. F.. Notes on Elliptic Curves I. J. reine u. angewandte Math., 212,7-25 (1963).
10. Birch, B. J., Swinnerton-Dyer, H. P. F. Notes on Elliptic Curves 2, J. reine u. angewandte Math., 218, 79-108 (1963).
11. Cassels, J. W. S.. Diophantine Equations with spccial reference to elliptic curves, J. London Math. Soc. 41, 193-291 (1966).
12. Mestre, J. -F., Courbcs elliptique, R et formule expticites. Seminaire de Theorie does Nombres, Paris 1981-82. 179-187. Birkhauser (1983).
13. Wiedemann, D., Solving sparse linear equations over finite fields, preprint.
14. Coppersmith, D., Odlyzko, A. M., and Schroeppel, R., Discrete logarithms in GF(p). IBM Research Report RC 10985 (1985).
15. Zimmer, H. G. On the difference of the Weil height and the Neron-Tate height. Math. Z. 147 (1976) 35-51.
16. Buhler, J., Gross, B., and Zagier, D., On the conjecture of Birch and Swinnerton-Dyer for an elliptic curve of rank 3, preprint.
17. Pohlig, S and Heilman, M., An improved algorithm for computing logarithms over GF(p) and its cryptgraphic significance, IEEE Inlorm. Theory IT-24 (1978). 106-110.
18. Pollard, J. M, Monte Carlo methods for index computation (mod p), Math. Comp. 32 (1978),918-924.
19. J Schoof, R. Elliptic Curves over finite fields and the computation of square roots mod p, Report 83-09. Math. Inst. Univ. v. Amsterdam (1983).
20. Fouvry, E., Theoreme de Brun-Titchmarsh; application au theoreme de Fermat. Invent. Math 79(1985). 383-407.
21. 2 + p). Math. Comp 42 (1984), 257-264.