Classes d'isomorphismes des courbes elliptiques supersingulières en caractéristique ≥ 3

Utilitas Mathematica

Volumn 52, Issue , 1997, Pages 241-253

  Morain, F ^a  

^a ÉCOLE POLYTECHNIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031283694     PISSN: 03153681     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (33)

1. A. O. L. ATKIN. The number of points on an elliptic curve modulo a prime. Draft, 1988.
2. A. O. L. ATKIN. The number of points on an elliptic curve modulo a prime (ii). Draft, 1992.
3. B. C. BERNDT AND R. J. EVANS. Sums of Gauss, Jacobi and Jacobsthal. J. Number Theory 11 (1979), 349-398.
4. B. J. BIRCH AND W. KUYK, Eds. Modular functions of one variable IV (1975), vol. 476 of Lecture Notes in Math., Springer. Proceedings International Summer School University of Antwerp, RUCA, July 17-Agust 3, 1972.
5. B. J. BIRCH AND W. KUYK, Eds. Modular functions of one variable IV (1975), vol. 476 of Lecture Notes in Math., Springer. Proceedings International Summer School University of Antwerp, RUCA, July 17-Agust 3, 1972.
6. H. DAVENPORT AND H. HASSE. Die Nullstellen der Kongruenzzetafunktionen in gewissen zyklischen Fällen. J. Reine Angew. Math. 172 (1935), 151-182.
7. M. DEURING. Die Typen der Multiplikatorenringe elliptischer Funktionenkörper. Abh. Math. Sem. Hamburg 14 (1941), 197-272.
8. R. J. EVANS. Determinations of Jacobsthal sums. Pacific J. Math. 110, 1 (1984), 49-58.
9. R. H. HUDSON AND K. S. WILLIAMS. Resolution of ambiguities in the evaluation of cubic and quartic Jacobsthal sums. Pacific J. Math. 99, 2 (1982), 379-386.
10. E. JACOBSTAHL. Über die Darstellung der Primzahlen der Form 4n + 1 als Summe zweier quadrate. J. Reine Angew. Math. 132 (1907), 238-245.
11. S. A. KATRE. Jacobsthal sums in terms of quadratic partitions of a prime. In Number Theory (1985), K. Alladi, Ed., vol. 1122 of Lecture Notes in Math., Springer-Verlag, pp. 153-162. Proceedings of the 4th Matscience Conference held at Ootacamund, India, January 5-10, 1984.
12. S. A. KATRE. Jacobsthal sums in terms of quadratic partitions of a prime. In Number Theory (1985), K. Alladi, Ed., vol. 1122 of Lecture Notes in Math., Springer-Verlag, pp. 153-162. Proceedings of the 4th Matscience Conference held at Ootacamund, India, January 5-10, 1984.
13. S. A. KATRE AND A. R. RAJWADE. Jacobsthal sums of prime order. Indian J. Pure Appl. Math. 17, 12 (Dec. 1986), 1345-1362.
14. S. A. KATRE AND A. R. RAJWADE. Resolution of sign ambiguity in the determination of the cyclotomic numbers of order 4 and the corresponding Jacobstahal sum. Math. Scand. 60 (1987), 52-62.
15. 2 mod p. Pacific J. Math. 5 (1955), 103-18.
16. n using Couveignes's algorithm. Research Report LIX/RR/95/09, École Polytechnique-LIX, Sept. 1995. An improved version is being submitted.
17. R. LERCIER AND F. MORAIN. Counting the number of points on elliptic curves over finite fields: strategies and performances. In Advances in Cryptology - EUROCRYPT '95; (1995), L. C. Guillou and J.-J. Quisquater, Eds., vol. 921 of Lecture Notes in Comput. Sci., pp. 79-94. International Conference on the Theory and Application of Cryptographic Techniques, Saint.-Malo, France, May 1995, Proceedings.
18. R. LERCIER AND F. MORAIN. Counting the number of points on elliptic curves over finite fields: strategies and performances. In Advances in Cryptology - EUROCRYPT '95; (1995), L. C. Guillou and J.-J. Quisquater, Eds., vol. 921 of Lecture Notes in Comput. Sci., pp. 79-94. International Conference on the Theory and Application of Cryptographic Techniques, Saint.-Malo, France, May 1995, Proceedings.
19. R. LIDL AND H. NIEDERREITER. Finite fields. No. 20 in Encyclopedia of mathematics and its applications. Reading: Addison-Wesley, 1983.
20. R. MCELIECE. Finite, fields for computer scientist and engineers. Kluwer international series in engineering and computer science. Kluwer Academic Publishers, 1988.
21. A. MENEZES AND S. VANSTONE. Isomorphism classes of elliptic curves over finite fields of characteristic 2. Utilitas Math. 38 (1990), 135-153.
22. A. J. MENEZES. Elliptic curve public key cryptosystems. Kluwer Academic Publishers, 1993.
23. J.-F. MESTRE. La méthode des graphes. Exemples et applications. In Proc. of the International Conference on class numbers und fundamental units of algebraic number fields (Nagoya, 1986), Nagoya Univ., pp. 217-242. Katata (Japan).
24. J.-F. MESTRE AND J. OESTERLÉ. La méthode des graphes. Preprint, 19??
25. F. MORAIN. Calcul du nombre de points sur une courbe elliptique dans un corps fini: aspects algorithmiques. J. Théor. Nombres Bonleaux 7 (1995), 255-282.
26. R. SCHOOF. Nonsingular plane cubic curves over finite fields. J. Combin. Theory Ser. A 46 (1987), 183-211.
27. R. SCHOOF. Counting points on elliptic curves over finite fields. J. Théor. Nombres Bordeaux 7 (1995), 219-254.
28. M. A. SHOKROLLAHI. Generation of optimal bilinear multiplication algorithms: theory and implementation. Tech. Rep. 8575-CS, Universität Bonn, Dec. 1992.
29. J. H. SILVERMAN. The arithmetic of elliptic curves, vol. 106 of Graduate Texts in Mathematics. Springer, 1986.
30. T. STORER. Cyclotomy and difference sets. Markham Publ. Co., Chicago, 1967.
31. R. G. SWAN. Factorization of polynomials over finite fields. Pacific J. Math. 12 (1962), 1099-1106.
32. E. WATERHOUSE. Abelian varieties over finite fields. Ann. Sci. École Norm. Sup. 2 (1969), 521-560.
33. J. WOLFMANN. Nombre de points rationnels de courbes algébriques sur des corps finis associées à des codes cycliques. C. R. Acad. Sci. Paris Sér. I Math. 305 (1987), 345-348.