Cyclicity statistics for elliptic curves over finite fields

Finite Fields and their Applications

Volumn 5, Issue 1, 1999, Pages 13-25

  Vladut S G ^a,b  

^a INSTITUTE FOR INFORMATION TRANSMISSION PROBLEMS   (Russian Federation)

^b AIX MARSEILLE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032621280     PISSN: 10715797     EISSN: None     Source Type: Journal    
DOI: 10.1006/ffta.1998.0225     Document Type: Article

References (18)

1. 1. H. Cohen, "A Course in Computational Number Theory," Graduate Texts in Math., Vol. 138, Springer-Verlag, Berlin, 1993.
2. 2. H. Cohen and H. W. Lenstra, Heuristics on class groups of number fields, in Lecture Notes in Math., Vol. 1068, pp. 33-62, Springer-Verlag, Berlin, 1984.
3. 3. E. Friedman and L. C. Washington, On the distribution of divisor class groups of curves over a finite field, in "Théorie des nombres" (Jean-Marie De Koninck and Claude Levesque, de Gruyter, Eds.), pp. 227-239, Berlin, 1989.
4. 4. E. W. Howe, On the group orders of elliptic curves over finite fields, Compositio Math. 85 (1993), 229-247.
5. 5. R. Gupta and R. Murty, Primitive points on elliptic curves, Compositio Math. 58(1986), 13-44.
6. 6. R. Gupta and R. Murty, Cyclicity and generation of points mod p on elliptic curves, Invent. Math. 101(1990), 225-235.
7. 7. S. Lang, "Elliptic Functions," Addison-Wesley, Reading, MA, 1973.
8. 8. S. Lang and H. Trotter, Primitive points on elliptic curves, Bull. Amer. Math. Soc. 83, No. 2 (1977), 289-292.
9. 9. H. W. Lenstra, Factoring integers with elliptic curves. Ann. of Math. 126(1987), 649-673.
10. 10. A. J. Menezes, "Elliptic Curve Public Key Cryptosystems," Kluwer Academic, Dordrecht, 1993.
11. 11. H.-G. Rück, Abelian surfaces and Jacobian varieties over finite fields, Compositio Math. 76(1990), 351-360.
12. 12. R. Schoof, Nonsingular plane cubic curves over finite fields, J. Combin. Theory Ser. A 46 (1987), 183-211.
13. 13. J.-P. Serre, Résumé du cours 1977-78, in "Collected Papers," Vol. 3, pp. 465-68, Springer-Verlag, Berlin, 1986.
14. 14. I. E. Shparlinski, "Computational and Algorithmic Problems in Finite Fields," Kluwer Academic, Dordrecht, 1992.
15. 15. J. Silverman, "The Arithmetic of Elliptic Curves," Graduate Texts in Math. Vol. 106, Springer-Verlag, Berlin, 1986.
16. 16. M. Tsfasman, On the structure of the group for elliptic curves over finite fields, in "Proc. of All-Union Algebraic Conference, Tbilisi, 1985."
17. 17. M. Tsfasman and S. Vladuts, "Algebraic-Geometric Codes," Kluwer Academic, Dordrecht, 1991.
18. 18. W. C. Waterhouse, Abelian varieties over finite fields, Ann. Sci. École Norm. Sup. (4) 2 (1969), 521-560.