Pacific Journal of Mathematics

Primality of the number of points on an elliptic curve over a finite field.

Neal Koblitz
Source: Pacific J. Math. Volume 131, Number 1 (1988), 157-165.
First Page: Show Hide
Primary Subjects: 11G05
Secondary Subjects: 11Y40, 14G15
Full-text: Open access
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.pjm/1102690074
Zentralblatt MATH identifier: 0608.10010
Mathematical Reviews number (MathSciNet): MR917870

References

[I] J. Brillhart, D. H. Lehmer, J. L. Selfridge, B. Tuckerman and S. S. Wagstaff, Jr., Factorization of b" 1, b = 2,3,5,6,7,10,11,12 up to high powers, Amer. Math. Soc, 1983.
Mathematical Reviews (MathSciNet): MR84k:10005
[2] W. Bosma, Primality testing using elliptic curves, Report 85-12, Mathematisch Instituut, Universiteit van Amsterdam, 1985.
[3] R. Gupta and M. R. P. Murty, Primitivepoints on elliptic curves,Compositio Math., 58 (1986), 13-44.
Mathematical Reviews (MathSciNet): MR87h:11050
Zentralblatt MATH: 0598.14018
[4] G. H. Hardy and J. E. Littlewood, Some problems of'Partitio numerorum'; III: on the expression of a number as a sum of primes, Acta Math.,44 (1923), 1-70.
Zentralblatt MATH: JFM 48.0143.04
[5] N. Koblitz, Introduction to Elliptic Curvesand Modular Forms, Springer-Verlag, New York, 1984.
Mathematical Reviews (MathSciNet): MR86c:11040
Zentralblatt MATH: 0553.10019
[6] N. Koblitz, Elliptic curvecryptosystems, Math, of Computation,48 (1987), 203-209.
Mathematical Reviews (MathSciNet): MR88b:94017
Zentralblatt MATH: 0622.94015
[7] S. Lang, Elliptic Curves: Diophantine Analysis, Springer-Verlag, New York, 1978.
Mathematical Reviews (MathSciNet): MR81b:10009
Zentralblatt MATH: 0388.10001
[8] S. Lang and J. Tate, eds., The Collected Papers of Emil Artin, Addison-Wesley, Reading, Mass., 1965.
Mathematical Reviews (MathSciNet): MR33:5416
[9] S. Lang and H. Trotter, Primitivepoints on ellipticcurves,Bull. Amer. Math. Soc, 83 (1977), 289-292.
Mathematical Reviews (MathSciNet): MR55:308
Zentralblatt MATH: 0345.12008
[10] H. W. Lenstra, Jr., Elliptic curves and number-theoretic algorithms, Report 86-19, Mathematisch Instituut, Universiteit van Amsterdam, 1986.
[II] V. S. Miller, Use of ellipticcurvesin cryptography, Abstracts for Crypto '85.
[12] R. Schoof, Elliptic curvesoverfinite fields and the computationof square roots mod/?, Math, of Computation, 44 (1985), 483-494 and 175-182.
Mathematical Reviews (MathSciNet): MR86e:11122
Zentralblatt MATH: 0579.14025
[13] E. Seah and H. C. Williams, Some primes of the form (an - l)/(a - 1), Math, of Comput., 33 (1979), 1337-1342.
Mathematical Reviews (MathSciNet): MR80g:10014
Zentralblatt MATH: 0417.10004
[14] J.-P. Serre, Proprietes galoisiennes des points d^ordre fini des courbes elliptiques, Inventiones Math., 15 (1972),259-331.
Mathematical Reviews (MathSciNet): MR52:8126
Zentralblatt MATH: 0235.14012
[15] D. Shanks, Solved and Unsolved Problems in Number Theory, 3rd ed., Chelsea Publ. Co., New York, 1985.
Mathematical Reviews (MathSciNet): MR86j:11001
Zentralblatt MATH: 0116.03002
[16] R. Spira, The complex sum of divisors, Amer. Math. Monthly,68 (1961), 120-124.
Mathematical Reviews (MathSciNet): MR26:6101
Zentralblatt MATH: 0102.03703

2013 © Pacific Journal of Mathematics

Pacific Journal of Mathematics

Pacific Journal of Mathematics

Turn MathJax Off
What is MathJax?