Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Computing division polynomials


Author: James McKee
Journal: Math. Comp. 63 (1994), 767-771
MSC: Primary 11Y16; Secondary 11G05, 11Y55, 11Y99
MathSciNet review: 1248973
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Recurrence relations for the coefficients of the nth division polynomial for elliptic curves are presented. These provide an algorithm for computing the general division polynomial without using polynomial multiplications; also a bound is given for the coefficients, and their general shape is revealed, with a means for computing the coefficients as explicit functions of n.


References [Enhancements On Off] (What's this?)

  • [1] Alfred V. Aho, John E. Hopcroft, and Jeffrey D. Ullman, The design and analysis of computer algorithms, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1975. Second printing; Addison-Wesley Series in Computer Science and Information Processing. MR 0413592 (54 #1706)
  • [2] R. Fricke, Die elliptischen Funktionen und ihre Anwendungen, Vol. 2, Teubner, Leipzig, 1922.
  • [3] Joseph H. Silverman, The arithmetic of elliptic curves, Graduate Texts in Mathematics, vol. 106, Springer-Verlag, New York, 1986. MR 817210 (87g:11070)
  • [4] H. Weber, Lehrbuch der Algebra. III, 3rd ed., Chelsea, New York, 1961.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 11Y16, 11G05, 11Y55, 11Y99

Retrieve articles in all journals with MSC: 11Y16, 11G05, 11Y55, 11Y99


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1994-1248973-7
PII: S 0025-5718(1994)1248973-7
Article copyright: © Copyright 1994 American Mathematical Society