Computing division polynomials
HTML articles powered by AMS MathViewer
- by James McKee PDF
- Math. Comp. 63 (1994), 767-771 Request permission
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
- Alfred V. Aho, John E. Hopcroft, and Jeffrey D. Ullman, The design and analysis of computer algorithms, Addison-Wesley Series in Computer Science and Information Processing, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1975. Second printing. MR 0413592 R. Fricke, Die elliptischen Funktionen und ihre Anwendungen, Vol. 2, Teubner, Leipzig, 1922.
- Joseph H. Silverman, The arithmetic of elliptic curves, Graduate Texts in Mathematics, vol. 106, Springer-Verlag, New York, 1986. MR 817210, DOI 10.1007/978-1-4757-1920-8 H. Weber, Lehrbuch der Algebra. III, 3rd ed., Chelsea, New York, 1961.
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Math. Comp. 63 (1994), 767-771
- MSC: Primary 11Y16; Secondary 11G05, 11Y55, 11Y99
- DOI: https://doi.org/10.1090/S0025-5718-1994-1248973-7
- MathSciNet review: 1248973