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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Computing division polynomials
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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.
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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