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Mathematics of Computation

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Computing division polynomials

Author: James McKee
Journal: Math. Comp. 63 (1994), 767-771
MSC: Primary 11Y16; Secondary 11G05, 11Y55, 11Y99
MathSciNet review: 1248973
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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
  • [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
  • [4] H. Weber, Lehrbuch der Algebra. III, 3rd ed., Chelsea, New York, 1961.

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Article copyright: © Copyright 1994 American Mathematical Society