Elliptic Curves Factorization Method for p^2q(<Special Issue>"Algorithmic Number Theory and Its Applications, Part 1")

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  • 合成数 P^2Q の素因数分解に適した楕円曲線(<特集>数論アルゴリズムとその応用,その1)
  • 合成数P2Qの素因数分解に適した楕円曲線
  • ゴウセイスウ P2Q ノ ソインスウ ブンカイ ニ テキシタ ダエン キョクセン

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Abstract

In this paper we propose new methods for selecting elliptic curves suited for the factorization of a composite number p^2q. The elliptic curves are selected from the curves which are parametrized by Atkin and Morain's method or Suyama's method. We show that, with our methods, it is possible to select the elliptic curves whose orders are divisible by 24, 32 or 64 over F_q. We also show that, with a computer search, these curves exist with sufficiently large probability.

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