On Algorithms for Computing Order of Elliptic Curves over Finite Fields

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  • 有限体上の楕円曲線の位数計算アルゴリズム
  • ユウゲンタイ ジョウ ノ ダエン キョクセン ノ イスウ ケイサン アルゴリズム

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This paper surveys recent advances of algorithms for computing order or elliptic curves over finite fields. Let p be the characteristic of the base field of a given elliptic curve. Following a usual convention, we denote a primo different from p by l. Then, for fields of large characteristic, l-adic method known as the SEA algorithm is efficient. Whereas, p-adic method runs much faster for fields of small characteristic.

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