Improvements in the CM-method of genus 2 hyperelliptic curve cryptosystems(<Special Issue>"Algorithmic Number Theory and Its Applications, Part 1")

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  • 虚数乗法論を用いた種数2超楕円曲線暗号の効率的な構成法について(<特集>数論アルゴリズムとその応用,その1)
  • 虚数乗法論を用いた種数2超楕円曲線暗号の効率的な構成法について
  • キョスウ ジョウホウロン オ モチイタ シュスウ 2 チョウダエン キョクセン アンゴウ ノ コウリツテキ ナ コウセイホウ ニ ツイテ

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Abstract

In this paper, we will present improvements in the secure genus 2 HEC (hyperelliptic curve) cryptosystem construction by using the CM theory. More precisely, we describe algorithmic improvements to reduce the number of significant digits necessary for the construction of class polynomials. In particular, the effectiveness of the "denominator guessing" method is estimated heuristically and verified by experiments. In addition, a secure HEC cryptosystem parameter is described. As it arises from class polynomials of degree 40 (of a CM field whose class number is 20), the practicality of the CM-method is improved.

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