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

Katsuyuki Takashima
2002 Nihon Oyo Suri Gakkai ronbunshi  
. In this paper , we will present improvements in the secure genus 2 HEC ( hyperel − liptic curve ) cryptosystem construction by using the CM theory. More precisely , we describe algorithmic improvements to reduce the number of signi 丘cant digits necessary fQr the con − struction of class polynomials . In particular, the effectiveness of the " denomi 皿 ator guessing " method is esti 皿 ated heuristically and verified by experiments . In addition , a secure HEC cryptosystem parameter is described
more » ... . 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. 1 は じめ に
doi:10.11540/jsiamt.12.4_269 fatcat:fdqq546dynd7rnc5wumbfgo4oi