Presentation	2000/7/18 ISEC2000-33 On Counting the Rational Points on Hyperelliptic Curves of genus 2 over Finite Fields Hisayoshi SATO, Masashi TAKAHASHI,
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Abstract(in English)	When constructing secure hyperelliptic curve cryptosystems, counting the number of rational points on hyperelliptic curve and its jacobian variety defined over finite fields is one of the most important problem. In this paper we propose an effcient method of counting the number of rational points. In this method, we improved the formula for the coefficients (modulo characteristic of defined fields) of the numerator of congruent zeta function which are related to the number of rational points on the Jacobian varieties, in order to implement efficiently. Moreover we report on some experimental results.
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Keyword(in English)	Public key cryptography / Hyperelliptic curve / Discrete logarithm problem / Jacobian variety
Paper #	ISEC2000-33
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Committee	ISEC
Conference Date	2000/7/18(1days)
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Registration To	Information Security (ISEC)
Language	ENG
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Title (in English)	ISEC2000-33 On Counting the Rational Points on Hyperelliptic Curves of genus 2 over Finite Fields
Sub Title (in English)
Keyword(1)	Public key cryptography
Keyword(2)	Hyperelliptic curve
Keyword(3)	Discrete logarithm problem
Keyword(4)	Jacobian variety
1st Author's Name	Hisayoshi SATO
1st Author's Affiliation	Systems Development Laboratory, Hitachi, Ltd.()
2nd Author's Name	Masashi TAKAHASHI
2nd Author's Affiliation	Systems Development Laboratory, Hitachi, Ltd.
Date	2000/7/18
Paper #	ISEC2000-33
Volume (vol)	vol.100
Number (no)	213
Page	pp.pp.-
#Pages	8
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