Presentation	2006-07-20 Square Root Calculation Algorithm over Type-II All One Polynomial Field Hidehiro KATOU, FENG Wang, Yasuyuki NOGAMI, Yoshitaka MORIKAWA,
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Abstract(in English)	The authors proposes a square root (SQRT) algorithm in F_ (m=r_0r_1…r_2^d, r_i: odd prime, d>0: integer). We compute the inverse SQRT in F_ using MW-ST algorithm. Then the Frobenius mappings with an addition chain are adopted for this SQRT algorithm, in which a lot of computations in a given extension field F_ are also reduce to those in a proper sub field by the norm computations. Those reductions of the field degree increases efficiency in the SQRT implementation. More specifically the Smart algorithm and proposed algorithm in F_, for example, were implemented on a Pentium4 (3.8FHz) computer using the C++ programming language and NTL Library. The computer simulations showed that, on average, the proposed algoithm accelerates the SQRT computation by 3 times in F_, compared to the Smart algorithm.
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Keyword(in English)	Elliptic curve / Square root calculation
Paper #	ISEC2006-10,SITE2006-7
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Committee	SITE
Conference Date	2006/7/13(1days)
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Registration To	Social Implications of Technology and Information Ethics (SITE)
Language	JPN
Title (in Japanese)	(See Japanese page)
Sub Title (in Japanese)	(See Japanese page)
Title (in English)	Square Root Calculation Algorithm over Type-II All One Polynomial Field
Sub Title (in English)
Keyword(1)	Elliptic curve
Keyword(2)	Square root calculation
1st Author's Name	Hidehiro KATOU
1st Author's Affiliation	Graduate School of Natural Science and Technology, Okayama University()
2nd Author's Name	FENG Wang
2nd Author's Affiliation	/ Graduate School of Natural Science and Technology, Okayama University
3rd Author's Name	Yasuyuki NOGAMI
3rd Author's Affiliation	Graduate School of Natural Science and Technology, Okayama University
4th Author's Name	Yoshitaka MORIKAWA
4th Author's Affiliation
Date	2006-07-20
Paper #	ISEC2006-10,SITE2006-7
Volume (vol)	vol.106
Number (no)	174
Page	pp.pp.-
#Pages	6
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