Presentation 2007-03-15
Universal η_T Pairing Algorithm over Arbitrary Extension Degree
Masaaki SHIRASE, Tsuyoshi TAKAGI, Eiji OKAMOTO,
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Abstract(in English) The η_T pairing on supersingular is one of the most efficient algorithms for computing the bilinear pairing [2]. The η_T pairing defined over finite field F_<3n> has embedding degree 6, so that it is particularly efficient for higher security with large extension degree n. Note that the extension degree n cannot be freely selected due to several attacks, for examples, we can securely use only n=97, 163, 167, 193,239,313,353,.... It is better that we can select many n's to implement the η_T pairing, since n corresponds to security level of the η_T pairing. However, the explicit algorithm over F_<3n> in [2] is designed just for n≡1 (mod 12). It is relative complicated to construct an explicit algorithm for n≢1 (mod 12). because it causes several variations based on extension degree n and the curve parameters. In this paper we present an explicit algorithm for computing η_T pairing with arbitrary extension degree n. However, the algorithm should contain many branch conditions depending on n and the curve parameters, that is undesirable for implementers of the η_T pairing. This paper then proposes the universal η_T pairing (η_T^^~ pairing), which satisfies the bilinearity of pairing (compatible with Tate pairing) without any branches in the program, and is as efficient as the original one. Therefore the proposed universal η_T pairing is suitable for the implementation of various extension degrees n with higher security.
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Keyword(in English) η_T pairing / Duursma-Lee algorithm / extension degree
Paper # IT2006-76,ISEC2006-131,WBS2006-73
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Committee ISEC
Conference Date 2007/3/8(1days)
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Language ENG
Title (in Japanese) (See Japanese page)
Sub Title (in Japanese) (See Japanese page)
Title (in English) Universal η_T Pairing Algorithm over Arbitrary Extension Degree
Sub Title (in English)
Keyword(1) η_T pairing
Keyword(2) Duursma-Lee algorithm
Keyword(3) extension degree
1st Author's Name Masaaki SHIRASE
1st Author's Affiliation School of Systems Information Science, Future University-Hakodate()
2nd Author's Name Tsuyoshi TAKAGI
2nd Author's Affiliation School of Systems Information Science, Future University-Hakodate
3rd Author's Name Eiji OKAMOTO
3rd Author's Affiliation Graduate School of Systems and Information Engineering, University of Tsukuba
Date 2007-03-15
Paper # IT2006-76,ISEC2006-131,WBS2006-73
Volume (vol) vol.106
Number (no) 596
Page pp.pp.-
#Pages 6
Date of Issue