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. |
Keyword(in Japanese) | (See Japanese page) |
Keyword(in English) | η_T pairing / Duursma-Lee algorithm / extension degree |
Paper # | IT2006-76,ISEC2006-131,WBS2006-73 |
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Committee | ISEC |
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Conference Date | 2007/3/8(1days) |
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Registration To | Information Security (ISEC) |
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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 |
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