Universal ηT pairing algorithm over arbitrary extension degree (情報理論)
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概要
- 論文の詳細を見る
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.
- 社団法人電子情報通信学会の論文
- 2007-03-08
著者
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Okamoto Eiji
Graduate School Of Systems And Information Engineering University Of Tsukuba
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Takagi Tsuyoshi
Future Univ.‐hakodate Hakodate‐shi Jpn
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Takagi Tsuyoshi
School Of Systems Information Science Future University-hakodate
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Okamoto Eiji
Univ. Tsukuba Tsukuba‐shi Jpn
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SHIRASE Masaaki
School of Systems Information Science, Future University-Hakodate
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Shirase Masaaki
Future University-hakodate
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Okamoto Eiji
Graduate School Of Systems And Information Engineering Univ. Of Tsukuba
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Shirase Masaaki
School Of Systems Information Science Future University-hakodate
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