Abstract
The η T pairing on supersingular is one of the most efficient algorithms for computing the bilinear pairing [3]. The η T pairing defined over finite field \({\mathbb F}_{3^n}\) has embedding degree 6, so that it is particularly efficient for higher security with large extension degree n. Note that the explicit algorithm over \({\mathbb F}_{3^n}\) in [3] is designed just for \(n \equiv 1\ (\bmod \ 12)\), and it is relatively complicated to construct an explicit algorithm for \(n \not \equiv 1\ (\bmod \ 12)\). 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.
In this paper we construct an explicit algorithm for computing the 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 (\(\widetilde{\eta_T}\) 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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Shirase, M., Kawahara, Y., Takagi, T., Okamoto, E. (2007). Universal η T Pairing Algorithm over Arbitrary Extension Degree. In: Kim, S., Yung, M., Lee, HW. (eds) Information Security Applications. WISA 2007. Lecture Notes in Computer Science, vol 4867. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77535-5_1
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DOI: https://doi.org/10.1007/978-3-540-77535-5_1
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