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The Tate Pairing Via Elliptic Nets

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Pairing-Based Cryptography – Pairing 2007 (Pairing 2007)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4575))

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Abstract

We derive a new algorithm for computing the Tate pairing on an elliptic curve over a finite field. The algorithm uses a generalisation of elliptic divisibility sequences known as elliptic nets, which are maps from ℤn to a ring that satisfy a certain recurrence relation. We explain how an elliptic net is associated to an elliptic curve and reflects its group structure. Then we give a formula for the Tate pairing in terms of values of the net. Using the recurrence relation we can calculate these values in linear time. Computing the Tate pairing is the bottleneck to efficient pairing-based cryptography. The new algorithm has time complexity comparable to Miller’s algorithm, and should yield to further optimisation.

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Authors and Affiliations

  1. Brown University, Providence, RI 02912, USA

    Katherine E. Stange

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  1. Katherine E. Stange
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Tsuyoshi Takagi Tatsuaki Okamoto Eiji Okamoto Takeshi Okamoto

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Stange, K.E. (2007). The Tate Pairing Via Elliptic Nets. In: Takagi, T., Okamoto, T., Okamoto, E., Okamoto, T. (eds) Pairing-Based Cryptography – Pairing 2007. Pairing 2007. Lecture Notes in Computer Science, vol 4575. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73489-5_19

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  • DOI: https://doi.org/10.1007/978-3-540-73489-5_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73488-8

  • Online ISBN: 978-3-540-73489-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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