Abstract
In 2007, Stange proposed a novel method for computing the Tate pairing on an elliptic curve over a finite field. This method is based on elliptic nets, which are maps from ℤn to a ring and satisfy a certain recurrence relation. In the present paper, we explicitly give formulae based on elliptic nets for computing the following variants of the Tate pairing: the Ate, Ate i , R-Ate, and optimal pairings. We also discuss their efficiency by using some experimental results.
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Ogura, N., Kanayama, N., Uchiyama, S., Okamoto, E. (2011). Cryptographic Pairings Based on Elliptic Nets. In: Iwata, T., Nishigaki, M. (eds) Advances in Information and Computer Security. IWSEC 2011. Lecture Notes in Computer Science, vol 7038. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25141-2_5
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DOI: https://doi.org/10.1007/978-3-642-25141-2_5
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