Abstract
When performing a Tate pairing (or a derivative thereof) on an ordinary pairing-friendly elliptic curve, the computation can be looked at as having two stages, the Miller loop and the so-called final exponentiation. As a result of good progress being made to reduce the Miller loop component of the algorithm (particularly with the discovery of “truncated loop” pairings like the R-ate pairing [18]), the final exponentiation has become a more significant component of the overall calculation. Here we exploit the structure of pairing-friendly elliptic curves to reduce to a minimum the computation required for the final exponentiation.
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Scott, M., Benger, N., Charlemagne, M., Dominguez Perez, L.J., Kachisa, E.J. (2009). On the Final Exponentiation for Calculating Pairings on Ordinary Elliptic Curves. In: Shacham, H., Waters, B. (eds) Pairing-Based Cryptography – Pairing 2009. Pairing 2009. Lecture Notes in Computer Science, vol 5671. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03298-1_6
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DOI: https://doi.org/10.1007/978-3-642-03298-1_6
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