Abstract
In this paper we describe an efficient implementation of the Tate and Ate pairings using Barreto-Naehrig pairing-friendly curves, on both a standard PC and on a 32-bit smartcard. First we introduce a sub-family of such curves with a particularly simple representation. Next we consider the issues that arise in the efficient implemention of field arithmetic in \({{\mathbb{F}}_{p^{12}}}\), which is crucial to good performance. Various optimisations are suggested, including a novel approach to the ‘final exponentiation’, which is faster and requires less memory than the methods previously recommended.
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Devegili, A.J., Scott, M., Dahab, R. (2007). Implementing Cryptographic Pairings over Barreto-Naehrig Curves. 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_10
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DOI: https://doi.org/10.1007/978-3-540-73489-5_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73488-8
Online ISBN: 978-3-540-73489-5
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