Abstract
According to some recent implementation reports on Ate–based pairings such as optimal ate pairing with Barreto–Naehrig curve whose embedding degree is 12, sparse multiplication accelerates Miller’s loop calculation in a pairing calculation. Especially, 7–sparse multiplication is available when the implementation uses affine coordinates, where 7–sparse means that the multiplicand or multiplier has 7 zeros among 12 coefficients. This paper extends it to pseudo 8–sparse multiplication. Then, some experimental results together with theoretic calculation costs are shown in order to evaluate its efficiency.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Lee, E., Lee, H.-S., Park, C.-M.: Efficient and generalized pairing computation on abelian varieties. IEEE Transactions on Information Theory 55(4), 1793–1803 (2009)
Vercauteren, F.: Optimal pairings. IEEE Transactions on Information Theory 56(1), 455–461 (2010)
Nogami, Y., Sakemi, Y., Kato, H., Akane, M., Morikawa, Y.: Integer Variable χ-based Cross Twisted Ate Pairing and Its Optimization for Barreto-Naehrig Curve. IEICE Transactions on Fundamentals of Electronics 2009(8), 1859–1867 (2009)
Aranha, D.F., Karabina, K., Longa, P., Gebotys, C.H., López, J.: Faster explicit formulas for computing pairings over ordinary curves. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 48–68. Springer, Heidelberg (2011)
Grewal, G., Azarderakhsh, R., Longa, P., Hu, S., Jao, D.: Efficient Implementation of Bilinear Pairings on ARM Processors. Cryptology ePrint Archive, Vol. 2012:408 (2012)
Barreto, P.S.L.M., Naehrig, M.: Pairing-Friendly Elliptic Curves of Prime Order. In: Preneel, B., Tavares, S. (eds.) SAC 2005. LNCS, vol. 3897, pp. 319–331. Springer, Heidelberg (2006)
Freeman, D., Scott, M., Teske, E.: A Taxonomy of Pairing-Friendly Elliptic Curves. Journal of Cryptology 23, 224–280 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Mori, Y., Akagi, S., Nogami, Y., Shirase, M. (2014). Pseudo 8–Sparse Multiplication for Efficient Ate–Based Pairing on Barreto–Naehrig Curve. In: Cao, Z., Zhang, F. (eds) Pairing-Based Cryptography – Pairing 2013. Pairing 2013. Lecture Notes in Computer Science, vol 8365. Springer, Cham. https://doi.org/10.1007/978-3-319-04873-4_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-04873-4_11
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-04872-7
Online ISBN: 978-3-319-04873-4
eBook Packages: Computer ScienceComputer Science (R0)