Abstract
We describe a high-speed software implementation of the η T pairing over binary supersingular curves at the 128-bit security level. This implementation explores two types of parallelism found in modern multi-core platforms: vector instructions and multiprocessing. We first introduce novel techniques for implementing arithmetic in binary fields with vector instructions. We then devise a new parallelization of Miller’s Algorithm to compute pairings. This parallelization provides an algorithm for pairing computation without increasing storage costs significantly. The combination of these acceleration techniques produce serial timings at least 24% faster and parallel timings 66% faster than the best previous result in an Intel Core platform, establishing a new state-of-the-art implementation of this pairing instantiation in this platform.
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References
Barreto, P.S.L.M., Gailbraith, S., Ó hÉigeartaigh, C., Scott, M.: Efficient Pairing Computation on Supersingular Abelian Varieties. Design, Codes and Cryptography 42(3), 239–271 (2007)
Wechsler, O.: Inside Intel Core Microarchitecture: Setting new standards for energy-efficient performance. Technology@Intel Magazine (2006)
Grabher, P., Groszschaedl, J., Page, D.: On Software Parallel Implementation of Cryptographic Pairings. In: Avanzi, R.M., Keliher, L., Sica, F. (eds.) Selected Areas in Cryptography. LNCS, vol. 5381, pp. 34–49. Springer, Heidelberg (2009)
Hankerson, D., Menezes, A., Scott, M.: Identity-Based Cryptography, ch. 12, pp. 188–206. IOS Press, Amsterdam (2008)
Intel 64 and IA-32 Architectures Software Developer’s Manual Volume 2: Instruction Set Reference, http://www.intel.com/Assets/PDF/manual/253666.pdf
Gueron, S., Kounavis, M.E.: Carry-Less Multiplication and Its Usage for Computing The GCM Mode. White paper, http://software.intel.com/
Hankerson, D., Menezes, A., Vanstone, S.: Guide to Elliptic Curve Cryptography. Springer, Secaucus (2003)
Fong, K., Hankerson, D., López, J., Menezes, A.: Field inversion and point halving revisited. IEEE Transactions on Computers 53(8), 1047–1059 (2004)
Karatsuba, A., Ofman, Y.: Multiplication of many-digital numbers by automatic computers (in Russian). Doklady Akad. Nauk SSSR 145, 293–294 (1962)
López, J., Dahab, R.: High-speed software multiplication in GF(2m). In: Roy, B., Okamoto, E. (eds.) INDOCRYPT 2000. LNCS, vol. 1977, pp. 203–212. Springer, Heidelberg (2000)
Beuchat, J., López-Trejo, E., Martínez-Ramos, L., Mitsunari, S., Rodríguez-Henríquez, F.: Multi-core implementation of the Tate pairing over supersingular elliptic curves. In: Garay, J.A., Miyaji, A., Otsuka, A. (eds.) CANS 2009. LNCS, vol. 5888, pp. 413–432. Springer, Heidelberg (2009)
Barreto, P.S.L.M., Lynn, B., Scott, M.: Efficient Implementation of Pairing-Based Cryptosystems. Journal of Cryptology 17(4), 321–334 (2004)
Barreto, P.S.L.M., Kim, H.Y., Lynn, B., Scott, M.: Efficient algorithms for pairing-based cryptosystems. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 354–368. Springer, Heidelberg (2002)
Miller, V.S.: The Weil Pairing, and Its Efficient Calculation. Journal of Cryptology 17(4), 235–261 (2004)
Hess, F., Smart, N.P., Vercauteren, F.: The eta pairing revisited. IEEE Trans. on Information Theory 52, 4595–4602 (2006)
Lee, H., Lee, E., Park, C.: Efficient and Generalized Pairing Computation on Abelian Varieties. IEEE Trans. on Information Theory 55(4), 1793–1803 (2009)
Mitsunari, S.: A Fast Implementation of η T Pairing in Characteristic Three on Intel Core 2 Duo Processor. Cryptology ePrint Archive, Report 2009/032 (2009)
Cesena, E.: Pairing with Supersingular Trace Zero Varieties Revisited. Cryptology ePrint Archive, Report 2008/404 (2008)
Cesena, E., Avanzi, R.: Trace Zero Varieties in Pairing-based Cryptography. In: Conference on Hyperelliptic curves, discrete Logarithms, Encryption, etc. (2009), http://inst-mat.utalca.cl/chile2009/Slides/Roberto_Avanzi_2.pdf
Vercauteren, F.: Optimal pairings. Cryptology ePrint Archive, Report 2008/096 (2008)
Beuchat, J., Brisebarre, N., Detrey, J., Okamoto, E., Rodríguez-Henríquez, F.: A Comparison Between Hardware Accelerators for the Modified Tate Pairing over \({\mathbb F}_{2^m}\) and \({\mathbb F}_{3^m}\). In: Galbraith, S.D., Paterson, K.G. (eds.) Pairing 2008. LNCS, vol. 5209, pp. 297–315. Springer, Heidelberg (2008)
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Aranha, D.F., López, J., Hankerson, D. (2010). High-Speed Parallel Software Implementation of the η T Pairing. In: Pieprzyk, J. (eds) Topics in Cryptology - CT-RSA 2010. CT-RSA 2010. Lecture Notes in Computer Science, vol 5985. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11925-5_7
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DOI: https://doi.org/10.1007/978-3-642-11925-5_7
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