Abstract
The advent of Pairing-based protocols has had a major impact on the applicability of cryptography to the solution of more complex real-world problems. However there has always been a question mark over the performance of such protocols. In response much work has been done to optimize pairing implementation, and now it is generally accepted that being pairing-based does not preclude a protocol from consideration as a practical proposition. However although a lot of effort has gone into the optimization of the stand-alone pairing, in many protocols the pairing calculation appears in a particular context within which further optimizations may be possible. It is the purpose of this paper to bridge the gap between theory and practice, and to show that even complex protocols may have a surprisingly efficient implementation. We also point out that in some cases the usually recommended pairing friendly curves may not in fact be optimal. We claim a new record with our implementation of a pairing at the AES-256 bit level.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Acar, T., Lauter, K., Naehrig, M., Shumow, D.: Affine pairings on ARM. Cryptology ePrint Archive, Report 2011/243 (2011), http://eprint.iacr.org/2011/243
Akinyele, J.A., Lehmann, C.U., Green, M.D., Pagano, M.W., Peterson, Z.N.J., Rubin, A.D.: Self-protecting electronic medical records using attribute-based encryption. Cryptology ePrint Archive, Report 2010/565 (2010), http://eprint.iacr.org/2010/565
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)
Barreto, P.S.L.M., Lynn, B., Scott, M.: Constructing Elliptic Curves with Prescribed Embedding Degrees. In: Cimato, S., Galdi, C., Persiano, G. (eds.) SCN 2002. LNCS, vol. 2576, pp. 257–267. Springer, Heidelberg (2003)
Barreto, P.S.L.M., Lynn, B., Scott, M.: Efficient implementation of pairing-based cryptosystems. Journal of Cryptography 17, 321–334 (2004)
Barreto, P.S.L.M., Galbraith, S., OhEigeartaigh, C., Scott, M.: Efficient pairing computation on supersingular abelian varieties. Designs, Codes and Cryptography 42, 239–271 (2007), http://eprint.iacr.org/2004/375
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)
Benger, N., Scott, M.: Constructing Tower Extensions for the Implementation of Pairing-Based Cryptography. In: Hasan, M.A., Helleseth, T. (eds.) WAIFI 2010. LNCS, vol. 6087, pp. 180–195. Springer, Heidelberg (2010)
Beuchat, J.-L., González-DÃaz, J.E., Mitsunari, S., Okamoto, E., RodrÃguez-HenrÃquez, F., Teruya, T.: High-Speed Software Implementation of the Optimal ate Pairing over Barretto-Naehrig Curves. In: Joye, M., Miyaji, A., Otsuka, A. (eds.) Pairing 2010. LNCS, vol. 6487, pp. 21–39. Springer, Heidelberg (2010)
Blake, I.F., Seroussi, G., Smart, N.P. (eds.): Advances in Elliptic Curve Cryptography, vol. 2. Cambridge University Press (2005)
Boneh, D., Boyen, X.: Efficient Selective-ID Secure Identity Based Encryption without Random Oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 223–238. Springer, Heidelberg (2004), http://www.cs.stanford.edu/~xb/eurocrypt04b/
Boneh, D., Di Crescenzo, G., Ostrovsky, R., Persiano, G.: Public Key Encryption with Keyword Search. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 506–522. Springer, Heidelberg (2004)
Boneh, D., Lynn, B., Shacham, H.: Short Signatures from the Weil Pairing. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 514–532. Springer, Heidelberg (2001)
Brezing, F., Weng, A.: Elliptic curves suitable for pairing based cryptography. Designs, Codes and Cryptology 37, 133–141 (2005)
Costello, C., Stebila, D.: Fixed argument pairings. Cryptology ePrint Archive, Report 2010/342 (2010), http://eprint.iacr.org/2010/342
Freeman, D., Scott, M., Teske, E.: A taxonomy of pairing friendly elliptic curves. Journal of Cryptography 23, 224–280 (2010)
Frey, G., Müller, M., Rück, H.: The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems. IEEE Transactions on Information Theory 45(5), 1717–1719 (1999)
Galbraith, S., Paterson, K., Smart, N.: Pairings for cryptographers. Discrete Applied Mathematics 156, 3113–3121 (2008)
Granger, R., Smart, N.P.: On computing products of pairings. Cryptology ePrint Archive, Report 2006/172 (2006), http://eprint.iacr.org/2006/172
Hess, F., Smart, N., Vercauteren, F.: The eta pairing revisited. IEEE Trans. Information Theory 52, 4595–4602 (2006)
Kachisa, E.J., Schaefer, E.F., Scott, M.: Constructing Brezing-Weng Pairing-Friendly Elliptic Curves Using Elements in the Cyclotomic Field. In: Galbraith, S.D., Paterson, K.G. (eds.) Pairing 2008. LNCS, vol. 5209, pp. 126–135. Springer, Heidelberg (2008)
Lauter, K., Montgomery, P.L., Naehrig, M.: An Analysis of Affine Coordinates for Pairing Computation. In: Joye, M., Miyaji, A., Otsuka, A. (eds.) Pairing 2010. LNCS, vol. 6487, pp. 1–20. Springer, Heidelberg (2010)
Lee, E., Lee, H.-S., Park, C.-M.: Efficient and generalized pairing computation on abelian varieties. IEEE Transactions on Information Theory 55, 1793–1803 (2009)
Lin, X., Zhao, C., Zhang, F., Wang, Y.: Computing the ate pairing on elliptic curves with embedding degree k = 9. IEICE Transactions 91-A(9), 2387–2393 (2008)
Liu, Z., Cao, Z.: On efficiently transferring the linear secret-sharing scheme matrix in ciphertext-policy attribute-based encryption. Cryptology ePrint Archive, Report 2010/374 (2010), http://eprint.iacr.org/2010/374
Menezes, A.J., Okamoto, T., Vanstone, S.A.: Reducing elliptic curve logarithms to logarithms in a finite field. IEEE Transactions on Information Theory 39(5), 1639–1646 (1993)
Miyaji, A., Nakabayashi, M., Takano, S.: New explicit conditions of elliptic curve traces for FR-reduction. IEICE Transactions on Fundamentals E84-A(5), 1234–1243 (2001)
El Mrabet, N., Guillermin, N., Ionica, S.: A study of pairing computation for elliptic curves with embedding degree 15. Cryptology ePrint Archive, Report 2009/370 (2009), http://eprint.iacr.org/2009/370
Odlyzko, A.M.: Discrete logarithms: the past and the future. Design, Codes and Cryptography 19, 129–145 (2000)
Oliveira, L., Aranha, D., Gouvêa, C., Scott, M., Câmara, D., López, J., Dahab, R.: TinyPBC: Pairings for authenticated identity-based non-interactive key distribution in sensor networks. Computer Communications 34, 485–493 (2011)
Park, J.H.: Inner-product encryption under standard assumptions. Designs, Codes and Cryptography 58, 235–257 (2011)
Pereira, G., SimplÃcio Jr., M., Naehrig, M., Barreto, P.: A family of implementation-friendly BN elliptic curves. Journal of Systems and Software 84, 1319–1326 (2011)
Sakai, R., Ohgishi, K., Kasahara, M.: Cryptosystems based on pairing. In: The 2000 Symposium on Cryptography and Information Security, Okinawa, Japan (2000)
Scott, M.: Computing the Tate Pairing. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 293–304. Springer, Heidelberg (2005)
Scott, M.: Miracl library (2011), http://www.shamus.ie
Solinas, J.: ID-based digital signature algorithms (2003), http://www.cacr.math.uwaterloo.ca/conferences/2003/ecc2003/solinas.pdf
Vercauteren, F.: Optimal pairings. IEEE Transactions on Information Theory 56(1), 455–461 (2010)
Waters, B.: Ciphertext-Policy Attribute-Based Encryption: An Expressive, Efficient, and Provably Secure Realization. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 53–70. Springer, Heidelberg (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Scott, M. (2011). On the Efficient Implementation of Pairing-Based Protocols. In: Chen, L. (eds) Cryptography and Coding. IMACC 2011. Lecture Notes in Computer Science, vol 7089. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25516-8_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-25516-8_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25515-1
Online ISBN: 978-3-642-25516-8
eBook Packages: Computer ScienceComputer Science (R0)