Designing an ASIP for Cryptographic Pairings over Barreto-Naehrig Curves

1. Menezes, A.J., Okamoto, T., Vanstone, S.A.: Reducing elliptic curve logarithms to logarithms in a finite field. IEEE Trans. Information Theory 39(5), 1639–1646 (1993)

   Article  MathSciNet  MATH  Google Scholar 

2. Frey, G., Rück, H.G.: A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves. Math. of Computation 62(206), 865–874 (1994)

   MathSciNet  MATH  Google Scholar 

3. Joux, A.: A one round protocol for tripartite Diffie-Hellman. In: Bosma, W. (ed.) ANTS 2000. LNCS, vol. 1838, pp. 385–394. Springer, Heidelberg (2000)

   Chapter  Google Scholar 

4. Boneh, D., Franklin, M.: Identity based encryption from the Weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001)

   Chapter  Google Scholar 

5. Boneh, D., Lynn, B., Shacham, H.: Short signatures from the Weil pairing. J. Cryptology 17(4), 297–319 (2004)

   Article  MathSciNet  MATH  Google Scholar 

6. Boneh, D.: A brief look at pairings based cryptography. In: Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science – FOCS 2007, pp. 19–26 (2007)

   Google Scholar 

7. 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)

   Chapter  Google Scholar 

8. Barker, E., Barker, W., Burr, W., Polk, W., Smid, M.: Recommendation for key management – part 1: General (revised). National Institute of Standards and Technology, NIST Special Publication 800-57 (2007) http://csrc.nist.gov/publications/nistpubs/800-57/sp800-57-Part1-revised2_Mar08-2007.pdf

9. Näslund, M.: Ecrypt yearly report on algorithms and keysizes (2007-2008) (2008), http://www.ecrypt.eu.org/ecrypt1/documents/D.SPA.28-1.1.pdf

10. Devegili, A.J., Scott, M., Dahab, R.: Implementing cryptographic pairings over Barreto-Naehrig curves. In: Takagi, T., Okamoto, T., Okamoto, E., Okamoto, T. (eds.) Pairing 2007. LNCS, vol. 4575, pp. 197–207. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

11. Grabher, P., Großschädl, J., Page, D.: On software parallel implementation of cryptographic pairings. Cryptology ePrint Archive, Report 2008/205 (2008), http://eprint.iacr.org/2008/205

12. Naehrig, M., Barreto, P.S.L.M., Schwabe, P.: On compressible pairings and their computation. In: Vaudenay, S. (ed.) AFRICACRYPT 2008. LNCS, vol. 5023, pp. 371–388. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

13. Devegili, A.J., Scott, M., Dahab, R.: Implementing cryptographic pairings over Barreto-Naehrig curves. Cryptology ePrint Archive, Report 2007/309 (2007), http://eprint.iacr.org/2007/390

14. Beuchat, J.-L., 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)

    Chapter  Google Scholar 

15. Beuchat, J.-L., Brisebarre, N., Detrey, J., Okamoto, E., Shirase, M., Takagi, T.: Algorithms and arithmetic operators for computing the η _t pairing in characteristic three. IEEE Trans. Comput. 57(11), 1454–1468 (2008)

    Article  MathSciNet  Google Scholar 

16. Beuchat, J.-L., Shirase, M., Takagi, T., Okamoto, E.: An algorithm for the η _t pairing calculation in characteristic three and its hardware implementation. In: Proc. 18th IEEE Symp. Computer Arithmetic – ARITH 2007, pp. 97–104 (2007)

    Google Scholar 

17. Beuchat, J.-L., Doi, H., Fujita, K., Inomata, A., Kanaoka, A., Katouno, M., Mambo, M., Okamoto, E., Okamoto, T., Shiga, T., Shirase, M., Soga, R., Takagi, T., Vithanage, A., Yamamoto, H.: FPGA and ASIC implementations of the η _t pairing in characteristic three. Cryptology ePrint Archive, Report 2008/280 (2008), http://eprint.iacr.org/2008/280

18. Shu, C., Kwon, S., Gaj, K.: FPGA accelerated Tate pairing based cryptosystems over binary fields. In: Proc. IEEE Int’l Conf. Field Programmable Technology – FPT 2006, pp. 173–180 (2006)

    Google Scholar 

19. Keller, M., Ronan, R., Marnane, W., Murphy, C.: Hardware architectures for the Tate pairing over GF(2^m). Computers & Electrical Eng. 33(5-6), 392–406 (2007)

    Article  MATH  Google Scholar 

20. Keller, M., Kerins, T., Crowe, F., Marnane, W.: FPGA implementation of a GF(2^m) Tate pairing architecture. In: Bertels, K., Cardoso, J.M.P., Vassiliadis, S. (eds.) ARC 2006. LNCS, vol. 3985, pp. 358–369. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

21. Ronan, R., Ó hÉigeartaigh, C., Murphy, C., Scott, M., Kerins, T.: FPGA acceleration of the Tate pairing in characteristic 2. In: Proc. IEEE Int’l Conf. Field Programmable Technology, pp. 213–220 (2006)

    Google Scholar 

22. Grabher, P., Page, D.: Hardware acceleration of the Tate pairing in characteristic three. In: Rao, J.R., Sunar, B. (eds.) CHES 2005. LNCS, vol. 3659, pp. 398–411. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

23. Jiang, J.: Bilinear pairing (Eta_T pairing) IP core. Technical report (2007), http://www.cs.cityu.edu.hk/~ecc/doc/etat_datasheet_v2.pdf

24. Kerins, T., Marnane, W.P., Popovici, E.M., Barreto, P.S.L.M.: Efficient hardware for the Tate pairing calculation in characteristic three. In: Rao, J.R., Sunar, B. (eds.) CHES 2005. LNCS, vol. 3659, pp. 412–426. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

25. Ronan, R., Murphy, C., Kerins, T., Ó hÉigeartaigh, C., Barreto, P.S.L.M.: A flexible processor for the characteristic 3 η _t pairing. Int’l J. High Performance Systems Architecture 1(2), 79–88 (2007)

    Article  Google Scholar 

26. Kömürcü, G., Savas, E.: An efficient hardware implementation of the Tate pairing in characteristic three. In: Proc. Third Int’l Conf. Systems – ICONS 2008, pp. 23–28 (2008)

    Google Scholar 

27. Barenghi, A., Bertoni, G., Breveglieri, L., Pelosi, G.: A FPGA coprocessor for the cryptographic Tate pairing over \(\mathbb{F}_p\). In: Proc. Fifth Int’l Conf. Information Technology: New Generations – ITNG 2008, pp. 112–119 (2008)

    Google Scholar 

28. Vejda, T., Page, D., Großschädl, J.: Instruction set extensions for pairing-based cryptography. In: Takagi, T., Okamoto, T., Okamoto, E., Okamoto, T. (eds.) Pairing 2007. LNCS, vol. 4575, pp. 208–224. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

29. Satoh, A., Takano, K.: A scalable dual-field elliptic curve cryptographic processor. IEEE Trans. Computers 52(4), 449–460 (2003)

    Article  Google Scholar 

30. Chen, G., Bai, G., Chen, H.: A high-performance elliptic curve cryptographic processor for general curves over GF(p) based on a systolic arithmetic unit. IEEE Trans. Circuits and Systems II: Express Briefs 54(5), 412–416 (2007)

    Article  Google Scholar 

31. Güneysu, T., Paar, C.: Ultra high performance ECC over NIST primes on commercial FPGAs. In: Oswald, E., Rohatgi, P. (eds.) CHES 2008. LNCS, vol. 5154, pp. 62–78. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

32. Galbraith, S.: Pairings. In: Blake, I.F., Seroussi, G., Smart, N.P. (eds.) Advances in Elliptic Curve Cryptography. London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge (2005)

    Google Scholar 

33. Miller, V.S.: The Weil pairing, and its efficient calculation. J. Cryptology 17, 235–261 (2004)

    Article  MathSciNet  MATH  Google Scholar 

34. Hess, F., Smart, N.P., Vercauteren, F.: The Eta pairing revisited. IEEE Trans. Information Theory 52(10), 4595–4602 (2006)

    Article  MathSciNet  MATH  Google Scholar 

35. Lee, E., Lee, H.S., Park, C.M.: Efficient and generalized pairing computation on Abelian varieties. Cryptology ePrint Archive, Report 2008/040 (2008), http://eprint.iacr.org/2008/040

36. Vercauteren, F.: Optimal pairings. Cryptology ePrint Archive, Report 2008/096 (2008), http://eprint.iacr.org/2008/096

37. Hess, F.: Pairing lattices. In: Galbraith, S.D., Paterson, K.G. (eds.) Pairing 2008. LNCS, vol. 5209, pp. 18–38. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

38. Barreto, P.S.L.M., Galbraith, S.D., Ó hÉigeartaigh, C., Scott, M.: Efficient pairing computation on supersingular Abelian varieties. Designs, Codes and Cryptography 42(3), 239–271 (2007)

    Article  MathSciNet  MATH  Google Scholar 

39. 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)

    Chapter  Google Scholar 

40. CoWare: Processor Designer (2009), http://www.coware.com/products/processordesigner.php

41. National Institute of Standards and Technology, NIST: FIPS 186-2: Digital Signature Standard (DSS) (2000), http://csrc.nist.gov/publications/fips/fips186-2/fips186-2-change1.pdf

42. Bernstein, D.J.: Curve25519: new Diffie-Hellman speed records. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T.G. (eds.) PKC 2006. LNCS, vol. 3958, pp. 207–228. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

43. Montgomery, P.: Modular multiplication without trial division. Mathematics of Computation 44(170), 519–521 (1985)

    Article  MathSciNet  MATH  Google Scholar 

44. Nibouche, O., Bouridane, A., Nibouche, M.: Architectures for Montgomery’s multiplication. IEE Proc. – Computers and Digital Techniques 150(6), 361–368 (2003)

    Article  MATH  Google Scholar 

45. Synopsys: Design Compiler (2009), http://www.synopsys.com/products/logic/design_compiler.html

46. Shu, C., Kwon, S., Gaj, K.: FPGA accelerated Tate pairing based cryptosystems over binary fields. Cryptology ePrint Archive, Report 2006/179 (2006), http://eprint.iacr.org/2006/179

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