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FPGA Implementation of a GF(2m) Tate Pairing Architecture

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Reconfigurable Computing: Architectures and Applications (ARC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3985))

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Abstract

This paper presents a hardware implementation of a dual mode Tate pairing/elliptic curve processor over fields of characteristic 2. The architecture can be reconfigured for different underlying field sizes and hence can support different security levels. The processor also performs elliptic curve point scalar multiplication. The performance of the architecture implemented on an FPGA is evaluated for various security levels.

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References

  1. Dutta, R., Barua, R., Sarkar, P.: Pairing-Based Cryptographic Protocols: A Survey. Cryptology ePrint Archive, Report 064/2004 (2004)

    Google Scholar 

  2. Boneh, D., Franklin, M.: Identity Based Encryption from the Weil Pairing. SIAM J. of Computing 32(3), 586–615 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  3. Zhao, M., Smith, S.W., Nicol, D.M.: Aggregated Path Authentication for Efficient BGP Security. In: Proc. 12th ACM Conference on Computer and Communications Security, pp. 128–138 (November 2005)

    Google Scholar 

  4. 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 

  5. Galbraith, S.D., Harrison, K., Soldera, D.: Implementing the Tate Pairing. In: Proc. Fifth Algorithmic Number Theory Symp (ANTS-V), pp. 324–337 (2002)

    Google Scholar 

  6. Duursma, I., Lee, H.-S.: Tate Pairing Implementation for Hyperelliptic Curves y 2 = x p − x + d. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 111–123. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  7. Barreto, P.S.L.M., Galbraith, S., O’hEigeartaigh, C., Scott, M.: Efficient Pairing Computation on Supersingular Abelian Varieties. Cryptology ePrint Archive, Report 375/2004 (2004)

    Google Scholar 

  8. Celoxica RC 2000 (2000), http://www.celoxica.com/products/rc2000/default.asp

  9. Kerins, T., Marnane, W.P., Popovici, E.M., Barreto, P.S.L.M.: Hardware Accelerators for Pairing Based Cryptosystems. In: IEE Proceedings on Information Security, vol. 155(1), pp. 47–56 (October 2005)

    Google Scholar 

  10. Ronan, R., O’hEigeartaigh, C., Murphy, C., Scott, M., Kerins, T., Marnane, W.P.: A Dedicated Processor for the eta Pairing. Cryptology ePrint Archive, Report 330/2005 (2005)

    Google Scholar 

  11. Knuth, D.: The Art of Computer Programming: Seminumerical Algorithms, 2nd edn., vol. 2. Addison-Wesley, Reading (1981)

    MATH  Google Scholar 

  12. Song, L., Parhi, K.: Low Energy Digit-Serial/Parallel Finite Field Multipliers. Kulwer Journal of VLSI Signal Processing Systems 19(2), 149–166 (1998)

    Article  Google Scholar 

  13. Shantz, S.C.: From Euclid’s GCD to Montgomery Multiplication to the Great Divide. TR-2001-95, Technical Report, Sun Microsystems (2001)

    Google Scholar 

  14. Karatsuba, A., Ofman, Y.: Multiplication on Many-Digital Numbers by Automatic Computers. Translation in Physics-Doklady 7, 595–596 (1963)

    Google Scholar 

  15. Keller, M., Kerins, T., Marnane, W.: FPGA Implementation of a GF(24m) Multiplier for use in Pairing Based Cryptosystems. In: Proc. International Conference on Field Programmable Logic and Applications 2005, pp. 594–597 (August 2005)

    Google Scholar 

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© 2006 Springer-Verlag Berlin Heidelberg

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Keller, M., Kerins, T., Crowe, F., Marnane, W. (2006). FPGA Implementation of a GF(2m) Tate Pairing Architecture. In: Bertels, K., Cardoso, J.M.P., Vassiliadis, S. (eds) Reconfigurable Computing: Architectures and Applications. ARC 2006. Lecture Notes in Computer Science, vol 3985. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11802839_44

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  • DOI: https://doi.org/10.1007/11802839_44

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-36708-6

  • Online ISBN: 978-3-540-36863-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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