Efficient Hardware for the Tate Pairing Calculation in Characteristic Three

1. Barreto, P.S.L.M., Kim, H.Y., Lynn, B., Scott, M.: Efficient implementation of pairing based cryptosystems. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 354–368. Springer, Heidelberg (2002)

   Chapter  Google Scholar 

2. Barreto, P.S.L.M.: The well-tempered pairing. In: 8th Workshop on Elliptic Curve Cryptography - ECC 2004, Bochum, Germany (2004) (Invited talk)

   Google Scholar 

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

4. Barreto, P.S.L.M.: A note on efficient computation of cube roots in characteristic 3. Cryptology ePrint Archive, Report 035/2004 (2004), http://eprint.iacr.org/2004/305

5. Bertoni, G., Guajardo, J., Kumar, S., Orlando, G., Paar, C., Wollinger, T.: Efficient GF(p ^m) Arithmetic Architectures for Cryptographic Applications. In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 158–175. Springer, Heidelberg (2003)

   Chapter  Google Scholar 

6. Blake, I., Seroussi, G., Smart, N.: Elliptic Curves in Cryptography. London Mathemtatical Lecture Note Series, vol. 265. Cambridge University Press, Cambridge (1999)

   MATH  Google Scholar 

7. DeWin, E., Bosselaers, A., Vandenberghe, S., De Gersem, P., Vandewalle, J.: A fast software implementation for arithemtic operations in GF(2ⁿ). In: Kim, K.-c., Matsumoto, T. (eds.) ASIACRYPT 1996. LNCS, vol. 1163, pp. 65–76. Springer, Heidelberg (1996)

   Chapter  Google Scholar 

8. Dutta, R., Barua, R., Sarkar, P.: Pairing-based cryptography: A survey. Cryptology ePrint Archive, Report 2004/064 (2004), http://eprint.iacr.org/2004/64

9. 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 

10. Frey, G., Rück, H.: A remark considering m-divisibility in the divisor class group of curves. Mathematics of Computation 62, 865–874 (1994)

    Article  MATH  MathSciNet  Google Scholar 

11. Galbraith, S., Harrison, K., Soldera, D.: Implementing the Tate pairing. In: Fieker, C., Kohel, D.R. (eds.) ANTS 2002. LNCS, vol. 2369, pp. 324–337. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

12. Granger, R., Page, D., Stam, M.: On Small Characteristic Algebraic Tori in Pairing-Based Cryptography. Cryptology ePrint Archive, Report 2004/132 (2004), http://eprint.iacr.org/2004/132

13. Granger, R., Page, D., Stam, M.: Hardware and Software Normal Basis Arithemtic for Paring Based Cryptography in Characteristic Three. Cryptology ePrint Archive, Report 157/2004 (2004), http://eprint.iacr.org/2004/157

14. Guajardo, J., Paar, C.: Efficient Algorithms for Elliptic Curve Cryptosystems. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 342–355. Springer, Heidelberg (1997)

    Google Scholar 

15. Karatsuba, A., Ofman, Y.: Multiplication of Multidigit numbers on Automata. Sov. Phys. Dokl (english translation) 7(7), 595–596 (1963)

    Google Scholar 

16. Kerins, T., Popovici, E.M., Marnane, W.P.: Algorithms and Architectures for use in FPGA implementations of Identity Based Encryption Schemes. In: Becker, J., Platzner, M., Vernalde, S. (eds.) FPL 2004. LNCS, vol. 3203, pp. 74–83. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

17. Kerins, T., Popovici, E.M., Marnane, W.P.: An FPGA Implementation of a Flexible Secure Elliptic Curve Crpytography Processor. In: Applied Reconfigurable Computing - ARC 2005, pp. 22–30. IADIS press (2005)

    Google Scholar 

18. Kerins, T., Marnane, W.P., Popovici, E.M.: Hardware Architectures for Arithemtic in GF(p^m) for use in Public Key Cryptography (2004) (preprint)

    Google Scholar 

19. Kerins, T., Marnane, W.P., Popovici, E.M., Barreto, P.S.L.M.: A Hardware Accelerator for Pairing Based Cryptosystems (2005) (preprint)

    Google Scholar 

20. Kwon, S.: Efficient Tate pairing computation for supersingular elliptic curves over binary fields. Cryptology ePrint Archive, Report 2004/303 (2004), http://eprint.iacr.org/2004/303

21. Miller, V.S.: Short Programs for functions on curves (1986) (unpublished manuscript), http://crypto.stanford.edu/miller/miller.pdf

22. Paar, C., Soria-Rodriguez, P.: Fast Arithemtic Architecturs for Public Key Algorithms over Galois Fields GF((2ⁿ)^m). In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 363–378. Springer, Heidelberg (1997)

    Google Scholar 

23. Page, D., Smart, N.P.: Hardware implementation of Finite Fields of Characteristic Three. In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 529–539. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

24. Schneier, B.: Appplied Cryptography, 2nd edn. John Wiley & Sons, Chichester (1996)

    Google Scholar 

25. Scott, M., Barreto, P.S.L.M.: Compressed Pairings. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 140–156. Springer, Heidelberg (2004); Updated version: Cryptology ePrint Archive, Report 2004/032, http://eprint.iacr.org/2004/303

26. Silverman, J.H.: The Arithemtic of Elliptic Curves. Graduate Studies in Mathematics, vol. 106. Springer, Berlin (1986)

    Google Scholar 

27. Verheul, E.R.: Evidence that XTR is more secure than supersingular elliptic curve cryptosystems. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 195–210. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

28. Xilinx Inc. Virtex-2 Platform FPGAs: Complete Data Sheet. Ds031 (2004), http://www.xilinx.com/bvdocs/publications/ds031.pdf

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