New Architecture for Multiplication in GF(2^m) and Comparisons with Normal and Polynomial Basis Multipliers for Elliptic Curve Cryptography

1. Massy, J.L., Omura, J.K.: Computational method and apparatus for finite field arithmetic, US Patent No. 4587627 (1986)

   Google Scholar 

2. Agnew, G.B., Mullin, R.C., Onyszchuk, I., Vanstone, S.A.: An implementation for a fast public key cryptosystem. J. Cryptology 3, 63–79 (1991)

   Article  MathSciNet  MATH  Google Scholar 

3. Wu, H., Hasan, M.A., Blake, I.F.: New low complexity bit-parallel finite field multipliers using weakly dual bases. IEEE Trans. Computers 47, 1223–1234 (1998)

   Article  MathSciNet  Google Scholar 

4. Reyhani-Masoleh, A., Hasan, M.A.: Low complexity sequential normal basis multipliers over GF(2^m). In: 16th IEEE Symposium on Computer Arithmetic, vol.16, pp. 188–195 (2003)

   Google Scholar 

5. Kwon, S., Gaj, K., Kim, C., Hong, C.: Efficient linear array for multiplication in GF(2^m) using a normal basis for elliptic curve cryptography. In: Joye, M., Quisquater, J.-J. (eds.) CHES 2004. LNCS, vol. 3156, pp. 76–91. Springer, Heidelberg (2004)

   Chapter  Google Scholar 

6. Menezes, A.J., Blake, I.F., Gao, S., Mullin, R.C., Vanstone, S.A., Yaghoobian, T.: Applications of Finite Fields. Kluwer Academic Publishers, Dordrecht (1993)

   MATH  Google Scholar 

7. Berlekamp, E.R.: Bit-serial Reed-Solomon encoders. IEEE Trans. Inform. Theory 28, 869–874 (1982)

   Article  MATH  Google Scholar 

8. Wang, M., Blake, I.F.: Bit serial multiplication in finite fields. SIAM J. Disc. Math. 3, 140–148 (1990)

   Article  MathSciNet  MATH  Google Scholar 

9. Morii, M., Kasahara, M., Whiting, D.L.: Efficient bit-serial multiplication and the discrete-time Wiener-Hopf equation over finite fields. IEEE Trans. Inform. Theory 35, 1177–1183 (1989)

   Article  MathSciNet  MATH  Google Scholar 

10. Fenn, S.T.J., Benaissa, M., Taylor, D.: GF(2^m) multiplication and division over the dual basis. IEEE Trans. Computers 45, 319–327 (1996)

    Article  MATH  Google Scholar 

11. Stinson, D.R.: On bit-serial multiplication and dual bases in GF(2^m). IEEE Trans. Inform. Theory 37, 1733–1736 (1991)

    Article  MathSciNet  MATH  Google Scholar 

12. NIST, Digital Signature Standard. FIPS Publication, 186-2 (February 2000)

    Google Scholar 

13. Wu, H., Hasan, M.A., Blake, I.F., Gao, S.: Finite field multiplier using redundant representation. IEEE Trans. Computers 51, 1306–1316 (2002)

    Article  MathSciNet  Google Scholar 

14. Feisel, S., von zur Gathen, J., Shokrollahi, M.: Normal bases via general Gauss periods. Math. Comp. 68, 271–290 (1999)

    Article  MathSciNet  MATH  Google Scholar 

15. Sunar, B., Koç, Ç.K.: An efficient optimal normal basis type II multiplier. IEEE Trans. Computers 50, 83–87 (2001)

    Article  MathSciNet  MATH  Google Scholar 

16. Menezes, A.J., van Oorschot, P.C., Vanstone, S.A.: Handboook of Applied Cryptography. CRC Press, Boca Raton (1996)

    Book  Google Scholar 

17. Zivkovic, M.: Table of primitive binary polynomials II. Math. Comp. 63, 301–306 (1994)

    Article  MathSciNet  MATH  Google Scholar 

18. Hankerson, D., Menezes, A.J., Vanstone, S.A.: Guide to Elliptic Curve Cryptography. Springer, Heidelberg (2004)

    MATH  Google Scholar 

19. Hankerson, D., Hernandez, J.L., Menezes, A.J.: Software implementation of elliptic curve cryptography over binary fields. In: Paar, C., Koç, Ç.K. (eds.) CHES 2000. LNCS, vol. 1965, pp. 1–24. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

20. Song, L., Parhi, K.K.: Efficient finite field serial/parallel multiplication. In: International Conference on Application Specific Systems, Architectures and Processors, pp. 19–21 (1996)

    Google Scholar 

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