Efficient Digit-Serial Normal Basis Multipliers over Binary Extension Fields

ACM Transactions on Embedded Computing Systems

Volumn 3, Issue 3, 2004, Pages 575-592

  Reyhani Masoleh, Arash ^a   Hasan, M Anwar ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Algorithms; Digit serial multiplier; finite field; normal basis; Security; security

Indexed keywords

EID: 85017122508     PISSN: 15399087     EISSN: 15583465     Source Type: Journal    
DOI: 10.1145/1015047.1015053     Document Type: Article

References (16)

1. Agnew, G. B., Mullin, R. C., Onyszchuk, I. M., Vanstone, S. A., 1991. An implementation for a fast public-key cryptosystem. J. Cryptol. 3, 63-79.
2. Elia, M., Leone, M., 2002. On the inherent space complexity of fast parallel multipliers for GF(2m). IEEE Trans. Comput. 51, 3 (Mar.), 346-351.
3. Gao, L., Sobelman, G. E., 2000. Improved VLSI designs for multiplication and inversion in GF(2m ) over normal bases. In Proceedings of 13th Annual IEEE International ASIC/SOC Conference. 97-101.
4. Hasan, M. A., Wang, M. Z., Bhargava, V. K., 1993. A modified Massey-Omura parallel multiplier for a class of finite fields. IEEE Trans. Comput. 42, 10 (Oct.), 1278-1280.
5. IEEE STD 1363-2000. 2000. IEEE Standard Specifications for Public-Key Cryptography.
6. Koc, C. K., Sunar, B., 1998. Low-complexity bit-parallel canonical and normal basis multipliers for a class of finite fields. IEEE Trans. Comput. 47, 3 (Mar.), 353-356.
7. Lidl, R., Niederreiter, H., 1994. Introduction to Finite Fields and Their Applications. Cambridge University Press.
8. Massey, J. L., Omura, J. K., 1986. Computational method and apparatus for finite field arithmetic. US Patent No. 4587627
9. Menezes, A. J., Blake, I. F., Gao, X., Mullin, R. C., Vanstone, S. A., Yaghoobian, T., 1993. Applications of Finite Fields. Kluwer Academic Publishers, Boston, MA.
10. Mullin, R. C., Onyszchuk, I. M., Vanstone, S. A., Wilson, R. M., 1988-1989. Optimal normal bases in GF(pn). Discrete Appl. Math. 22, 149-161.
11. Reyhani-Masoleh, A., Hasan, M. A., 2001. Fast normal basis multiplication using general purpose processors. Tech. Rep. CORR 2001-25 Deparment. of C & O, University of Waterloo, Canada.
12. Reyhani-Masoleh, A., Hasan, M. A., 2002a. A new construction of Massey-Omura parallel multiplier over GF(2m). IEEE Trans. Comput. 51, 5 (May), 511-520.
13. Reyhani-Masoleh, A., Hasan, M. A., 2002b. Efficient digit-serial normal basis multipliers over GF(2m). In IEEE International Symposium on Circuits and Systems, ISCAS 2002. 781-784.
14. Reyhani-Masoleh, A., Hasan, M. A., 2003. Efficient multiplication beyond optimal normal bases. IEEE Trans. Comput., Special Issue on Cryptographic Hardware and Embedded Systems 52, 4 (Apr.), 428-439.
15. Sunar, B., Koc, C. K., 2001. An efficient optimal normal basis type II multiplier. IEEE Trans. Comput. 50, 1 (Jan.), 83-88.
16. Wang, C. C., Truong, T. K., Shao, H. M., Deutsch, L. J., Omura, J. K., Reed, I. S., 1985. VLSI architectures for computing multiplications and inverses in GF(2m). IEEE Trans. Comput. 34, 8 (Aug.), 709-716.