Efficient architectures for computations over variable dimensional galois fields

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

Volumn 45, Issue 11, 1998, Pages 1205-1211

  Hasan, M A ^a,b   Ebtedaei, M ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

^b AGERE SYSTEMS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER ARCHITECTURE; CRYPTOGRAPHY; MATRIX ALGEBRA; POLYNOMIALS;

GALOIS FIELDS; REED SOLOMON CODES;

COMPUTATIONAL COMPLEXITY;

EID: 0032205396     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/81.735445     Document Type: Article

References (14)

1. E.R. Berlekamp, Algebraic Coding Theory. New York: McGraw-Hill, 1968.
2. N. Koblitz, "Elliptic curve cryptosystems," Math. Comp., vol. 48, pp. 203-209, 1993.
3. M.A. Hasan, V.K. Bhargava, and T. Le-Ngoc, "Algorithms and architectures for the design of a VLSI Reed-Solomon codec," in Reed-Solomon Codes and Their Applications, S. B. Wicker and V. K. Bhargava, Eds. Piscataway, NJ: IEEE Press, June 1994, ch. 4, pp. 60-107.
4. 2155," IEEE J. Select. Areas Commun., vol. 11, pp. 804-813, June 1993.
5. R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications. Cambridge: Cambridge University Press, 1986.
6. Y.R. Shayan, "Versatile Reed-Solomon decoders," Ph.D. dissertation, Concordia Univ., Montreal, Canada, 1990.
7. E.D. Mastrovito, "VLSI architectures for computations in Galois fields," Ph.D. dissertation, Dept. Elect. Eng., Linköping University, Linköping, Sweden, 1991.
8. B. Green and G. Drolet, "A universal Reed-Solomon decoder chip," in Proc. I6th Biennial Symp. Communications, Kingston, ON, May 1992, pp. 327-330.
9. M.A. Hasan and V.K. Bhargava, "Architecture for a low complexity rate-adaptive Reed-Solomon encoder," IEEE Trans. Comput., pp. 938-942, June 1995.
10. E.R. Berlekamp, "Bit-serial Reed-Solomon encoder," IEEE Trans. Inform. Theory, vol. IT-28, no. 6, pp. 869-874, Nov. 1982.
11. M.Z. Wang and I.F. Blake, "Bit serial multiplication in finite fields," SIAM J. Disc. Math., vol. 3, pp. 140-148, Feb. 1990.
12. S.T.J. Fenn, M. Benessia, and D. Taylor, "GF(2m) multiplication and division over the dual basis," IEEE Trans. Comput., vol. 45, pp. 319-327, Mar. 1996.
13. W.W. Peterson and E.J. Weldon, Error Correction Codes. Cambridge, MA: MIT Press, 1972.
14. M. Ebtedaei, "Architectures for universal Reed-Solomon encoders and decoders using flexible GF(2m) arithmetic units," Master's thesis, Dept. of Elect, and Comp. Eng., Univ. of Waterloo, Waterloo, Canada, 1996.