A new representation of elements of finite fields GF(2 m) yielding small complexity arithmetic circuits

IEEE Transactions on Computers

Volumn 47, Issue 9, 1998, Pages 938-946

  Drolet, Germain ^a,b  

^a ROYAL MILITARY COLLEGE OF CANADA   (Canada)

^b IEEE   (Canada)

Author keywords

Canonical basis; Dual basis; Galois field arithmetic; Normal basis; VLSI implementation

Indexed keywords

EID: 0000895310     PISSN: 00189340     EISSN: None     Source Type: Journal    
DOI: 10.1109/12.713313     Document Type: Article

References (27)

1. F.J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes. New York: North-Holland, 1977.
2. N. Koblitz, A Course in Number Theory and Cryptography, GTM. Springer-Verlag, 1987.
3. m)," IEEE Trans. Computers, vol. 41, no. 8, pp. 962-971, Aug. 1992.
4. m) Where q = 3, 5," IEE Proc., Part E, vol. 140, no. 2, pp. 92-94, Mar. 1993.
5. m)," IEE Proc., Part E, vol. 139, no. 3, pp. 230-236, May 1992.
6. m)," Information and Computers, vol. 83, pp. 21-40, 1989.
7. m)," IEEE Trans. Computers, vol. 33, no. 4, pp. 357-360, Apr. 1984.
8. C. Paar, "A New Architecture Parallel Finite Field Multiplier with Low Complexity Based on Composite Fields," IEEE Trans. Computers, vol. 45, no. 7, pp. 856-861, July 1996.
9. E. Mastrovito, "VLSI Architectures for Computations in Galois Fields," PhD thesis, Dept. of Electrical Eng., Linköping Univ., Linköping, Sweden, 1991.
10. m)," Electronics Letters, vol. 28, no. 24, pp. 2,259-2,261, Nov. 1992.
11. m)," IEEE Trans. Computers, vol. 42, no. 8, pp. 1,010-1,015, Aug. 1993.
12. m)," IEEE J. Selected Areas Comm., vol. 6, pp. 578-586, Apr. 1988.
13. J.L. Massey and J.K. Omura, "Computational Method and Apparatusfor Finite Field Arithmetic," U.S. Patent Application, 1981.
14. m) for Certain Values of m," Topics in Discrete Mathematics 106/107, pp. 497-502. North-Holland, 1992.
15. D.B. Gravel, "Improved VLSI Design for Decoding Concatenated Codes Comprising an Irreducible Cydic Code and a Reed-Solomon (N, K) Code," MEng dissertation, Royal Military College of Canada, Kingston, Ontario, May 1995.
16. D.B. Gravel, G. Drolet, and C.N. Rozon, "Improved VLSI Design for Decoding Concatenated Codes Comprising an Irreducible Cydic Code and a Reed-Solomon Code," Information Theory and Applications II. Springer-Verlag, 1996.
17. m) Using Normal Bases," Information and Computation, vol. 78, no. 3, pp. 171-177, Sept. 1988.
18. m)," IEEE Trans. Computers, vol. 34, no. 8, pp. 709-716, Aug. 1985.
19. E.R. Berlekamp and J. Justesen, "Some Long Cyclic Linear Binary Codes Are Not So Bad," IEEE Trans. Information Theory, vol. 20, pp. 351-356, May 1974.
20. M.A. Hasan, M.Z. Wang, and V.K. Bhargava, "A Modified Massey-Omura Parallel Multiplier for a Class of Finite Fields," IEEE Trans. Computers, vol. 42, no. 10, pp. 1,278-1,280, Oct. 1993.
21. D.E. Knuth, The Art of Computer Programming, Vol. 2, Seminumerical Algorithms. Reading, Mass.: Addison-Wesley, 1969.
22. m)," J. Cryptology, vol. 6, pp. 3-13, 1993.
23. Y. Sugiyama, "An Algorithm for Solving Discrete Time Wiener-Hopf Equations Based on Euclid's Algorithm," IEEE Trans. Information Theory, vol. 32, pp. 394-409, May 1986.
24. F.G. Gustavson and D.Y.Y. Yun, "Fast Computation of Padé Approximants and Toeplitz Systems of Equations Via the Extended Euclidean Algorithm," Technical Report RC 7551 (#32645) 3/ 9/ 79, IBM, Yorktown Heights, N.Y.
25. R.P. Brent, F.G. Gustavson, and D.Y.Y. Yun, "Fast Solution of Toeplitz Systems of Equations and Computation of Padé Approximants," J. Algorithms, vol. 1, pp. 259-295, 1980.
26. R.R. Bitmead and B.D.O. Anderson, "Assymptotically Fast Solution of Toeplitz and Related Systems of Linear Equations," Linear Algebra and its Applications, vol. 34, pp. 103-116, 1980.
27. S. Lin and D.J. Costello, Error Control Coding: Fundamentals and Applications. Prentice Hall, 1983.