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| A. Pincin, "A New Algorithm for Multiplication in Finite Fields," IEEE Transactions on Computers, vol. 38, no. 7, pp. 1045-1049, July, 1989. | |||
| BibTex | x | ||
| @article{ 10.1109/12.30855, author = {A. Pincin}, title = {A New Algorithm for Multiplication in Finite Fields}, journal ={IEEE Transactions on Computers}, volume = {38}, number = {7}, issn = {0018-9340}, year = {1989}, pages = {1045-1049}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.30855}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Computers TI - A New Algorithm for Multiplication in Finite Fields IS - 7 SN - 0018-9340 SP1045 EP1049 EPD - 1045-1049 A1 - A. Pincin, PY - 1989 KW - algorithm; multiplication; finite fields; sums and products; normal basis representation; highly composite number; parallel implementation; parallel algorithms. VL - 38 JA - IEEE Transactions on Computers ER - | |||
[1] A. V. Aho, J. E. Hopcroft, and J. D. Ullman,The Design and Analysis of Computer Algorithms. Menlo Park, CA: Addison-Wesley, 1974.
[2] T. Beth, N. Cot, and I. Ingemarson, Eds.,Advances in Cryptology: Proceedings of Eurocrypt '84, Lecture Notes in Computer Science 209. Berlin, Germany: Springer-Verlag, 1985.
[3] G. R. Blakey and D. Chaum, Eds.,Advances in Cryptology: Proceeding of Crypto '84, Lecture Notes in Computer Science 1986. Berlin, Germany: Springer-Verlag, 1985.
[4] M. Blum and S. Micali, "How to generate cryptographically strong sequences of pseudo-random bits,"SIAM J. Comput., vol. 13, Nov. 1984.
[5] W. Diffie and M. Hellman, "New directions in cryptography,"IEEE Trans. Inform. Theory, vol. IT-22, pp. 644-654, 1976.
[6] S. W. Golomb,Shift Register Sequences, rev. ed. Laguna Hills, CA: Aegean Park Press, 1982.
[7] N. Jacobson,Lectures in Abstract Algebra, Vol. 2, Princeton, NJ: Van Nostrand, 1959.
[8] N. Jacobson,Lecture in Abstract Algebra, Vol. 3, Princeton, NJ: Van Nostrand, 1959.
[9] J. L. Massey and J. K. Omura, "Computational method and apparatus for finite field arithmetic," U.S. Patent Application, submitted 1981.
[10] J.H. McClellan and C.M. Rader,Number Theory in Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975.
[11] F. J. McWilliams and N. J. A. Sloane,The Theory of Error Correcting Codes, New York: North Holland, 1977.
[12] A. Pincin, "Optimal multiplication algorithms in finite fields," Thesis, Instit. of Elec. Eng., Universita degli Studi di Padova, Padova, Italy, July 1986.
[13] A. Pincin, "Bases for finite fields and a canonical decomposition for a normal basis generator,"Commun. Algebra, vol. 17, June 1989.
[14] J. M. Pollard, "The fast Fourier transform in a finite field,"Math. Comput., vol. 25, pp. 365-374, 1971.
[15] A. Schonhage, "Fast multiplication of polynomials over fields of characteristic 2,"Acta Informatica, vol. 7, pp. 395-398, 1977.
[16] P. K. S. Wah and M. Z. Wang, "Realization and application of the Massey-Omura lock," inProc. Intern. Zurich Seminar, Mar. 6-8, 1984, pp. 175-182.
[17] C. C. Wang, T. K. Truong, H. M. Shao, L. J. Deutsch, J. K. Omura, and I. S. Reed, "VLSI architecture for computing multiplications and inverses in GF(2m),"IEEE Trans. Comput., vol. C-34, pp. 709-716, Aug. 1985.
[18] C. C. Wang, "Exponentiation in finite fieldGF(2m)," Ph.D. dissertation, School Eng. Appl. Sci., Univ. of California, Los Angeles, June 1985.
[19] S. W. Winograd, "On multiplication in algebraic extension fields,"Theoret. Comput. Sci., vol. 8, p. 359-377, 1979.
[20] C. S. Yeh, I. S. Reed, and T. K. Truong, "Systolic multipliers for finite fieldsGF(2m),"IEEE Trans. Comput., vol. C-33, pp. 357- 360.
[21] K. Yiu and K. Peterson, "A single-chip VLSI implementation of the discrete exponentiation public key distribution system," inProc. GLOBECOM '82, 1982, pp. 173-179.