
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
ASCII Text  x  
"LowComplexity BitParallel Systolic Montgomery Multipliers for Special Classes of GF(2^m)," IEEE Transactions on Computers, vol. 54, no. 9, pp. 10611070, September, 2005.  
BibTex  x  
@article{ 10.1109/TC.2005.147, author = {}, title = {LowComplexity BitParallel Systolic Montgomery Multipliers for Special Classes of GF(2^m)}, journal ={IEEE Transactions on Computers}, volume = {54}, number = {9}, issn = {00189340}, year = {2005}, pages = {10611070}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2005.147}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  LowComplexity BitParallel Systolic Montgomery Multipliers for Special Classes of GF(2^m) IS  9 SN  00189340 SP1061 EP1070 EPD  10611070 PY  2005 KW  Index Terms Bitparallel systolic multiplier KW  finite field KW  irreducible trinomial KW  montgomery multiplication KW  irreducible AOP. VL  54 JA  IEEE Transactions on Computers ER   
[1] E.R. Berlekamp, Algebraic Coding Theory. New York: McGrawHill, 1968.
[2] M.Y. Rhee, Cryptography and Secure Communications. Singapore: McGrawHill, 1994.
[3] N. Kobliz, “Elliptic Curve Cryptography,” Math. Computation, vol. 48, no. 177, pp. 203209, Jan. 1987.
[4] C. Paar, “A New Architecture for a Parallel Finite Field Multiplier with Low Complexity Based on Composite Fields,” IEEE Trans. Computers, vol. 45, no. 7, pp. 856861, July 1996.
[5] C.K. Koc and B. Sunar, “LowComplexity BitParallel Canonical and Normal Basis Multipliers for a Class of Finite Fields,” IEEE Trans. Computers, vol. 47, no. 3, pp. 353356, Mar. 1998.
[6] B. Sunar and C.K. Koc, “Mastrovito Multiplier for All Trinomials,” IEEE Trans. Computers, vol. 48, no. 5, pp. 522527, May 1999.
[7] M. Diab and A. Poli, “New BitSerial Systolic Multiplier for ${\rm GF}(2^{m})$ Using Irreducible Trinomials,” Electronics Letters, vol. 27, no. 20, pp. 11831184, June 1991.
[8] J.H. Guo and C.L. Wang, “A LowComplexity PowerSum Circuit for ${\rm GF}(2^{m})$ and Its Applications,” IEEE Trans. Circuits and Systems II, vol. 47, no. 10, pp. 10911097, Oct. 2000.
[9] C.L. Wang and J.L. Lin, “Systolic Array Implementation of Multipliers for ${\rm GF}(2^{m})$ ,” IEEE Trans. Circuits and Systems II, vol. 38, pp. 796800, July 1991.
[10] C.S. Yeh, S. Reed, and T.K. Truong, “Systolic Multipliers for Finite Fields ${\rm GF}(2^{m})$ ,” IEEE Trans. Computers, vol. 33, no. 4, pp. 357360, Apr. 1984.
[11] C.Y. Lee, E.H. Lu, and J.Y. Lee, “BitParallel Systolic Multipliers for ${\rm GF}(2^{m})$ Fields Defined by AllOne and EquallySpaced Polynomials,” IEEE Trans. Computers, vol. 50, no. 5, pp. 385393, May 2001.
[12] C.Y. Lee, E.H. Lu, and L.F. Sun, “LowComplexity BitParallel Systolic Architecture for Computing $AB^{2}+C$ in a Class of Finite Field ${\rm GF}(2^{m})$ ,” IEEE Trans. Circuits and Systems II, vol. 48, no. 5, pp. 519523, May 2001.
[13] C.K. Koc and T. Acar, “Montgomery Multiplication in ${\rm GF}(2^{k}$ ),” Designs, Codes and Cryptography, vol. 14, no. 1, pp. 5769, Apr. 1998.
[14] H. Wu, “Montgomery Multiplier and Squarer for a Class of Finite Fields,” IEEE Trans. Computers, vol. 51, no. 5, pp. 521529, May 2002.
[15] J.C. Bajard, L. Imbert, C. Negre, and T. Plantard, “Efficient Multiplication in GF($p^{k}$ ) for Elliptic Curve Cryptography,” Proc. IEEE Symp. Computer Arithmetic, pp. 181187, June 2003.
[16] C.L. Wang, “BitLevel Systolic Array for Fast Exponentiation in ${\rm GF}(2^{m})$ ,” IEEE Trans. Computers, vol. 43, no. 7, pp. 838841, July 1994.
[17] C.Y. Lee, “Low Complexity BitParallel Systolic Multiplier over ${\rm GF}(2^{m})$ Using Irreducible Trinomials,” IEE Proc. Computers and Digital Technology, vol. 150, pp. 3942, Jan. 2003.
[18] A.J. Menezes, Applications of Finite Fields. Kluwer Academic, 1993.
[19] I.F. Blake, S. Gao, and R.L. Lambert, “Construction and Distribution Problems for Irreducible Trinomials over Finite Fields,” Applications of Finite Fields, pp. 1932, Oxford: Clarendon Press, 1996.
[20] W. Stahnke, “Primitive Binary Polynomials,” Math. Computation, vol. 27, pp. 977980, 1973.
[21] R.P. Brent and P. Zimmermann, “Algorithms for Finding Almost Irreducible and Almost Primitive Trinomials,” Proc. Conf. in Honor of Professor H.C. Williams, May 2003.
[22] G. Seroussi, “Table of LowWeight Binary Irreducible Polynomials,” Visual Computing Dept., Hewlett Packard Laboratories, Aug. 1998, http://www.hpl.hp.com/techreports/98HPL98135.html .
[23] P.L. Montgomery, “Modular Multiplication without Trial Division,” Math. Computation, no. 44, pp. 519521, 1985.