
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
KuYoung Chang, Dowon Hong, HyunSook Cho, "Low Complexity BitParallel Multiplier for GF(2^m) Defined by AllOne Polynomials Using Redundant Representation," IEEE Transactions on Computers, vol. 54, no. 12, pp. 16281630, December, 2005.  
BibTex  x  
@article{ 10.1109/TC.2005.199, author = {KuYoung Chang and Dowon Hong and HyunSook Cho}, title = {Low Complexity BitParallel Multiplier for GF(2^m) Defined by AllOne Polynomials Using Redundant Representation}, journal ={IEEE Transactions on Computers}, volume = {54}, number = {12}, issn = {00189340}, year = {2005}, pages = {16281630}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2005.199}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Low Complexity BitParallel Multiplier for GF(2^m) Defined by AllOne Polynomials Using Redundant Representation IS  12 SN  00189340 SP1628 EP1630 EPD  16281630 A1  KuYoung Chang, A1  Dowon Hong, A1  HyunSook Cho, PY  2005 KW  Index Terms Bitparallel multiplier KW  redundant representation KW  finite field arithmetic KW  AOP KW  Karatsuba method. VL  54 JA  IEEE Transactions on Computers ER   
[1] M. Ciet, J.J. Quisquater, and F. Sica, “ A Secure Family of Composite Finite Fields Suitable for Fast Implementation of Elliptic Curve Cryptography,” Proc. Int'l Conf. Cryptology in India (INDOCRYPT 2001), pp. 108116, 2001.
[2] G. Drolet, “A New Representation of Elements of Finite Fields $GF(2^m)$ Yielding Small Complexity Arithmethic Circuits,” IEEE Trans. Computers, vol. 47, no. 9, pp. 938946, Sept. 1998.
[3] W. Geiselmann and R. Steinwandt, “ A Redundant Representation of $GF(q^n)$ for Designing Arithmetic Circuits,” IEEE Trans. Computers, vol. 52, no. 7, pp. 848853, July 2003.
[4] M.A. Hasan, M.Z. Wang, and V.K. Bhargava, “ A Modified MasseyOmura Parallel Multiplier for a Class of Finite Fields,” IEEE Trans. Computers, vol. 42, no. 10, pp. 12781280, Oct. 1993.
[5] T. Itoh and S. Tsujii, “Structure of Parallel Multiplications for a Class of Fileds $GF(2^m)$ ,” Information and Computers, vol. 83, pp. 2140, 1989.
[6] D.E. Knuth, The Art of Computer Programming, vol. 2. Addison Wesley, 1998.
[7] C.H. Kim, S. Oh, and J. Lim, “A New Hardware Architecture for Operations in $GF(2^n)$ ,” IEEE Trans. Computers, vol. 51, no. 1, pp. 9092, Jan. 2002.
[8] 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.
[9] M. Leone, “A New Low Complexity Parallel Multiplier for a Class of Finite Fields,” Proc. Cryptographic Hardware and Embedded Systems (CHES 2001), pp. 160170, 2001.
[10] R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications. New York: Cambridge Univ. Press, 1994.
[11] C.Y. Lee, E.H. Lu, and J.Y. Lee, “BitParallel Systolic Multipliers for $GF(2^m)$ Fields Defined by AllOne and Equally Spaced Polynomials,” IEEE Trans. Computers, vol. 50, no. 5, pp. 385393, May 2001.
[12] A.J. Menezes, I.F. Blake, X. Gao, R.C. Mullin, S.A. Vanstone, and T. Yaghoobian, Applications of Finite Fields. Kluwer Academic, 1993.
[13] A.J. Menezes, P.C. Oorschot, and S.A. Vanstone, Handbook of Applied Cryptography. CRC Press, 1997.
[14] M. Elia, M. Leone, and C. Visentin, “Low Complexity BitParallel Multipliers for with Generator Polynomial $x^m + x^k+1$ ,” Electronic Letters, vol. 35, no. 7, pp. 551552, Apr. 1999.
[15] J. Omura and J. Massey, “Computational Method and Apparatus for Finite Field Arithmetic,” US Patent Number 4,587,627, May 1986.
[16] A. ReyhaniMasoleh and M.A. Hasan, “A New Construction of MasseyOmura Parallel Multiplier over $GF(2^m)$ ,” IEEE Trans. Computers, vol. 51, no. 5, pp. 511520, May 2002.
[17] A. ReyhaniMasoleh and M.A. Hasan, “Efficient Multiplication beyond Optimal Normal Bases,” IEEE Trans. Computers, vol. 52, no. 4, pp. 428439, Apr. 2003.
[18] J.H. Silverman, “Fast Multiplication in Finite Fields $GF(2^N)$ ,” Proc. Cryptographic Hardware and Embedded Systems (CHES 1999), pp. 122134, 1999.
[19] N. Takagi, J.I. Yoshiki, and K. Takagi, “ A Fast Algorithm for Multiplicative Inversion in $GF(2^m)$ Using Normal Basis,” IEEE Trans. Computers, vol. 50, no. 5, pp. 394398, May 2001.
[20] H. Wu and M.A. Hasan, “ Low Complexity BitParallel Multipliers for a Class of Finite Fields,” IEEE Trans. Computers, vol. 47, no. 8, pp. 883887, Aug. 1998.
[21] H. Wu, M.A. Hasan, I.F. Blake, and S. Gao, “Finite Field Multiplier Using Redundant Representation,” IEEE Trans. Computers, vol. 51, no. 11, pp. 13061316, Nov. 2002.