This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A New Finite-Field Multiplier Using Redundant Representation
May 2008 (vol. 57 no. 5)
pp. 716-720
A novel finite field multiplier using redundant representation is proposed. The proposed architecture compares favorably to the previously similar proposals. For the class of fields that there exists a type I optimal normal basis, the proposed multiplier has lower complexity and smaller critical path delay in comparison to all the reported normal basis multipliers.

[1] T. Beth and D. Gollman, “Algorithm Engineering for Public Key Algorithms,” IEEE J. Selected Areas in Comm., vol. 7, no. 4, pp. 458-465, May 1989.
[2] G. Drolet, “A New Representation of Elements of Finite Fields GF(2m) Yielding Small Complexity Arithmetic Circuits,” IEEE Trans. Computers, vol. 47, no. 9, pp. 938-946, Sept. 1998.
[3] M. Feng, “A VLSI Architecture for Fast Inversion in $GF(2^{m})$ ,” IEEE Trans. Computers, vol. 38, no. 10, pp. 1383-1386, Oct. 1989.
[4] L. Gao and G.E. Sobelman, “Improved VLSI Designs for Multiplication and Inversion in $GF(2^{M})$ over Normal Bases,” Proc. 13th Ann. IEEE Int'l ASIC/SOC Conf., pp. 97-101, 2000.
[5] W. Geiselmann and D. Gollmann, “Symmetry and Duality in Normal Basis Multiplication,” Proc. Sixth Int'l Conf. Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes, pp. 230-238, July 1988.
[6] D. Hankerson, A. Menezes, and S. Vanstone, Guide to Elliptic Curve Cryptography. Springer, 2003.
[7] R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications, second ed. Cambridge Univ. Press, 1997.
[8] J.L. Massey and J.K. Omura, Computational Method and Apparatus for Finite Field Arithmetic, US patent 4,587,627, 1986.
[9] A. Rayhani-Masoleh and A. Hasan, “Low Complexity Word-Level Sequential Normal Basis Multipliers,” IEEE Trans. Computers, vol. 54, no. 2, pp. 98-110, Feb. 2005.
[10] A. Reyhani-Masoleh and M.A. Hasan, “Efficient Digit-Serial Normal Basis Multipliers over $GF(2^{m})$ ,” ACM Trans. Embedded Computing Systems, special issue on embedded systems and security, vol. 3, no. 3, pp. 575-592, Aug. 2004.
[11] G.B. Agnew, R.C. Mullin, I.M. Onyszchuk, and S.A Vanstone, “An Implementation for a Fast Public-Key Cryptosystem,” J. Cryptology, vol. 3, pp. 63-79, 1991.
[12] J.H. Silverman, “Fast Multiplication in Finite Fields ${\rm GF}(2^{N})$ ,” Proc. First Int'l Workshop Cryptographic Hardware and Embedded Systems, pp. 122-134, 1999.
[13] J.K. Wolf, “Efficient Circuits for Multiplying in ${\rm GF}(2^{m})$ for Certain Values of $m$ ,” Discrete Math., vols. 106/107, pp. 497-502, 1992.
[14] 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.1306-1316, Nov. 2002.

Index Terms:
Finite field arithmetic, Redundant representation, optimal normal basis, cyclotomic field, multiplier.
Citation:
Ashkan Hosseinzadeh Namin, Huapeng Wu, Majid Ahmadi, "A New Finite-Field Multiplier Using Redundant Representation," IEEE Transactions on Computers, vol. 57, no. 5, pp. 716-720, May 2008, doi:10.1109/TC.2007.70834
Usage of this product signifies your acceptance of the Terms of Use.