Abstract
The important arithmetic operations over finite fields include exponentiation, division, and inversion. An exponentiation operation can be implemented using a series of squaring and multiplication operations over GF(2m) using a binary method, while division and inversion can be performed by the iterative application of an AB 2 operation. Hence, it is important to develop a fast algorithm and efficient hardware for squaring, multiplication, and AB 2 operations. The current paper presents new architectures for the simultaneous com-putation of multiplication and squaring operations, and the computation of an AB 2 operation over GF(2m) generated by an irreducible AOP of degree m. The proposed architectures offer a significant improvement in reducing the hardware complexity compared with previous architectures, and can also be used as a kernel circuit for exponentiation, division, and inversion architectures. Furthermore, since the proposed architectures include regularity, modularity and concurrency, they can be easily designed on VLSI hardware and used in IC cards.
This research was supported by University IT Research Center Project
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
C. L. Wang, and J. L. Lin, “Systolic array implementation of multipliers for finite field GF(2m)”, IEEE Trans. Circuits System, vol. 38, pp. 796–800, July, 1991.
S. W. Wei, “A systolic power-sum for GF(2m)”, IEEE Trans. Computer, vol. 43, pp. 226–229, Feb. 1994.
J. H. Guo and C. L. Wang, “Bit-serial Systolic Array Implementation of Euclid’s Algorithm for Inversion and Division in GF(2m)”, Proc. 1995 Int. Symp. VLSI Technology, Systems, and Applications, pp. 113–117, 1997.
C. L. Wang and J. H. Guo, “New Systolic Array for C + AB 2, Inversion and Division in GF(2m)”, IEEE Trans. Computer, vol. 49, pp. 1120–1125, Oct., 2000.
T. Itoh, and S. Tsujii, “Structure of parallel multipliers for a class of fields GF(2m)”, Info. Trans., pp. 21–40, 1989.
M. A. Hasan, M. Z. Wang, and V. K. Bhargava, “A modified Massey-Omura parallel multipliers for a class of finite fields”, IEEE Trans. Computer, C-42, pp.1278–1280, 1993.
S. T. J. Fenn, M. G. Parker, M. Benaissa, and D. Taylor, “Bit-serial multiplication in GF(2m) using irreducible all-one polynomials”, IEE Proc. Compu., Digit. Tech., vol. 144, pp. 391–393, 1997.
D. E. Knuth, The art of computer programming, Vol. 2: seminumerical algorithms. Addison-Wesley, Reading, Mass., 2nd edition, 1981.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lee, WH., Heo, YJ., Yoo, KY. (2003). Efficient Architecture for Exponentiation and Division in GF(2m) Using Irreducible AOP. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44839-X_93
Download citation
DOI: https://doi.org/10.1007/3-540-44839-X_93
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40155-1
Online ISBN: 978-3-540-44839-6
eBook Packages: Springer Book Archive