Abstract
The performance of public-key cryptosystems is mainly appointed by the underlying finite field arithmetic. Among the basic arithmetic operations over finite field, the multiplicative inversion is the most time consuming operation. In this paper, a fast inversion algorithm over GF(2m) with the polynomial basis representation is proposed. The proposed algorithm executes in about 27.5% or 45.6% less iterations than the extended binary gcd algorithm (EBGA) or the montgomery inverse algorithm (MIA) over GF(2163), respectively. In addition, we propose a new hardware architecture to apply for low-complexity systems. The proposed architecture takes approximately 48.3% or 24.9% less the number of reduction operations than [4] or [8] over GF(2239), respectively. Furthermore, it executes in about 21.8% less the number of addition operations than [8] over GF(2163).
This research was supported by the MIC(Ministry of Information and Communication), Korea, under the ITRC(Information Technology Research Center) support program supervised by the IITA(Institute of Information Technology Assessment).
This is a preview of subscription content, log in via an institution to check access.
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
Certicom Research, SEC 2: Recommended Elliptic Curve Domain Parameters, version 1.0 (September 2000)
Guo, J.H., Wang, C.L.: Hardware-efficient systolic architecture for inversion and division in GF(2m). IEE Proc. Comput. Digital Tech. 145(4), 272–278 (1998)
Guo, J.H., Wang, C.L.: Systolic Array Implementation of Euclid’s Algorithm for Inversion and Division in GF(2m). IEEE Transactions on Computers 47(10), 1161–1167 (1998)
Gutub, A., Tenca, A.F., Savas, E., Koc, C.K.: Scalable and unified hardware to compute Montgomery inverse in GF(p) and GF(2m). In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 484–499. Springer, Heidelberg (2003)
Hankerson, D., Hernandez, J.L., Menezes, A.: Software Implementation of Elliptic Curve Cryptography Over Binary Fields. In: Paar, C., Koç, Ç.K. (eds.) CHES 2000. LNCS, vol. 1965, pp. 1–24. Springer, Heidelberg (2000)
Lorenzo, R.: New Algorithm for Classical Modular Inverse. In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 57–70. Springer, Heidelberg (2003)
Takagi, N.: A VLSI Algorithm for Modular Division Based on the Binary GCD Algorithm. IEICE Trans. Fundamentals E81-A, 724–728 (1998)
Watanabe, Y., Takagi, N., Takagi, K.: A VLSI Algorithm for Division in GF(2m) Based on Extended Binary GCD Algorithm. IEICE Trans. Fundamentals E85-A, 994–999 (2002)
Wu, C.H., Wu, C.M., Shieh, M.D., Hwang, Y.T.: Systolic VLSI Realization of a Novel Iterative Division Algorithm over GF(2m): a High-Speed, Low-Complexity Design. In: IEEE International Symposium on Circuits and Systems, May 2001, pp. 33–36 (2001)
Wu, C.H., Wu, C.M., Shieh, M.D., Hwang, Y.T.: An Area-Efficient Systolic Division Circuit over GF(2m) for Secure Communication. In: IEEE International Symposium on Circuits and Systems, August 2002, pp. 733–736 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kim, S., Chang, N.S., Kim, C.H., Park, YH., Lim, J. (2005). A Fast Inversion Algorithm and Low-Complexity Architecture over GF(2m). In: Hao, Y., et al. Computational Intelligence and Security. CIS 2005. Lecture Notes in Computer Science(), vol 3802. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11596981_1
Download citation
DOI: https://doi.org/10.1007/11596981_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30819-5
Online ISBN: 978-3-540-31598-8
eBook Packages: Computer ScienceComputer Science (R0)