Abstract
This paper presents a new digit-serial systolic multiplier over GF(2m) for cryptographic applications. When input data come in continuously, the proposed array produces multiplication results at a rate of one every ⌈m/D ⌉ +2 clock cycles, where D is the selected digit size. Since the inner structure of the proposed array is tree-type, critical path increases logarithmically proportional to D. Therefore, the computation delay of the proposed architecture is significantly less than previously proposed digit-serial systolic multipliers whose critical path increases proportional to D. Furthermore, since the new architecture has the features of regularity, modularity, and unidirectional data flow, it is well suited to VLSI implementations.
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
Blahut, R.E.: Theory and Practice of Error Control Codes. Addison-Wesley, Reading (1983)
Blake, F., Seroussi, G., Smart, N.P.: Elliptic Curves in Cryptography. Cambridge University Press, Cambridge (1999)
Jain, S.K., Song, L., Parhi, K.K.: Efficient Semisystolic Architectures for Finite-Field Arithmetic. IEEE Trans. VLSI Syst. 6(1), 101–113 (1998)
Zhang, T., Parhi, K.K.: Systematic Design Approach of Mastrovito Multipliers over GF(2m). In: Proc. of the 2000 IEEE Workshop on Signal Processing Systems (SiPS): Design and Implementation, Lafayette, LA, October 2000, pp. 507–516 (2000)
Yeh, C.S., Reed, I.S., Trung, T.K.: Systolic Multipliers for Finite Fields GF(2m). IEEE Trans. Comput C-33(4), 357–360 (1984)
Wang, C.L., Lin, J.L.: Systolic Array Implementation of Multipliers for Finite Field GF(2m). IEEE Trans. Circuits and Syst. 38(7), 796–800 (1991)
Orlando, G., Paar, C.: A Super-Serial Galois Fields Multiplier for FPGAs and its Application to Public-Key Algorithms. In: Proc. of the 7th Annual IEEE Symposium on Field Programmable Computing Machines, FCCM 1999, Napa Valley, California, April 1999, pp. 232–239 (1999)
Hasan, M.A., Bhargava, V.K.: Bit-Serial Systolic Divider and Multiplier for Finite Fields GF(2m). IEEE Trans. Comput 41(8), 972–980 (1992)
Tsai, W.C., Wang, S.J.: Two Systolic Architectures for Multiplication in GF(24m). IEE Proc. Comput. Digit. Tech. 147(6), 375–382 (2000)
Paar, C., Fleischmann, P., Soria-Rodriguez, P.: Fast Arithmetic for Public-Key Algorithms in Galois Fields with Composite Exponents. IEEE Tans. Comput. 48(10), 1025–1034 (1999)
Song, L., Parhi, K.K.: Low Energy Digit-Serial/Parallel Finite Field Multipliers. J. VLSI Signal Processing 19(2), 149–166 (1998)
Guo, J.H., Wang, C.L.: Digit-Serial Systolic Multiplier for Finite Field GF(2m). IEE Proc. Comput. Digit. Tech. 145(2), 143–148 (1998)
Kim, C.H., Han, S.D., Hong, C.P.: An Efficient Digit-Serial Systolic Multiplier for Finite Fields GF(2m). In: Proc. on 14th Annual IEEE International Conference of ASIC/SOC, pp. 361–365 (2001)
Mekhallalati, M.C., Ashur, A.S., Ibrahim, M.K.: Novel Radix Finite Field Multiplier for GF(2m). J. VLSI Signal Processing 15(3), 233–245 (1998)
Kung, S.Y.: VLSI Array Processors. Prentice Hall, Englewood Cliffs (1988)
NIST, Recommended elliptic curves for federal government use (May 1999), http://csrc.nist.gov
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kim, C.H., Kwon, S., Hong, C.P., Kim, H. (2004). A New Systolic Array for Least Significant Digit First Multiplication in GF(2m). In: Laganá, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds) Computational Science and Its Applications – ICCSA 2004. ICCSA 2004. Lecture Notes in Computer Science, vol 3045. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24767-8_69
Download citation
DOI: https://doi.org/10.1007/978-3-540-24767-8_69
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22057-2
Online ISBN: 978-3-540-24767-8
eBook Packages: Springer Book Archive