Abstract
This paper presents a design for an efficient architecture of a reconfigurable bit-serial polynomial basis multiplier for Galois field GF(2m). The multiplier operates on the Most Significant Bit (MSB)-first for finite field multiplication. The design is flexible enough to configure different value of irreducible polynomial degree m for multiplication. Since the multiplier is doing a bit-serial processing with the gated clock technique, thus the design would be suitable for low power devices. Another advantage of the proposed architecture is the improvement of its maximum clock frequency and the high order of flexibility which allows an easy configuration for different field sizes.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Kim, H.S., Lee, S.W.: LFSR multipliers over GF(2m) defined by all-one polynomial. INTEGRATION, the VLSI journal 40, 473–478 (2007)
Kitsos, P., Theodoridis, G., Koufopavlou, O.: An efficient reconfigurable multiplier architecture for Galois field GF(2m). Microelectronics Journal 34, 975–980 (2003)
Menezes, A.J., Oorschot, P.C., Vanstone, S.A.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1997)
Li, H., Zhang, C.N.: Efficient cellular automata based versatile multiplier for GF(2m). J Inform. Sci. Engng. 18, 479–488 (2002)
Chandrakasan, A.P., Brodersen, R.W.: Low power digital CMOS design. Kluwer Academic Publishers, Dordrecht (1995)
Koc, C.K., Sunar, B.: Low-complexity bit-parallel canonical and normal basis multipliers for a class of finite fields. IEEE Transactions on Computers 47(3), 353–356 (1998)
Lee, C.Y., Lu, E.H., Lee, J.Y.: Bit-parallel systolic multipliers for GF(2m) fields defined by all-one and equally spaced polynomials. IEEE Transactions on Computers 50(5), 385–393 (2001)
Kim, H.S., Yoo, K.Y.: AOP arithmetic architectures over GF(2m). Appl. Math. Comput. 58, 7–18 (2004)
Jeon, J.C., Kim, H.S., Lee, H.M., Yoo, K.Y.: Bit-serial AB2 multiplier using modified inner product. J. Inform. Sci. Eng. 18, 507–518 (2002)
Song, L., Parhi, K.K.: Efficient finite field serial/parallel multiplication. In: Proceedings of the 10th IEEE Int. Conference on Application-Specific Systems, Architectures, and Processors (ASAP 1996), pp. 72–82. IEEE Computer Society Press, Los Alamitos (1996)
Hasan, M.A., Ebtedaei, M.: Efficient architectures for computations over variable dimensional Galois field. IEEE Trans. Circuits Syst. I. Fundam. Theory Appl. 45(11) (1998)
Koblitz, N.: Elliptic curve cryptosystems. Mathematics of Computation 48(177), 203–209 (1987)
National Institute of Standards and Technology (NIST). Digital Signature Standard (DSS), pp. 186–200. Federal information processing standards (FIPS) publication (2000)
Lin, S., Costello, D.: Error Control Coding: Fundamentals and Applications. Prentice-Hall, Englewood Cliffs (1983)
Fenn, S.T.J., Parker, M.G., Benaissa, M., Tayler, D.: Bit-serial multiplication in GF(2m) using irreducible all-one polynomial. IEE Proc. Comput. Digit. Tech. 144(6), 391–393 (1997)
Itoh, T., Tsujii, S.: Structure of parallel multipliers for a class of fields GF(2m). Inform. Comput. 83, 21–40 (1989)
Scott, P.A., Travares, S.E., Peppard, L.E.: A fast VLSI multiplier for GF(2m). IEEE J. Sel. Areas Commun. sac-4, 62–65 (1986)
Hutter, M., Großschadl, J., Kamendje, G.: A Versatile and Scalable Digit-Serial/Parallel Multiplier Architecture for Finite Fields GF(2m). In: Proceedings of the 4th International Conference on Information Technology: Coding and Computing, pp. 692–700 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nikooghadam, M., Malekian, E., Zakerolhosseini, A. (2008). A Versatile Reconfigurable Bit-Serial Multiplier Architecture in Finite Fields GF(2m). In: Sarbazi-Azad, H., Parhami, B., Miremadi, SG., Hessabi, S. (eds) Advances in Computer Science and Engineering. CSICC 2008. Communications in Computer and Information Science, vol 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89985-3_28
Download citation
DOI: https://doi.org/10.1007/978-3-540-89985-3_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-89984-6
Online ISBN: 978-3-540-89985-3
eBook Packages: Computer ScienceComputer Science (R0)