Abstract
Elliptic Curve Public Key Cryptosystems are becoming increasingly popular for use in mobile devices and applications where bandwidth and chip area are limited. They provide much higher levels of security per key length than established public key systems such as RSA. The underlying operation of elliptic curve point multiplication requires modular multiplication, division/inversion and addition/subtraction. Division is by far the most costly operation in terms of speed. This paper proposes a new divider architecture and implementation on FPGA for use in an ECC processor.
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
Miller, V.S.: Use of Elliptic Curves in Cryptography. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 417–426. Springer, Heidelberg (1986)
Koblitz, N.: Elliptic Curve Cryptosystems. Math. Comp. 48, 203–209 (1987)
Blake, I., Seroussi, G., Smart, N.: Elliptic Curves in Cryptography. London Mathematical Society Lecture Note Series, vol. 265. Cambridge University Press, Cambridge (2000)
Ernst, M., Jung, M., Madlener, F., Huss, S., Blümel, R.: A Reconfigurable System on Chip Implementation for Elliptic Curve Cryptography over GF(2n). In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 381–399. Springer, Heidelberg (2003)
Kerins, T., Popovici, E., Marnane, W., Fitzpatrick, P.: Fully Parameterizable Elliptic Curve Cryptography Processor over GF(2m)’. In: Glesner, M., Zipf, P., Renovell, M. (eds.) FPL 2002. LNCS, vol. 2438, pp. 750–759. Springer, Heidelberg (2002)
IEEE Standards Department. IEEE 1363/D13 Standard Specifications for Public Key Cryptography (2000)
ANSI X9.62. Public Key Cryptography for the Financial Services Industry. The Elliptic Curve Digital Signature Algorithm (ECDSA) (1999)
Orlando, G., Paar, C.: A Scalable GF(p) Elliptic Curve Processor Architecture for Programmable Hardware. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 348–363. Springer, Heidelberg (2001)
Kaliski Jr., B.S.: The Montgomery Inverse and it’s applications. IEEE Trans. on Computers 44(8), 1064–1065 (1995)
Montgomery, P.L.: Modular Multiplication without Trial Division. Math. Computation 44, 519–521 (1985)
Daly, A., Marnane, W.: Efficient Architectures for Implementing Montgomery Modular Multiplication and RSA Modular Exponentiation on Reconfigurable Logic. In: 10th Intl Symposium on FPGA (FPGA 2002), February 2002, pp. 40–49 (2002)
Gutub, A., Tenca, A.F., Koc, C.K.: Scalable VLSI Architecture for GF(p) Montgomery Modular Inverse Computation. In: IEEE Computer Society Annual Symposium on VLSI, April 2002, pp. 53–58 (2002)
Gutub, A., Tenca, A.F., Savas, E., Koc, C.K.: Scalable and unified hardware to compute Montgomery inverse in GF(p) and GF(2n). In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 484–499. Springer, Heidelberg (2003)
Daly, A., Marnane, W., Popovici, E.: Fast Modular Inversion in the Montgomery Domain on Reconfigurable Logic. In: Irish Signals and Systems Conference 2003 (July 2003) (to appear)
Savas, E., Koc, C.K.: The Montgomery Modular Inverse - Revisited. IEEE Trans. on Computers 49(7), 763–766 (2000)
Kobayashi, T., Morita, H.: Fast Modular Inversion Algorithm to Match any Operation Unit. IEICE Trans. Fundamentals E82-A(5), 733–740 (1999)
Shantz, S.C.: From Euclid’s GCD to Montgomery Multiplication to the Great Divide. Technical Report TR-2001-95, Sun Microsystems Laboratories (2001)
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
Daly, A., Marnane, W., Kerins, T., Popovici, E. (2003). Fast Modular Division for Application in ECC on Reconfigurable Logic. In: Y. K. Cheung, P., Constantinides, G.A. (eds) Field Programmable Logic and Application. FPL 2003. Lecture Notes in Computer Science, vol 2778. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45234-8_76
Download citation
DOI: https://doi.org/10.1007/978-3-540-45234-8_76
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40822-2
Online ISBN: 978-3-540-45234-8
eBook Packages: Springer Book Archive