Abstract
Here we describe new tools to be used in fields of the form Gf(2n), that help describe properties of elliptic curves defined over GF(2n). Further, utilizing these tools we describe a new elliptic curve point compression method, which provides the most efficient use of bandwidth whenever the elliptic curve is defined by y 2+xy=x 3+a 2 x 2 +a 6 and the trace of a 2 is zero.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Antipa, A., Brown, D.R.L., Menezes, A., Struik, R., Vanstone, S.A.: Validation of Elliptic Curve Public Keys. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 211–223. Springer, Heidelberg (2002)
Blake, I.F., Smart, N., Seroussi, G.: Elliptic Curves in Cryptography. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (1999)
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)
King, B., Rubin, B.: Revisiting the point halving algorithm. Technical Report
Koblitz, N.: Elliptic curve cryptosystems. Mathematics of Computation 48(177), 203–209 (1987)
Knudsen, E.W.: Elliptic Scalar Multiplication Using Point Halving. In: Lam, K.-Y., Okamoto, E., Xing, C. (eds.) ASIACRYPT 1999. LNCS, vol. 1716, pp. 135–149. Springer, Heidelberg (1999)
Lidl, R., Niederreiter, H.: Finite Fields, 2nd edn. Cambridge University Press, Cambridge (1997)
Menezes, A.: Elliptic Curve Public Key Cryptosystems. Kluwer Academic Publishers, Dordrecht (1993)
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)
NIST, Recommended elliptic curves for federal use, http://www.nist.gov
Schroeppel, R.: Elliptic Curves: Twice as Fast! In: Rump session of CRYPTO 2000 (2000)
Seroussi, G.: Compact Representation of Elliptic Curve Points over \({F_2^n}\). HP Labs Technical Reports, pp. 1–6, http://www.hpl.hp.com/techreports/98/HPL-98-94R1.html
Silverman, J.: The Arithmetic of Elliptic Curves. Springer, New York (1986)
Smart, N.P.: A note on the x-coordinate of points on an elliptic curve in characteristic two. Information Processing Letters 80(5), 261–263 (2001)
IEEE P1363 Appendix A, http://www.grouper.org/groups/1363
WTLS Specification, http://www.wapforum.org
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
King, B. (2004). A Point Compression Method for Elliptic Curves Defined over GF(2n). In: Bao, F., Deng, R., Zhou, J. (eds) Public Key Cryptography – PKC 2004. PKC 2004. Lecture Notes in Computer Science, vol 2947. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24632-9_24
Download citation
DOI: https://doi.org/10.1007/978-3-540-24632-9_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21018-4
Online ISBN: 978-3-540-24632-9
eBook Packages: Springer Book Archive