Overview of Addition Formulas for Elliptic Curves Over GF (2n) In Cryptography

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Published: Nov 12, 2018
Keywords:
Elliptic Curves over GF (2n), Projective Coordinate, Cryptography.

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Iqbal H. Jebril
Faculty of Computer Science and Information Technology, University of Malaya
Rosli Salleh
Faculty of Computer Science and Information Technology, University of Malaya
Al-Shawabkeh M.
Faculty of Computer Science and Information Technology, University of Malaya

Abstract

There are several techniques for projective coordinate that can be used for speeding up the computation kP over GF (2n). In this paper we overview all this techniques method in projective coordinate and introduce a new efficient formula in projective coordinates. This formula used the idea of reducing the number of underlying field multiplication. Elliptic curve protocols and applications can be implemented with better performance using the suggested formula.


Keywords: Elliptic Curves over GF (2n), Projective Coordinate, Cryptography.


Corresponding author: E-mail: [email protected]

Article Details

Issue
Vol. 5 No. 1 (2005)
Section
Original Research Articles

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References

[1] http://www.certicom.com, Jan. 2001.
[2] De Win, E., Bosselaers, A., Vanderberghe, S., De Gersem P. and Vandewalle, J, 1996. A fast software implementation for artithmetic operations in GF(2),” Advances in Cryptology, Proc. Asiacrypt’96, LNCS 1163, K. Kim and T. Matsumoto, Eds., Springer-Verlag, p. 65-76.
[3] Eberle, H., Gura, N., Chang Shantz S. and Gupta, V, 2003. A Cryptographic Processor for Arbitrary Elliptic Curves over GF(2m), Sun Microsystems Laboratories, Ins. Printed in U.S.A. May.
[4] Hankerson, D., Lopez, J. and Menezes, A, 2000. Software Implementation of Elliptic Curve Cryptography over Binary Fields, Proc. Cryptographic Hardware and Embedded Systems-CHES 2000, pp. 1-24.
[5] IEEE P1363, 2001. Standard Specifications for Public Key Cryptography, draft.
[6] Gutub, A. and Ibrahim, M, 2003. Power-Time Flexible Architecture for GF (2k) Elliptic Curve Cryptosystem Computation, GLSVLSI, Washington, DC, pp.237-240.
[7] Kim, J. H. and Ho Lee, D, 2002. A Compact Finite Field Processor over GF (2m) for Elliptic Curve Cryptography, IEEE TRANSACTIONS ON COMPUTERS, pp. 340-343.
[8] Konstantinov, E., Stamatiou, Y. and Zaroliagis, G, 2002. A Software Library for Elliptic Curve Cryptography, Springer-Verlang, pp. 625-637.
[9] Lopez, J. and Dahab, R, 1999. Fast multiplication on elliptic curve over GF (Gm) without Precomposition. Proc. Cryptographic Hardware and Embedded Systems (CHES’99), pp. 316-327, Springer-Verlang.
[10] Lopez, J. and Dahab, R, 1998. Improved algorithms for elliptic curve arithmetic in GF ((2n)m), SAC’98, LNCS 1556, pp. 201-212, Springer-Verlag.
[11] Lopez, J. and Dahab, R, 1998. An Improvement of Guajardo-Paar Method for Multiplication on Non-Supersingular Elliptic Curve, Proc. 18th’l Conf. Chilean Computer Science Soc., vol. 1, pp. 1-10.