Elliptic Curve Point Multiplication Using MBNR and Point Halving

-----------------------------------------------------------------------ABSTRACT---------------------------------------------------------The fast implementation of elliptic curve cryptosystems relies on the efficient computation of scalar multiplication. As generalization of double base number system of a number k to multi-base number system (MBNR) provides a faster method for the scalar multiplication is most important and costly operation (in terms of time) in ECC, there is always a need of developing a faster method with lower cost. In this paper we optimize the cost of scalar multiplication using halving and add method instead doubling and tripling methods. The cost is reduced from 40% to 50% with respect to the other fastest techniques

[1]  Vassil S. Dimitrov,et al.  Efficient Quintuple Formulas for Elliptic Curves and Efficient Scalar Multiplication Using Multibase Number Representation , 2007, ISC.

[2]  Laurent Imbert,et al.  Fast Elliptic Curve Point Multiplication using Double-Base Chains , 2005, IACR Cryptol. ePrint Arch..

[3]  Kwok-Wo Wong,et al.  Fast elliptic scalar multiplication using new double-base chain and point halving , 2006, Appl. Math. Comput..

[4]  J. Olivos,et al.  Speeding up the computations on an elliptic curve using addition-subtraction chains , 1990, RAIRO Theor. Informatics Appl..

[5]  Alfred Menezes,et al.  Software Implementation of Elliptic Curve Cryptography over Binary Fields , 2000, CHES.

[6]  Laurent Imbert,et al.  Efficient and Secure Elliptic Curve Point Multiplication Using Double-Base Chains , 2005, ASIACRYPT.

[7]  Erik Woodward Knudsen,et al.  Elliptic Scalar Multiplication Using Point Halving , 1999, ASIACRYPT.

[8]  Patrick Longa,et al.  Accelerating the Scalar Multiplication on Elliptic Curve Cryptosystems over Prime Fields , 2008, IACR Cryptol. ePrint Arch..

[9]  Laurent Imbert,et al.  Extended Double-Base Number System with Applications to Elliptic Curve Cryptography , 2006, INDOCRYPT.

[10]  Whitfield Diffie,et al.  New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.

[11]  N. Koblitz.  Elliptic curve cryptosystems , 1987 .

[12]  Victor S. Miller,et al.  Use of Elliptic Curves in Cryptography , 1985, CRYPTO.

[13]  Marc Joye,et al.  Trading Inversions for Multiplications in Elliptic Curve Cryptography , 2006, Des. Codes Cryptogr..

[14]  Graham A. Jullien,et al.  Theory and applications for a double-base number system , 1997, Proceedings 13th IEEE Sympsoium on Computer Arithmetic.

[15]  Tibor Juhas.  The use of elliptic curves in cryptography , 2007 .

[16]  Alfred Menezes,et al.  Field inversion and point halving revisited , 2004, IEEE Transactions on Computers.