A Combination of Joint Sparse Form and Frobenius Map in Scalar Multiplication of Elliptic Curve over GF(2^{mn} )

Lee et al proposed two methods to speed up the computation of scalar multiplication of elliptic curve defined over GF(2
^mn
) with a medium size of m in the range 10 les m les 20. In these methods, Frobenius map is utilized to expand the integer k and each coefficient of the expansion is represented as a binary string. In this paper, with the application of joint sparse form (JSF) to the coefficients, some variations of Lee et al's methods are proposed to achieve a better performance.