A Combination of a New Five-Element JSF and Frobenius Map in Point Multiplication of ECC Over GF(2mn)

Based on the existing researches of joint sparse form (JSF), a new five-element JSF is proposed in this paper. For every pair of integers with l binary representations length, it is proved that the average joint hamming weight of its new five- element JSF is 0.333l. Besides, Lee et al proposed a point multiplication algorithm of elliptic curve over GF(2 mn ) with 10≤m≤20, in which Frobenius map was used to expand the integer k and each coefficient of the expansion is represented as a binary string. In this paper, with the application of the new five- element JSF to the coefficients, some variations of Lee et al's algorithm are proposed, and it can achieve a better performance with a few more storages.