Seven element joint sparse form for pairs of integers and its application
Pan Zhi-shu · Journal of Communications · 2009
Many elliptic curve cryptosystems require the computation of the multiple point multiplication aP+bQ.Solinas, Li X J and Zhang Y J suggested respectively three and five element joint sparse form(JSF),and the number of point addition of the multiple point multiplication was decreased from 0.75l to 0.5l,0.387l and 0.365 4l respectively.The definition and algorithm of seven element JSF was presented,and then it's showed that the average joint Hamming density is only 0.341 5.The number of point addition of the multiple point multiplication is further decreased to 0.341 5l.So,computing aP+bQ by using seven element JSF is faster than by previous JSF representations.