Research on Fast Arithmetic of Elliptic Curve over GF(3~m)
Lei Feng-yu · 2009
The arithmetic on supersingular and non-supersingular elliptic curve over GF(3m) were researched,and computational formulas of point addition,2P,3P and 3kP in affine coordinate were given and confirmed.Based on these,a new 3kP recursive algorithm was proposed which was prior to multiple tripling point algorithms when the speed ratio of field inversion to field multiplication was high.Furthermore,we proposed a new variable length sliding window base-3 wr NAF scalar multiplication algorithm which can reduce the cost of tripling points needed in kP computation.