This invention provides a method for accelerating multiplication of an elliptic curve point Q(x,y) by a scalar k, the method comprising the steps of selecting an elliptic curve over a finite field Fq where q is a prime power such that there exists an endomorphism ψ, where ψ(Q)=λ·Q for all points Q(x,y) on the elliptic curve; and using smaller representations ki of the scalar k in combination with the mapping y to compute the scalar multiple of the elliptic curve point Q.