Patent ID: 7110538

Claim:
A method for multiplying an elliptic curve point Q(x,y) by a scalar k to provide a point kQ, the method comprising the steps of: a) selecting an elliptic curve of order n over a finite field F such that there exists an endomorphism ψ where ψ (Q)=λ(Q) for all point Q (x,y) on the elliptic curve, and λ is an integer; b) establishing a representation of said scalar k as a combination of components k i and said integer λ of the form k i = ∑ i = 0 i = ⁢ ⁢ k i ⁢ λ i mod n; c) combining said representation and said point Q to form a composite representation of a multiple of the form k 0 Q+k 1 ψ(Q)+ . . . corresponding to kQ; and d) computing a value corresponding to said point kQ from said composite representation of kQ.