1. A method of generating a signature implemented over an elliptic curve public key encryption scheme utilizing information maintained secret in one computing device comprising the steps of: i) initiating the computation of a coordinate a point on the elliptic curve from a pair of other points on said curve by performing on said one device an initial set of sufficient steps in the computation to inhibit recognition of information pertaining to the identity of said other points; ii) transferring to another computing device remote from the one device the results of said steps; iii) performing at least such additional steps in said computation at said other device to permit the completion of said computation at said one device; and iv) transferring the result of said additional steps to said one device for incorporation in said signature.