New trapdoor one-way function on elliptic curves and their applications to shorter signatures and asymmetric encryption

Abstract From the Canadian patent

The present invention provides a new trapdoor one-way function. In a general sense, some quadratic algebraic integer z is used. One then finds a curve E and a rational map defining z on E. The rational map z is the trapdoor oneway function. A judicious selection of z will ensure that z can be efficiently computed, that it is difficult to invert that determination of , z from the rational functions defined by z is difficult and knowledge of , z allows one to invert z on a certain set of elliptic curve points. Every rational map is a composition of a translation and an endomorphism. The most secure part of the rational map is the endomorphism as the translation is easy to invert. If the …