ISD method implementation over curves with j-invariant 0

摘要

In this paper, we revisited the elliptic scalar multiplication method namely the Integer Sub-Decomposition (ISD) method. This method was proposed in 2013 and it is an extension from a well-known GLV method. But the original ISD method deals with trivial endomorphism which only works on integer number field. By extending the ISD method into complex quadratic field, more solutions can be obtained. And allowing ISD method to work in complex quadratic field will enable the ISD method to be applicable on special curves, such as curves with j-invariant 0. The curves with j-invariant 0 has one special endomorphism over complex number field. And since in ISD method, three endomorphisms are needed, the second and third endomorphism is chosen in such a way that they belong to the same field as the first endomorphism.