Elliptic curve encryption processor, processing method of the processor using elliptic curves, and program for causing a computer to execute point scalar multiplication on elliptic curves

摘要

An object is to make a conventional GLV scalar multiplication applicable to a wider range of elliptic curves. An elliptic curve encryption processor includes an input section 2 that inputs information indicating an elliptic curve E, a point P on the elliptic curve, and an operation value K; an embedding operation section 3 that maps the point P on the elliptic curve E to a Jacobi variety of an algebraic curve corresponding to the elliptic curve E, thereby obtaining a point on the Jacobi variety of the algebraic curve corresponding to the elliptic curve E as an embedding point D; a homomorphic processing section 4 that performs a mapping by a homomorphism on the Jacobi variety of the algebraic curve, thereby obtaining a mapping point εD; a projection operation section 5 that performs a mapping to the elliptic curve E, thereby obtaining a projection point P′ on the elliptic curve; and a computing section 6 that performs a computation using the operation value K and the projection point P′.