Subgroup on the original determination apparatus of rational points group on the curve, the program and the recording medium

摘要

PROBLEM TO BE SOLVED: To reduce operating costs.;SOLUTION: It is discriminated as to whether a point P on an elliptic curve defined on a finite field GF (q) is an element in the partial group of a GF (q^m) rational point group on this elliptic curve. Σ^m-1_i0ϕⁱP is calculated, where ϕis Frobenius mapping of P, and it is discriminated whether the result is a unit element of the partial group for conducting this discrimination. Calculation of Σ^m-1_i0ϕⁱP is constituted of, for example, a ϕ-fold P computing device, and an elliptic adder is as shown in Figure 2, and the number of times of elliptic addition is reduced in comparison with conventional calculation.;COPYRIGHT: (C)2002,JPO