Elliptic curve calculation device, elliptic curve order calculation device, elliptic curve construction device, elliptic curve application device, elliptic curve calculation method, elliptic curve order calculation method, elliptic curve construction method, recording medium on which an elliptic curve calculation program is recorded , Recording medium recording elliptic curve order calculation program, and recording medium recording elliptic curve configuration program

摘要

PROBLEM TO BE SOLVED: To provide an elliptic curve calculating device capable of calculating a point on an elliptic curve, an elliptic curve order calculating device capable of calculating an order of an elliptic curve, and an elliptic curve forming device capable of forming an elliptic curve of high security, by less calculation amount. ;SOLUTION: A random number generating part 501 generates a random numbers t; an elliptic curve setting part 502 selects an elliptic curve E: y2=x3-3x+t; an elliptic curve finite judging part 503 judges whether or not orders m1, m2 of elliptic curves Ep1, Ep2 reduced from an elliptic curve EQ on a rational number field with prime numbers p1, p2 used as divisors are prime elements to each other; and an elliptic curve condition judging part 505 judges safety of an elliptic curve E by using the calculated order.;COPYRIGHT: (C)2000,JPO