DEVICE AND METHOD FOR CALCULATING ELLIPTIC CURVE, DEVICE AND METHOD FOR CALCULATING ELLIPTIC CURVE ORDER, DEVICE AND METHOD FOR FORMING ELLIPTIC CURVE, ELLIPTIC CURVE APPLICATION DEVICE, RECORDING MEDIUM WHERE ELLIPTIC CURVE CALCULATING PROGRAM IS RECORDED, RECORDING MEDIUM WHERE ELLIPTIC CURVE ORDER CALCULATING PROGRAM IS RECORDED, AND RECORDING MEDIUM WHERE ELLIPTIC CURVE FORMING PROGRAM IS RECORDED

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.