1. A cryptographic device executing elliptic-curve cryptosystem by using a secret key, comprising: a randomization unit for setting as an initial point a point R on an elliptic curve generated on the basis of random numbers; a unit for performing scalar multiplication by using the initial point, a scalar value d for elliptic-curve cryptosystem, and a point P on an elliptic curve; a randomization nullification unit for executing Q-R′ by using a point R′ related to the point R and a point Q obtained by the multiplication; and a unit for outputting a result of the nullification.