1. A cryptographic device executing elliptic-curve cryptosystem by using a secret key, comprising: a randomization unit that sets as an initial point a point R on an elliptic curve generated on the basis of random numbers; a setting unit that sets [2^n×R] which is a value obtained by scalar-multiplying the point R, to a point R′ wherein n is an integer; a unit that performs scalar multiplication by using the initial point, a scalar value d for elliptic-curve cryptosystem, and a point P on an elliptic curve and performs multiplication by 2 on the point R′; a randomization cancellation unit that executes Q−R′ by using a point R′ related to the point R, R′ being obtained by multiplication by 2, and a point Q obtained by the multiplication; and a unit that outputs a result of the cancellation used for the secret key encrypting a plain text.