To enable the calculation of addition [kP+lQ] of scalar multiple point applying a public key regulated in a public key cipher only by the false addition and double addition.

When a base point P is defined as "one dimension of a set V/Fq" on a manifold V/Fq defined on an finite field Fq, a secret key (d) is defined as "one dimension of a set Z". The public key is set as two public key pairs Q, R and the public key pairs Q, R consisting of Q=dP, R=(d+1)P, or R=(d-1)P and either of these R are created. In signature verification specified in the public key cipher system, the execution of the calculation of the addition [kP+lQ] of the scalar multiple point by only the false addition and the double addition is made possible by arithmetic processing applied to the above mentioned public key.