A calculation device for calculating two groups G and GT the orders of which are identical to each other and in which a bilinear mapping from two elements belonging to the group G and to the group GT is existent is provided. A public key, a master key, an attribute value number, a user number, and a random number are input, an attribute value indicated by the attribute value number is summed up with an element of the master key, an attribute value secret, the reciprocal of the sum, is generated, a user-specific random number is generated by using the user number and the random number, a user-specific secret is generated from the user-specific random number and the public key, and the attribute value secret is exponentiated to the user-specific secret to generate a user-specific attribute value secret key.