It is an object of this invention to implement a predicate encryption scheme with delegation capability. A cryptographic process is performed using dual vector spaces (dual distortion vector spaces) of a space V and a space V* paired through a pairing operation. An encryption device generates as a cipher vector a vector in which transmission information is embedded, the cipher vector being the vector of the space V. Using a predetermined vector of the space V* as a key vector, a decryption device performs the pairing operation on the cipher vector generated by the encryption device and the key vector to decrypt the cipher vector and to extract information concerning the transmission information.