It is an object to implement a functional proxy re-encryption scheme. A decryption device 300 transmits to a re-encryption device 400 a decryption key k*rk which is generated by converting, using conversion information W1, a decryption key k* in which is set one of attribute information x and attribute information v corresponding to each other, and encrypted conversion information ψrk which is generated by encrypting the conversion information W1 with one of attribute information x′ and attribute information v′ corresponding to each other being set. The re-encryption device 400 generates a re-encrypted ciphertext CT, constituted by a ciphertext crenc which is generated by setting at least one of additional information H and additional information Θ corresponding to each other in a ciphertext cenc in which is set the other one of the attribute information x and the attribute information v, and a decryption key k*renc which is generated by setting at least the other one of the additional information H and the additional information Θ in the decryption key k*rk.