The present invention aims to allow for addition of an attribute category without reissuing a public parameter. A cryptographic system 10 uses an indexing technique in dual system encryption in dual pairing vector spaces. Specifically, for a transmission-side vector tj for index j, the cryptographic system 10 sets information J assigned to the index j in advance as a coefficient of a predetermined basis vector. For a reception-side vector for index j′ corresponding to the index j, the cryptographic system 10 sets information J′ having an inner-product of 0 with the information J as a coefficient of a basis vector corresponding to the predetermined basis vector.