An inner-product predicate encryption scheme with improved flexibility without a restriction that the dimensions of an attribute vector x→ and a predicate vector v→ should be equivalent. A ciphertext having an element c0 and an element ct for each index t included in a set Ix→ is decrypted with a decryption key having an element k0 and an element kt for each index t included in a set Iv→ by computing a product of pairing operations between corresponding pairs of basis vectors on the element c0 and the element k0 and on the element ct and the element kt.