Hierarchical predicate encryption (HPE) for inner products with enhanced efficiency of operations. A cryptographic processing system includes a key generation device, an encryption device, and a decryption device. The key generation device generates, as a decryption key skL, a vector in which predicate information v{right arrow over ( )}t is embedded in a basis vector of a basis B*t for each integer t of t=1, . . . , L. The encryption device generates, as a ciphertext ct, a vector in which attribute information x{right arrow over ( )}t is embedded in a basis vector of a basis Bt for at least some integer t of t=1, . . . , L. The decryption device performs a pairing operation on the decryption key skL generated by the key generation device and the ciphertext ct generated by the encryption device, and decrypts the ciphertext ct.