Decryption device, cryptographic system, and decryption method

A cryptographic system comprising:

• an encryption device to generate a ciphertext by setting, in the ciphertext, one of a predicate vector of arithmetic branching programs (ABP) and an attribute vector over a basis B, wherein the basis B and a basis B* are dual bases in dual vector spaces, which are generated based on a length (n′) of a public attribute vector and a length (n) of a secret attribute vector such that each of the basis B and the basis B* consists of L partial bases, wherein L is an integer equal to n′+n, each of n′ and n is an integer greater than or equal to 1, and the public attribute vector is published;
• a key generation device to generate a decryption key by setting, in the decryption key, the other one of the predicate vector and the attribute vector over the basis B*;
• and
• a decryption device to decrypt the ciphertext by performing a pairing operation on the ciphertext generated by the encryption device and the decryption key generated by the key generation device.

A decryption method comprising:

• acquiring a ciphertext in which one of a predicate vector of arithmetic branching programs (ABP) and an attribute vector is set over a basis B, wherein the basis B and a basis B* are dual bases in dual vector spaces, which are generated based on a length (n′) of a public attribute vector and a length (n) of a secret attribute vector such that each of the basis B and the basis B* consists of L partial bases, wherein L is an integer equal to n′+n, each of n′ and n is an integer greater than or equal to 1, and the public attribute vector is published;
• acquiring a decryption key in which the other one of the predicate vector and the attribute vector is set over the basis B*;
• and
• decrypting the ciphertext by performing a pairing operation on the acquired ciphertext and the acquired decryption key.