We Claim:
[Claim 1] An encryption system comprising:
a master key generation device to generate a public key and a secret key for a first user as a master public key and a master secret key;
a user key generation device to generate a public key and a secret key for a second user as a user public key and a user secret key by using the master public key;
an administration device including a data save unit to save encryption data encrypted with the user public key and an arithmetic operation unit to acquire a procedure of operation using data as an arithmetic procedure, to select encryption data which has been encrypted from data for use in the arithmetic procedure, from the data save unit, to perform homomorphic operation on the encryption data based on the arithmetic procedure, and to output an operation result of the homomorphic operation as an encryption operation result; and
a master decryption device to acquire the encryption operation result and to
decrypt the acquired encryption operation result with the master secret key.
[Claim 2] The encryption system according to claim 1, wherein
the master key generation device transmits the master public key and the
master secret key to the master decryption device, and transmits only the master public
key to the user key generation device and the administration device.
[Claim 3] The encryption system according to claim 1 or 2, wherein
the master key generation device generates the master public key and the master secret key by using a generator configuring a cyclic group on an elliptic curve capable of calculating a pairing map, and
the user key generation device generates the user public key and the user secret key by using the master public key and a randomly-selected natural number.

[Claim 4] The encryption system according to any one of claims 1 to 3, wherein
the arithmetic operation unit acquires the arithmetic procedure including multiplication.
[Claim 5] The encryption system according to any one of claims 1 to 4, further
comprising:
an encryption device to acquire data to be encrypted, to encrypt the acquired data with the user public key, and to transmit the encrypted data as the encryption data to the administration device; and
a user decryption device to acquire the encryption operation result from the
administration device and to decrypt the acquired encryption operation result with the
user secret key.
[Claim 6] The encryption system according to claim 5, wherein
the master key generation device transmits the master public key and the master secret key to the master decryption device, and transmits only the master public key to the user key generation device, the encryption device and the administration device, and
the user key generation device transmits the user public key and the user secret
key to the user decryption device, and transmits only the user public key to the
encryption device and the administration device.
[Claim 7] The encryption system according to claim 5 or 6, wherein
the encryption device acquires the data to be encrypted and a user identifier for identifying a user, and transmits the encryption data and the user identifier to the administration device,
the data save unit stores the encryption data and the user identifier in association with each other, and

the arithmetic operation unit acquires the arithmetic procedure and a second
user identifier, which is a user identifier of the second user, selects, from the data save
unit, encryption data which has been encrypted from data for use in the arithmetic
procedure and is associated with the second user identifier, and performs the
homomorphic operation on the selected encryption data based on the arithmetic
procedure.
[Claim 8] An encryption method comprising:
by a master key generation device, generating a public key and a secret key for a first user as a master public key and a master secret key;
by a user key generation device, generating a public key and a secret key for a second user as a user public key and a user secret key by using the master public key;
by an administration device, acquiring a procedure of operation using data as an arithmetic procedure, selecting encryption data which has been encrypted from data for use in the arithmetic procedure, from a data save unit to save encryption data encrypted with the user public key, performing homomorphic operation on the encryption data based on the arithmetic procedure, and outputting an operation result of the homomorphic operation as an encryption operation result; and
by a master decryption device, acquiring the encryption operation result and
decrypting the acquired encryption operation result with the master secret key.
[Claim 9] An encryption program that causes a computer to execute:
a master key generation process of generating a public key and a secret key for a first user as a master public key and a master secret key;
a user key generation process of generating a public key and a secret key for a second user as a user public key and a user secret key by using the master public key;
a homomorphic operation process of acquiring a procedure of operation using

data as an arithmetic procedure, selecting encryption data which has been encrypted from data for use in the arithmetic procedure, from a data save unit to save encryption data encrypted with the user public key, performing homomorphic operation on the encryption data based on the arithmetic procedure, and outputting an operation result of i the homomorphic operation as an encryption operation result; and
an operation result decryption process of acquiring the encryption operation result and decrypting the acquired encryption operation result with the master secret key.