Re-encryption device, re-encryption method, computer readable medium, and cryptographic system

A re-encryption method comprising:

• generating a re-encryption key for re-encrypting a target ciphertext generated by an encryption device, using a master re-encryption key that cannot decrypt a ciphertext generated by the encryption device, but can generate a re-encryption key for changing an access range for a ciphertext generated by the encryption device;
• and
• re-encrypting the target ciphertext to generate a re-encrypted ciphertext, using the re-encryption key,
• wherein the master re-encryption key includes a key element k*r in which a parameter w{right arrow over ( )} is set, the parameter w{right arrow over ( )} corresponding to a parameter y{right arrow over ( )} set in a cipher element c1 included in the ciphertext generated by the encryption device,
• wherein the re-encryption key for re-encrypting the target ciphertext includes a key element k{tilde over ( )}*r in which a random number r{tilde over ( )} is embedded in the key element k*r, a cipher element c{tilde over ( )}r in which a parameter x{right arrow over ( )}′ indicating a changed access range is set, and an element D{tilde over ( )} in which the random number r{tilde over ( )} is encrypted, and
• wherein the re-encrypted ciphertext includes an element K in which the cipher element c1 is decrypted with the key element k{tilde over ( )}*r, the cipher element c{tilde over ( )}r, and an element E in which the element D{tilde over ( )} is set.

A non-transitory computer readable medium storing a re-encryption program that causes a computer to function as a re-encryption device to perform:

• a re-encryption key generation process of generating a re-encryption key for re-encrypting a target ciphertext generated by an encryption device, using a master re-encryption key that cannot decrypt a ciphertext generated by the encryption device, but can generate a re-encryption key for changing an access range for a ciphertext generated by the encryption device;
• and
• a re-encryption process of re-encrypting the target ciphertext to generate a re-encrypted ciphertext, using the re-encryption key generated by the re-encryption key generation process,
• wherein the master re-encryption key includes a key element k*r in which a parameter w{right arrow over ( )} is set, the parameter w{right arrow over ( )} corresponding to a parameter y{right arrow over ( )} set in a cipher element c1 included in the ciphertext generated by the encryption device,
• wherein the re-encryption key for re-encrypting the target ciphertext includes a key element k{tilde over ( )}*r in which a random number r is embedded in the key element k*r, a cipher element c{tilde over ( )}r in which a parameter x{right arrow over ( )}′ indicating a changed access range is set, and an element D{tilde over ( )} in which the random number r is encrypted, and
• wherein the re-encrypted ciphertext includes an element K in which the cipher element c1 is decrypted with the key element k{tilde over ( )}*r, the cipher element c{tilde over ( )}r, and an element E in which the element D{tilde over ( )} is set.

A cryptographic system comprising:

• an encryption device to generate a ciphertext;
• a master re-encryption key generation device to generate a master re-encryption key that cannot decrypt a ciphertext generated by the encryption device, but can generate a re-encryption key for changing an access range for a ciphertext generated by the encryption device, the master re-encryption key including a key element k*r in which a parameter w{right arrow over ( )} is set, the parameter w{right arrow over ( )} corresponding to a parameter y{right arrow over ( )} set in a cipher element c1 included in the ciphertext generated by the encryption device;
• a re-encryption device to generate a re-encryption key for re-encrypting a target ciphertext generated by the encryption device, using the master re-encryption key generated by the master re-encryption key generation device, the re-encryption key including a key element k{tilde over ( )}*r in which a random number r{tilde over ( )} is embedded in the key element k*r, a cipher element c{tilde over ( )}r in which a parameter x{right arrow over ( )}′ indicating a changed access range is set, and an element D{tilde over ( )} in which the random number r is encrypted, and re-encrypt the target ciphertext, using the generated re-encryption key, so as to generate a re-encrypted ciphertext including an element K in which the cipher element c1 is decrypted with the key element k{tilde over ( )}*r, the cipher element c{tilde over ( )}r, and an element E in which the element D{tilde over ( )} is set;
• and
• a decryption device to decrypt at least one of the ciphertext generated by the encryption device and the re-encrypted ciphertext generated by the re-encryption device.