Digital watermark system, digital watermark method and program

1. A digital watermark system that realizes digital watermark for a cryptographic function, comprising:

a memory; and

a processor configured to:

take as input a security parameter and generate a watermark embedding key for embedding information representative of a watermark in a circuit that realizes the cryptographic function, and a watermark extraction key for extracting information representative of the watermark from a circuit in which a watermark is embedded;

take as input a master private key used for the cryptographic function, the watermark embedding key, and information representative of a watermark, and generate a circuit, wherein the circuit comprises the watermark and a program code to perform the cryptographic function, and the cryptographic function comprises encryption of data, decryption of data, and generation of a signature of the data; and

take as input the watermark extraction key and the circuit, extract information representative of a watermark from the circuit for authenticating the program code.

2. The digital watermark system according to claim 1 , wherein the cryptographic function is a function provided by an encryption scheme that is secure based on a computationally difficult problem n and has an all-but-N security proof.

3. The digital watermark system according to claim 2 , wherein the processor

simulates the problem π from the master private key, and

generates a circuit that takes as input the problem I, the watermark embedding key, a query in security proof, and a random number used when generating an answer to the query, and simulates the answer, as the circuit with the watermark embedded therein and realizing the cryptographic function.

4. The digital watermark system according to claim 3 , wherein the processor

verifies whether or not an answer output by inputting the query and the random number to the circuit is correct, using a master public key used for the cryptographic function, and

extracts information representative of the watermark, using a total number of the answers that have been verified as correct.

5. A digital watermark method executed by a digital watermark system that realizes digital watermark for a cryptographic function, the method comprising the steps of:

a key generating process in which a security parameter is taken as input and a watermark embedding key for embedding information representative of a watermark in a circuit that realizes the cryptographic function, and a watermark extraction key for extracting information representative of the watermark from a circuit in which a watermark is embedded are generated;

an embedding process in which a master private key used for the cryptographic function, the watermark embedding key, and information representative of a watermark are taken as input, and generating a circuit, wherein the circuit comprises the watermark and a program code to perform the cryptographic function, and the cryptographic function comprises encryption of data, decryption of data, and generation of a signature of the data; and

an extraction process in which the watermark extraction key and the circuit, are taken as input, and information representative of a watermark is extracted from the circuit for authenticating the program code.

6. A non-transitory computer-readable recording medium having a program causing a computer to execute the digital watermark method of claim 5 .