a fingerprints embedment system employing an anonymous fingerprinting method using a bilinear diffie - hellman problem includes three participants , introduces system parameters and generates a public key and a secret key of each of the first and the second participant . the anonymous fingerprinting method registers information on the first participant to a third participant based on the system parameters and the public and the secret key of the first participant , wherein the third participant issues a certificate based on the information of the first participant and authenticates a fairness of the first participant based on the certificate . thereafter , the anonymous fingerprinting method embeds fingerprints into a digital content to be bought by the first participant and , when an illegal duplicate of the digital content or an illegally redistributed duplicate is found , identifies a traitor , which illegally duplicates the digital content or redistributes the illegally duplicated digital content , with the first participant .