Collusion Resistant Watermarking Schemes for Cryptographic Functionalities

A cryptographic watermarking scheme embeds message into a program while preserving its functionality. Essential security of the watermarking schemes requires that no one could remove the marking message of a marked program without substantially changing its functionality. In practical applications, it is common to mark a program with multiple different messages, e.g. in the secretleaker tracing scenarios. Thus, it is usually required that the watermarking scheme should be secure against the “collusion attacks”, where the adversary can obtain multiple watermarked programs embedded with different messages for the same functionality. However, current works in this area have not formally considered this requirement. In this paper, we formally address the problem and give new security definition for watermarking schemes that captures the collusion attacks. Then we explore the existence of watermarking schemes secure under our new security definition: – On the negative side, we observe that all current watermarking schemes either do not support multi-message embedding inherently or are vulnerable to the collusion attacks. – On the positive side, we construct watermarking scheme secure against the collusion attacks for pseudorandom function (PRF). This is achieved by introducing a new message-embedding technique in the watermarking settings and is built on a newly presented primitive, namely, private multiprogrammable PRF. Based on our watermarking scheme for PRF, we also construct watermarking schemes for various other cryptographic functionalities. ⋆ This work was mainly done when doing the internship at The Hong Kong Polytechnic University. ⋆⋆ Corresponding author. ⋆ ⋆ ⋆ The second to the fifth authors are sorted in the alphabetical order.