From Weak to Strong Watermarking

Abstract

Abstract. The informal goal of a watermarking scheme is to "mark" a digital object, such as a picture or video, in such a way that it is difficult for an adversary to remove the mark without destroying the content of the object. Although there has been considerable work proposing and breaking watermarking schemes, there has been little attention given to the formal security goals of such a scheme. In this work, we provide a new complexity-theoretic definition of security for watermarking schemes. We describe some shortcomings of previous attempts at defining watermarking security, and show that security under our definition also implies security under previous definitions. We also propose two weaker security conditions that seem to capture the security goals of practice-oriented work on watermarking and show how schemes satisfying these weaker goals can be strengthened to satisfy our definition.

How to Watermark Cryptographic Functions

“…To the best of our knowledge, this is the first provably secure watermarking scheme for functions (program) in terms of theoretical cryptography. Our security notion is based on the notion of strong watermarking introduced by Hopper et al [8]. Their definition takes into account only perceptual objects and they modeled the notion of similarity by a perceptual metric space on objects that measures the distance between objects.…”

“…Our definitions of the non-removability and unforgeability are game-based definitions and based on the notion of strong watermarking by Hopper et al [8]. Our definitions are specialized to focus on cryptographic functions (do not consider metric spaces).…”

“…The non-removability states that even if the adversary is given marked functions, it cannot find a function that is similar to a marked function but does not contain any mark. This is based on the security against removal introduced by Hopper et al [8]. The unforgeability states that the adversary cannot find a new marked function.…”

“…The unforgeability states that the adversary cannot find a new marked function. This is based on the security against insertion introduced by Hopper et al [8].…”

“…Hopper, Molnar, and Wagner proposed a rigorous complexity-theoretic (game-based) definition of security for watermarking schemes, but they focused on watermarking for only perceptual objects [8]. They gave no concrete construction that satisfies their security definition.…”