Power: A Metric for Evaluating Watermarking Algorithms

An important parameter in evaluating data hiding methods is hiding capacity [3] [11] [12], [16] i.e. the amount of data that a certain algorithm can “hide” until reaching allowable distortion limits. One fundamental difference between watermarking [4] [5] [7] [8] [9] [13] [14] [17] [18] [19] [20] [21] [22] [23] and generic data hiding resides exactly in the main applicability and descriptions of the two domains. Data hiding aims at enabling Alice and Bob to exchange messages [1] [6] [15] in a manner as resilient and stealthy as possible, through a medium controlled by evil Mallory. On the other hand, digital watermarking is deployed by Alice to prove ownership over a piece of data, to Jared the Judge, usually in the case when Tim the Thief 1 benefits from using/selling that very same piece of data (or maliciously modified versions of it). In the digital framework, watermarking algorithms that make use of information hiding techniques have been developed and hiding capacity was naturally used as a metric in evaluating their power to hide information. Whereas the maximal amount of information that a certain algorithm can “hide” (while keeping the data within allowable distortion bounds) is certainly related to the ability to assert ownership in court, it is not directly measuring its “power of persuasion” (i.e. how convinced will Jared the Judge and the Jury be when presenting the Portions of this work are supported by Grant EIA-9903545 from the National Science Foundation, and by sponsors of the Center for Education and Research in Information Assurance and Security. 1Tim’s middle name is Mallory. algorithm and applying it on an object in dispute), in part also because it doesn’t consider directly the existence and power of watermarking attacks. In this paper we show why, due to its particularities, watermarking requires a different metric, more closely related to its ultimate purpose, claiming ownership in a court of law. We define one suitable metric (watermarking power) and show how it relates to derivates of hiding capacity. We prove that there are cases where considering hiding capacity is sub-optimal as a metric in evaluating watermarking methods whereas the metric of watermarking power delivers good results.