On the security of non-forgeable robust hash functions

In many applications, it is often desirable to extract a consistent key from a multimedia object (e.g., an image), even when the object has gone through a noisy channel. For example, the extracted key can be used to generate content dependent watermarks to mitigate copy attacks, or for two or more parties to establish a session key from their noisy versions of the same object. Robust hash functions are useful in extracting such consistent keys. It differs from cryptographic hash functions in that small noise in the messages would yield the same hash value with high probability. However, the security of robust hash functions is not well understood. In this paper, we study different security notions of robust hash functions w.r.t. forgery attacks, where the goal of the attacker is to estimate the key (hash value) extracted from a given message. We show that information- theoretical security against forgery under chosen message attacks is not possible, in the sense that given enough number of observations of message/hash pairs, the entropy of the hash value of another message can be reduced arbitrarily. We further give a construction that is computationally secure, where computing the hash value can still be computationally infeasible even its entropy may not be high.