Secure Robust Hash Functions and Their Applications in Non-Interactive Communications

A robust hash function allows different parties to extract a consistent key from a common fuzzy source, e.g., an image gone through noisy channels, which can then be used to establish a cryptographic session key among the parties without the need for interactions. These functions are useful in various communication scenarios, where the security notions are different. The authors study these different security notions in this paper and focus on forgery attacks, where the objective of the attack is to compute the extracted key (hash value) of a given message. This paper will examine information-theoretical security against forgery under chosen message attacks. The authors prove that it is not possible due to the entropy of the hash value of a given message can be reduced arbitrarily when sufficient message/hash pairs have been observed. In this regard, the authors give a computationally secure scheme, where it is computationally infeasible to compute the hash value even when its entropy may not be high.