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The authors undertake a general study of hash functions secure under correlated inputs, meaning that security should be maintained when the adversary sees hash values of many related high-entropy inputs. Such a property is satisfied by a random oracle, and its importance is illustrated by study of the "Avalanche effect," a well-known heuristic in cryptographic hash function design. One can interpret "Security" in different ways: e.g., asking for one-wayness or that the hash values look uniformly and independently random; the latter case can be seen as a generalization of correlation-robustness introduced by Ishai et al. (CRYPTO 2003). They give specific applications of these notions to password-based login and efficient search on encrypted data.
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