Query-Complexity Amplification for Random Oracles

Increasing the computational complexity of evaluating a hash function, both for the honest users as well as for an adversary, is a useful technique employed for example in password-based cryptographic schemes to impede brute-force attacks, and also in so-called proofs of work (used in protocols like Bitcoin) to show that a certain amount of computation was performed by a legitimate user. A natural approach to adjust the complexity of a hash function is to iterate it c times, for some parameter c, in the hope that any query to the scheme requires c evaluations of the underlying hash function. However, results by Dodis et al. (Crypto 2012) imply that plain iteration falls short of achieving this goal, and designing schemes which provably have such a desirable property remained an open problem.

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