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Liskov proposed several weakened versions of the random oracle model, called Weakened Random Oracle Models (WROMs), to capture the vulnerability of ideal compression functions, which are expected to have the standard security of hash functions, i.e., collision resistance, second-preimage resistance, and one-wayness properties. The WROMs offer additional oracles to break such properties of the random oracle. In this paper, the authors investigate whether public-key encryption schemes in the random oracle model essentially require the standard security of hash functions by the WROMs.
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