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An adaptive reprogramming theorem is established that accommodates quantum advice, and has a tighter overall security loss that only scales in the cubic-root of n , with an attack that matches the number of queries required in order to reach constant advantage.
A generic indistinguishability lifting theorem is established: if the two base oracles are indistinguishable under quantum queries, then their corresponding keyed oracles are too, up to an O(q^2) multiplicative loss in distinguishing advantage, where q is the number of queries made by the adversary.
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