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This work defines and construct a proof of conditional min-entropy, which certifies optimal min-entropy even conditioned on an adversarially chosen transcript, and shows an application of this primitive to randomness beacons, where each pulse should have high min-entropy conditioned on all previous messages.
A certified randomness protocol in the quantum random oracle model is obtained that proves unconditional security of this protocol against adversaries making subexponentially-many adaptive quantum queries to the random oracle.
The simulation theorem is established by proving the stronger statement that parallel-query quantum algorithms cannot distinguish the uniform distribution over oracles from oracles drawn from so-called dense distributions, and a coupling theorem is a coupling theorem that relates the uniform distribution over oracles t...
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