Online-Extractability in the Quantum Random-Oracle Model

We show the following generic result: When a quantum query algorithm in random-oracle model outputs classical value t that is promised to be some tight relation with H(x) for x, then x can efficiently extracted almost certainty. The extraction by means of suitable simulation random oracle and works online, meaning it straightline, i.e., without rewinding, on-the-fly, during protocol execution (almost) disturbing it. technical core our result new commutator bound bounds operator norm unitary describes evolution compressed (which used simulate above) measurement extracts x. two applications online extractability result. commit-and-open $$\Sigma $$ -protocols setting, we offer first complete post-quantum security proof textbook Fujisaki-Okamoto transformation, adjustments facilitate proof, including concrete bounds.