Double-sided: tight proofs for guessing games in the quantum random oracle model

AbstractThe semi-classical One-Way to Hiding (SC-O2H) lemma given by Ambainis et al. (CRYPTO 2019) is a crucial technique to solve the reprogramming problem in the quantum random oracle model (QROM), which can lead to quadratically better bounds for many cases involving guessing games. To achieve tighter bounds, Bindel et al. (TCC, 2019) introduced the double-sided One-Way to Hiding (DS-O2H) lemma, which avoids the loss of query times suffered by the SC-O2H lemma. However, the potential of the DS-O2H lemma to provide better bounds for guessing games has not been considered by far. In this paper, a new double-sided O2H lemma is proposed. By using it, we for the first time give fully tight bounds for several cases involving guessing games. In summary, we show the following results in the QROM: (i) The hardness of inverting a random oracle with the leakage of a one-way injective function can be tightly reduced to the hardness of inverting the involved one-way injective function. (ii) Duman et al. (PKC 2023) introduced the randomness recoverability and defined two transformations $$\textsf {ACWC}_0$$ ACWC 0