Juan Garay

We give novel and tighter lifting theorems for security games in the quantum random oracle model (QROM), as well as in Noisy Intermediate-Scale Quantum (NISQ) settings such as the hybrid query model, the noisy oracle and the bounded-depth models. At the core of our main results lies a novel measure-and-reprogram framework that we call coherent reprogramming. This framework gives a tighter lifting theorem for query complexity problems. Secondly, we provide, for the first time, a hybrid lifting theorem for hybrid algorithms that can perform both quantum and classical queries, as well as a lifting theorem for quantum algorithms with access to noisy oracles or bounded quantum depth. At the core of these results lies a novel measure-and-reprogram framework, called hybrid coherent measure-and-reprogramming, tailored specifically for hybrid algorithms. Equipped with both lifting theorems, we are able to prove directly both quantum and NISQ security and complexity results by calculating a single combinatorial quantity, relying solely on classical reasoning. Crucially, we derive the first direct product theorems in the average case, both in the quantum and the hybrid settings— i.e., an enabling tool to determine the hardness of solving multi-instance security games. This allows us to derive in a straightforward manner the hardness of various security games, for example (i) the non-uniform hardness of salted games, (ii) the hardness of specific cryptographic tasks such as the multiple instance version of one-wayness and collision-resistance, and (iii) uniform or non-uniform hardness of many other games.