Nonadaptive One-Way to Hiding Implies Adaptive Quantum Reprogramming

TL;DR

This paper demonstrates that adaptive quantum reprogramming security results can be derived from nonadaptive one-way to hiding theorems, challenging previous beliefs about their independence.

Contribution

It shows that adaptive reprogramming results in quantum cryptography follow from nonadaptive theorems, simplifying the understanding of quantum security proofs.

Findings

Adaptive reprogramming results derive from nonadaptive theorems

Contradicts prior beliefs about independence of adaptive frameworks

Simplifies quantum security proof techniques

Abstract

An important proof technique in the random oracle model involves reprogramming it on hard to predict inputs and arguing that an attacker cannot detect that this occurred. In the quantum setting, a particularly challenging version of this considers adaptive reprogramming wherein the points to be reprogrammed (or the output values they should be programmed to) are dependent on choices made by the adversary. Some quantum frameworks for analyzing adaptive reprogramming were given by Unruh (CRYPTO 2014, EUROCRYPT 2015), Grilo-H\"ovelmanns-H\"ulsing-Majenz (ASIACRYPT 2021), and Pan-Zeng (PKC 2024). We show, counterintuitively, that these adaptive results follow from the \emph{nonadaptive} one-way to hiding theorem of Ambainis-Hamburg-Unruh (CRYPTO 2019). These implications contradict beliefs (whether stated explicitly or implicitly) that some properties of the adaptive frameworks cannot be provided by the Ambainis-Hamburg-Unruh result.