Beyond NISQ Assumptions: One-time Memory in the Classically Accessible Random-Oracle Model

Abstract: Quantum information enables many cryptographic primitives that are impossible in the classical world. A line of works has developed cryptographic protocol under the assumption that quantum adversaries are restricted to noisy intermediate-scale quantum (NISQ) computing power, enabling strong one-time functionalities. But the advent of early fault-tolerant quantum computers eras will allow deeper logical quantum circuits, calling into questions the applicability of these NISQ-based assumptions. In this work, we adapt the classically accessible random oracle model (CAROM) as in [BDF+11] and [AK22], in which adversaries are only allowed to classically query the random oracle. The restriction is well motivated for NISQ quantum adversaries and may remain plausible in the presence of early fault-tolerant quantum computers. Then, we show that an efficient simulation-secure one-time memory (OTM) is possible under CAROM. Our protocol uses only BB84 states and has quadratic communication: for a $λ$-bit message and integer-valued parameters $n=n(λ)$ and $\ell=\ell(λ)$, the construction uses $n\ell$ qubits and $(n+2)λ$ classical bits, and for any quantum adversary with at most $2<sup>{\ell/2-1}-1$ classical queries to the random oracle, its simulation advantage is at most $(n+3)\left(\frac{3}{4}\right)<sup>n.$ Hence exponentially small simulation advantage in $n$.