Quantum One-Time Programs

Anne Broadbent, Gus Gutoski, Douglas Stebila

Abstract. A one-time program is a hypothetical device by which a user may evaluate a circuit on exactly one input of his choice, before the device self-destructs. One-time programs cannot be achieved by software alone, as any software can be copied and re-run. However, it is known that every circuit can be compiled into a one-time program using a very basic hypothetical hardware device called a one-time memory. At first glance it may seem that quantum information, which cannot be copied, might also allow for one-time programs. But it is not hard to see that this intuition is false: one-time programs for classical or quantum circuits based solely on quantum information do not exist, even with computational assumptions. This observation raises the question, “what assumptions are required to achieve one-time programs for quantum circuits? ” Our main result is that any quantum circuit can be compiled into a one-time program assuming only the same basic one-time memory devices used for classical circuits. Moreover, these quantum one-time programs achieve statistical universal composability (UC-security) against any malicious user. Our construction employs methods for computation on authenticated quantum data, and we present a new quantum authentication scheme called the trap scheme for this purpose. As a corollary, we establish UC-security of a recent protocol for delegated quantum computation. 1

Djabeur Mohamed Seifeddine Zekrifa

Aparna Gupte, Jiahui Liu, Justin Raizes +2 more

One-time programs (Goldwasser, Kalai and Rothblum, CRYPTO 2008) are functions that can be run on any single input of a user's choice, but not on a second input. Classically, they are unachievable without trusted hardware, but the destructive nature of quantum measurements seems to provide a quantum path to constructing them. Unfortunately, Broadbent, Gutoski and Stebila showed that even with quantum techniques, a strong notion of one-time programs, similar to ideal obfuscation, cannot be achieved for any non-trivial quantum function. On the positive side, Ben-David and Sattath (Quantum, 2023) showed how to construct a one-time program for a certain (probabilistic) digital signature scheme, under a weaker notion of one-time program security. There is a vast gap between achievable and provably impossible notions of one-time program security, and it is unclear what functionalities are one-time programmable under the achievable notions of security. In this work, we present new, meaningful, yet achievable definitions of one-time program security for probabilistic classical functions. We show how to construct one time programs satisfying these definitions for all functions in the classical oracle model and for constrained pseudorandom functions in the plain model. Finally, we examine the limits of these notions: we show a class of functions which cannot be one-time programmed in the plain model, as well as a class of functions which appears to be highly random given a single query, but whose one-time program form leaks the entire function even in the oracle model.

Aparna Gupte, Jiahui Liu, Luowen Qian +3 more

One-time programs (OTPs) aim to let a user evaluate a program on a single input while revealing nothing else. Classical OTPs require hardware. Quantum measurement suggests a physical basis for one-time use, yet deterministic functionalities remain impossible due to gentle-measurement attacks (Broadbent, Gutoski and Stebila, 2013). Recent constructions cover randomized functionalities with high-entropy outputs (Gunn, Movassagh 2025; Gupte et al., 2025), but the strongest achievable security remains unclear. Inspired by classical obfuscation, we ask for a "best-possible" one-time compiler that, for any functionality, leaks the least information compared with any other one-time implementation. We prove that such a generic compiler cannot exist even for classical randomized functionalities assuming $\mathsf{SZK} \not\subseteq \mathsf{BQP}$. We then identify a natural subclass: testable OTP compilers, which output quantum states augmented with reflection programs for themselves. We formulate a simplified, generalized Single-Effective-Query (SEQ) simulation security notion for quantum channels, using self-adjoint implementations whose behavior under arbitrary quantum interactions depends only on the channel. SEQ security implies best-possible testable one-time security. We construct SEQ-secure OTPs for all quantum functionalities in the classical oracle model, giving the first positive results for arbitrary quantum channels beyond classical randomized functionalities. SEQ security could thus serve as a testable one-time analogue of virtual black-box (VBB) security. Finally, we propose stateful quantum indistinguishability obfuscation (stateful quantum iO): quantum state obfuscation for stateful quantum programs. It implies best-possible testable OTPs and is achievable in the classical oracle model, offering an approach towards best-possible testable OTPs in the plain model.

Vijayarangan Natarajan

Marie-Christine Roehsner, Joshua A. Kettlewell, Tiago B. Batalhão +2 more

One-time programs, computer programs which self-destruct after being run only once, are a powerful building block in cryptography and would allow for new forms of secure software distribution. However, ideal one-time programs have been proved to be unachievable using either classical or quantum resources. Here we relax the definition of one-time programs to allow some probability of error in the output and show that quantum mechanics offers security advantages over purely classical resources. We introduce a scheme for encoding probabilistic one-time programs as quantum states with prescribed measurement settings, explore their security, and experimentally demonstrate various one-time programs using measurements on single-photon states. These include classical logic gates, a program to solve Yao's millionaires problem, and a one-time delegation of a digital signature. By combining quantum and classical technology, we demonstrate that quantum techniques can enhance computing capabilities even before full-scale quantum computers are available.