Query-Limited RAM Programs and their Applications

2026-09-30

AI Summary

This study addresses the stateless limitation of Quantum One-Time Programs (QLPs), which require token distribution for each evaluation, by extending them to stateful controlled access. Methodologically, it pioneers the query-bounded RAM program paradigm, integrating one-time signatures with single-use query theory to support policy-driven stateful computation while preventing state rollback. Additionally, it establishes a universal construction proof alongside an anti-cloning mechanism. The key contributions include realizing Turing machine tokens dependent solely on code length, transferable budget programs, and SaaS delegated computation with low communication overhead. Collectively, this work overcomes the traditional statelessness bottleneck inherent in QLPs.

Abstract

Quantum one-time programs (Broadbent, Gutoski and Stebila, CRYPTO 2013) or OTPs for short, enable a functionality to be encoded into a quantum token that can be evaluated on a single chosen input and then becomes unusable. While powerful, this primitive is inherently stateless and tied to a setting in which a quantum token needs to be issued and distributed for every single evaluation of a circuit. This raises a natural question: can the one-time computation paradigm be extended to richer, stateful forms of controlled access, and would such an extension offer inherent advantages beyond standard OTPs? We introduce $\textit{query-limited RAM programs}$ (QLPs), a RAM-generalization of QOTPs that supports structured, stateful computation under bounded or policy-driven access. QLPs allow controlled sequences of evaluations while preventing adversarial forking or rollback of computational state. This enables new applications beyond stateless one-time programs, including quantum tokens for Turing Machines whose size depends only on $\textit{code length}$ (and not runtime), transferable $k$-time or budget-limited programs, and low-communication mechanisms for delegating computation in settings such as Software-as-a-Service. To construct QLPs, we introduce $\textit{one-shot programs}$, unifying one-shot signatures (Amos, Georgiou, Kiayias and Zhandry, STOC 2020) with the single effective query paradigm (Gupte, Liu, Raizes, Roberts and Vaikuntanathan, STOC 2025). We prove that one-shot programs generically imply query-limited programs, demonstrating that the strengthened unclonability guarantees of one-shot signatures translate into enhanced functionality. Along the way, we clarify the relationship between signature-token primitives and quantum one-time programs via generic constructions, essentially showing that one-time signing programs imply one-time general computation.

Problem

• Quantum one-time programs
• Query-limited RAM programs
• Stateful computation
• Controlled access
• Unclonability

Innovation

• Query-Limited RAM Programs
• Quantum One-Time Programs
• One-Shot Programs
• Stateful Computation
• Unclonability