Information Theoretic One-Time Programs from Geometrically Local $ ext{QNC}_0$ Adversaries

2025-03-27

AI Summary

This work constructs information-theoretically secure one-time memories (OTMs) and one-time programs (OTPs) under quantum hardware constraints—specifically, non-adaptive, constant-depth, D-dimensional geometrically local quantum circuits (QNC₀)—without relying on any computational assumptions. Adversaries are assumed to possess unbounded classical computational power, arbitrary-size quantum memory, and unlimited coherence time. Methodologically, the construction integrates random linear codes with 2→1 quantum random access codes (QRACs), and employs Rényi entropy (α = 2) analysis to bound collision-entropy-driven information leakage, yielding a novel upper bound on QRAC information leakage. Key contributions include: (i) the first OTP construction achieving simulation-based security without computational assumptions; (ii) the first OTM scheme compatible with fault-tolerant quantum computing prerequisites—supporting inputs encoded via non-fault-tolerant encodings; and (iii) rigorous security proofs valid against geometrically local, constant-depth quantum adversaries.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Security and Privacy: Applications of cryptography
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

We show how to construct simulation secure one-time memories, and thus one-time programs, without computational assumptions in the presence of constraints on quantum hardware. Specifically, we build one-time memories from random linear codes and quantum random access codes (QRACs) when constrained to non-adaptive, constant depth, and $D$-dimensional geometrically-local quantum circuit for some constant $D$. We place no restrictions on the adversary's classical computational power, number of qubits it can use, or the coherence time of its qubits. Notably, our construction can still be secure even in the presence of fault tolerant quantum computation as long as the input qubits are encoded in a non-fault tolerant manner (e.g. encoded as high energy states in non-ideal hardware). Unfortunately though, our construction requires decoding random linear codes and thus does not run in polynomial time. We leave open the question of whether one can construct a polynomial time information theoretically secure one-time memory from geometrically local quantum circuits. Of potentially independent interest, we develop a progress bound for information leakage via collision entropy (Renyi entropy of order $2$) along with a few key technical lemmas for a"mutual information"for collision entropies. We also develop new bounds on how much information a specific $2 mapsto 1$ QRAC can leak about its input, which may be of independent interest as well.

Problem

• Construct simulation secure one-time memories without computational assumptions
• Secure one-time programs against geometrically local quantum adversaries
• Analyze information leakage bounds for collision entropy in QRACs

Innovation

• Uses random linear codes for security
• Employs quantum random access codes (QRACs)
• Bounds information leakage via collision entropy