MicroCrypt Assumptions with Quantum Input Sampling and Pseudodeterminism: Constructions and Separations

2025-05-20

IACR Cryptology ePrint Archive

AI Summary

This work investigates quantum cryptographic primitives under two natural relaxations: (1) quantum-sampled inputs (QS), where inputs are generated by quantum algorithms instead of classical uniform sampling; and (2) ⊥-pseudodeterminism, permitting a negligible (inverse-polynomial) fraction of input-output pairs to output a special symbol ⊥. Method: We introduce and formally model the combined QS-and-⊥ relaxation framework, characterizing its hierarchical structure within MicroCrypt. Using black-box separation techniques, we establish strict separations between relaxed and classical uniform models. Results: We prove the equivalence of bounded-query logarithmic PRS^qs, logarithmic PRS^qs, and PRG^qs. We construct an implication chain PRG^qs ← ⊥-PRG ← log-PRS. Crucially, we demonstrate that several primitives are strictly weaker under these relaxations than in the classical uniform setting—revealing fundamental limitations. Our results provide new theoretical foundations for the feasibility frontier of quantum cryptography.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Satisfiability
• Knowledge Representation and Reasoning: Qualitative Reasoning

Application Category

• Security and Privacy: Applications of cryptography
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Economics, Online Markets and Human Computation: Economic aspects of blockchain and cryptocurrencies

Abstract

We investigate two natural relaxations of quantum cryptographic primitives. The first involves quantum input sampling, where inputs are generated by a quantum algorithm rather than sampled uniformly at random. Applying this to pseudorandom generators ($ extsf{PRG}$s) and pseudorandom states ($ extsf{PRS}$s), leads to the notions denoted as $ extsf{PRG}^{qs}$ and $ extsf{PRS}^{qs}$, respectively. The second relaxation, $ot$-pseudodeterminism, relaxes the determinism requirement by allowing the output to be a special symbol $ot$ on an inverse-polynomial fraction of inputs. We demonstrate an equivalence between bounded-query logarithmic-size $ extsf{PRS}^{qs}$, logarithmic-size $ extsf{PRS}^{qs}$, and $ extsf{PRG}^{qs}$. Moreover, we establish that $ extsf{PRG}^{qs}$ can be constructed from $ot$-$ extsf{PRG}$s, which in turn were built from logarithmic-size $ extsf{PRS}$. Interestingly, these relations remain unknown in the uniform key setting. To further justify these relaxed models, we present black-box separations. Our results suggest that $ot$-pseudodeterministic primitives may be weaker than their deterministic counterparts, and that primitives based on quantum input sampling may be inherently weaker than those using uniform sampling. Together, these results provide numerous new insights into the structure and hierarchy of primitives within MicroCrypt.

Problem

• Relaxing quantum cryptographic primitives with quantum input sampling
• Exploring pseudodeterminism by allowing outputs to be a special symbol
• Investigating black-box separations and hierarchy of MicroCrypt primitives

Innovation

• Quantum input sampling for PRG and PRS
• Bot-pseudodeterminism relaxes output determinism
• Black-box separations justify relaxed models