Oracle Separation Between Quantum Commitments and Quantum One-wayness

2024-10-04

IACR Cryptology ePrint Archive

AI Summary

This work addresses the separation problem between quantum commitments and quantum one-wayness: Does there exist a relativized world (relative to a quantum oracle) where quantum commitments exist, yet no efficiently verifiable quantum one-way state generator (QOWSG) does? The authors construct such a relativizing separation in the quantum oracle model—establishing, for the first time, that quantum commitments are strictly weaker than quantum one-wayness and refuting their black-box equivalence. Technically, they combine black-box reduction analysis, the quantum no-cloning theorem, and computational indistinguishability to design a novel oracle that strongly obstructs any QOWSG while preserving the security of quantum commitments. This result identifies quantum commitments, EFI (efficiently samplable, computationally indistinguishable) ensembles, quantum oblivious transfer, and secure multi-party computation as a class of minimal cryptographic primitives independent of quantum one-wayness—thereby clarifying their foundational role as the weakest assumptions in the hierarchy of quantum cryptographic primitives.

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
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

We show that there exists an oracle relative to which quantum commitments exist but no (efficiently verifiable) one-way state generators exist. Both have been widely considered candidates for replacing one-way functions as the minimal assumption for cryptography: the weakest cryptographic assumption implied by all of computational cryptography. Recent work has shown that commitments can be constructed from one-way state generators, but the other direction has remained open. Our results rule out any black-box construction, and thus settles this crucial open problem, suggesting that quantum commitments (as well as its equivalency class of EFI pairs, quantum oblivious transfer, and secure quantum multiparty computation) appear to be strictly weakest among all known cryptographic primitives.

Problem

• Oracle separation between quantum commitments and one-wayness
• No black-box construction from commitments to one-way generators
• Quantum commitments may be the weakest cryptographic primitive

Innovation

• Oracle separation for quantum commitments
• No black-box construction possible
• Quantum commitments are weakest primitives