Exponentially Secure Inefficiently-Verifiable One-Way State Generators and Their Equivalence to Efficiently Indistinguishable Quantum State Pairs

Core Concepts

Exponentially secure inefficiently-verifiable one-way state generators (IV-OWSGs) are precisely equivalent to efficiently indistinguishable (EFI) quantum state pairs, with an exponential security loss in the reduction.

Abstract

The paper investigates the relationship between two fundamental primitives in quantum cryptography: one-way state generators (OWSGs) and efficiently indistinguishable (EFI) quantum state pairs. Key highlights: The authors introduce a weaker variant of OWSGs called inefficiently-verifiable one-way state generators (IV-OWSGs), where the verification algorithm is not required to be efficient. They show that IV-OWSGs and EFI pairs are equivalent, but with an exponential loss in the reduction. Specifically, they prove that (mixed) IV-OWSGs imply EFI pairs, and EFI pairs imply (mixed) IV-OWSGs, with the latter implication having an exponential security loss. Crucially, all their results hold in the general setting where the state generation algorithm of OWSGs can output mixed states, in contrast to prior work that only considered pure states. As a consequence of their results, the authors establish that exponentially secure (mixed) OWSGs imply a number of useful cryptographic primitives, such as non-interactive commitments, quantum computational zero knowledge, oblivious transfer, and general multiparty computation. The proof techniques involve shadow tomography and careful analysis of the statistical and computational properties of the constructed commitment scheme.

Stats

There are no key metrics or important figures used to support the author's key logics.

Quotes

"If EFI pairs exist, then IV-OWSGs exist." "Exponentially secure IV-OWSGs imply EFI pairs, with an exponential security loss in the reduction."

Key Insights Distilled From

Exponential Quantum One-Wayness and EFI Pairs

by Giulio Malav... at arxiv.org 04-23-2024

https://arxiv.org/pdf/2404.13699.pdf

Deeper Inquiries

What are the implications of the equivalence between IV-OWSGs and EFI pairs for the foundations of quantum cryptography

The equivalence between Inefficiently-Verifiable One-Way State Generators (IV-OWSGs) and Exponentially Secure Fully Insecure (EFI) pairs has significant implications for the foundations of quantum cryptography. It sheds light on the relationship between these fundamental primitives and provides insights into the minimal assumptions required for various cryptographic applications in the quantum realm. This equivalence suggests that the security and functionality of EFI pairs can be achieved through the construction of IV-OWSGs, showcasing the interconnectedness of different cryptographic primitives in quantum settings. Understanding this equivalence helps in establishing a unified framework for quantum cryptographic protocols and systems, enabling the development of more efficient and secure quantum cryptographic schemes.

Can the exponential security loss in the reduction from IV-OWSGs to EFI pairs be improved, or is it inherent to the construction

The exponential security loss in the reduction from IV-OWSGs to EFI pairs is a crucial aspect of the construction and is inherent to the nature of the transformation. This loss signifies the trade-off between the security guarantees provided by IV-OWSGs and the computational indistinguishability properties of EFI pairs. While it may seem like a significant drawback, it is a necessary compromise to establish the equivalence between these primitives. Improving this security loss without compromising the integrity of the cryptographic constructions would require innovative approaches and potentially new insights into the underlying principles of quantum cryptography. As of now, the exponential security loss serves as a key characteristic of the relationship between IV-OWSGs and EFI pairs.

Are there any other cryptographic primitives that can be constructed from exponentially secure OWSGs, beyond what is mentioned in the paper

Exponentially secure One-Way State Generators (OWSGs) have the potential to be leveraged for the construction of various cryptographic primitives beyond what is explicitly mentioned in the paper. Some of these primitives could include quantum key distribution protocols, quantum secure multi-party computation schemes, quantum digital signatures, and quantum secure communication channels. By utilizing the security properties of exponentially secure OWSGs, it may be possible to enhance the security and efficiency of these cryptographic functionalities in quantum communication and computation scenarios. Exploring the broader applicability of exponentially secure OWSGs in cryptographic protocols could lead to advancements in quantum secure communication and information processing.