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."