Computational Cryptography from Pseudoentanglement
Researchers show efficient pseudoentanglement implies EFI pairs, tying it to minimal quantum-crypto assumptions.
An arXiv cs.CR paper relates pseudoentanglement to computational cryptography through EFI pairs. The authors show that pseudoentanglement under two operational definitions, with efficient state generation, is sufficient for EFI pairs, and with a prior converse they establish equivalence under the second definition. Supporting lemmas connect computational entanglement measures to distances between states and to distinguishability of mixtures. They also give the first continuity relation for a computational entanglement measure.
- Efficient pseudoentanglement is shown to imply EFI pairs
- Equivalence holds under one operational definition
- Authors prove a continuity result for a computational entanglement measure
- Work links quantum information theory with minimal crypto assumptions
Full article248 words · extracted from arxiv.org · click to collapse
The advent of pseudoentanglement and computational entanglement theory bootstrapped a wave of research at the intersection of computer science and information theory. In parallel, computational cryptography has undergone substantial development, prompted by the introduction of pseudorandom states and followed by the establishment of a baseline for the computational hardness required for quantum cryptography, from which EFI pairs emerge as a central primitive. We study the connection between pseudoentanglement and computational cryptography through EFI pairs. Our goal is to enable the use of resources arising from computational entanglement theory in the field of cryptography. For this, we establish the relation between operational instances of pseudoentanglement and the hierarchy of minimal assumptions for computational cryptography. We show that the existence of pseudoentanglement under two different operational definitions, with efficient state generation, is a sufficient condition for the existence of EFI pairs. Combined with a previously established result that the converse also holds under the second definition, this allows us to also demonstrate their equivalence. This places pseudoentanglement alongside other minimal assumptions in cryptography, not only offering an alternative perspective on this fundamental problem, but also building a bridge that allows insights from either area to inform the other. While proving these theorems, we introduce and demonstrate technical lemmas in quantum information and computational entanglement theory, relating the computational entanglement measures to the distance between states, establishing distinguishing conditions for mixtures of two families given pairwise distances between their states, and demonstrating the first continuity relation for a computational entanglement measure.
Text extracted automatically; images, tables and formatting may be missing. Original: https://arxiv.org/abs/2609.29917