Computational Cryptography from Pseudoentanglement

2026-09-24

AI Summary

This study investigates the intrinsic connection between pseudo-entanglement and computational cryptographic EFI pairs, aiming to harness computational entanglement-theoretic resources for cryptography. Methodologically, it integrates techniques from computational entanglement theory and quantum information theory by introducing novel lemmas and analyzing mixed-state distinguishability conditions to bridge these domains. The primary contributions include establishing, for the first time, the equivalence between pseudo-entanglement and EFI pairs, proving that the efficient generation of pseudo-entanglement is both necessary and sufficient for the existence of EFI pairs. Furthermore, this work reveals a novel relationship between computational entanglement measures and state distances, alongside the first continuity relation in this context. These results establish both concepts as minimal assumptions for cryptography, providing foundational perspectives and technical tools for the field.

Abstract

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.

Problem

• pseudoentanglement
• computational cryptography
• EFI pairs
• computational entanglement
• minimal assumptions

Innovation

• Pseudoentanglement
• EFI pairs
• Computational cryptography
• Computational entanglement
• Quantum information