Pseudoentanglement supports secure quantum cryptography assumptions
Computational Cryptography from Pseudoentanglement
Cryptography and Security
Summary
Creating truly secure communication methods is tricky, especially with quantum computers coming along. The paper explores a connection between a quantum property called pseudoentanglement and the foundations of computational cryptography used to secure information. The authors show that if certain types of pseudoentangled states can be efficiently created, then key cryptographic constructs known as EFI pairs must also exist, and vice versa. This means that ideas from quantum entanglement theory and computational cryptography can inform and strengthen each other.
What this means in practice
- •For quantum cryptography engineers: Design cryptographic protocols that rely on pseudoentanglement assumptions for quantum-secured communications.
- •For quantum hardware designers: Create efficient quantum state generators that produce pseudoentangled states useful for secure quantum cryptography.
A theory result. No direct application yet.
Authors
Ilia Ryzov, Manuel Goulão, Faedi Loulidi, David Elkouss
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.