Pseudorandom quantum authentication

TL;DR

This paper introduces a cost-effective quantum authentication scheme based on pseudorandom unitaries, providing security against quantum polynomial-time adversaries with weaker assumptions than classical cryptography.

Contribution

It presents the first pseudorandom quantum authentication scheme that requires only polylogarithmic circuit depth and minimal shared keys, even without quantum-secure one-way functions.

Findings

Scheme guarantees indistinguishability from maximally mixed states

Allows efficient verification and recovery of original states

Constructs cryptographic primitives like verifiable pseudorandom density matrices

Abstract

We introduce the pseudorandom quantum authentication scheme (PQAS), an efficient method for encrypting quantum states that relies solely on the existence of pseudorandom unitaries (PRUs). The scheme guarantees that for any eavesdropper with quantum polynomial-time (QPT) computational power, the encrypted states are indistinguishable from the maximally mixed state. Furthermore, the receiver can verify that the state has not been tampered with and recover the original state with asymptotically unit fidelity. Our scheme is cost-effective, requiring only polylogarithmic circuit depth and a single shared key to encrypt a polynomial number of states. Notably, the PQAS can potentially exist even without quantum-secure one-way functions, requiring fundamentally weaker computational assumptions than semantic classical cryptography. Additionally, PQAS is secure against attacks that plague protocols based on QPT indistinguishability from Haar random states, such as chosen-plaintext attacks (CPAs) and attacks that reveal meta-information such as quantum resources. We relate the amount of meta-information that is leaked to quantum pseudoresources, giving the concept a practical meaning. As an application, we construct important cryptographic primitives, such as verifiable pseudorandom density matrices (VPRDMs), which are QPT-indistinguishable from random mixed states while being efficiently verifiable via a secret key, as well as verifiable noise-robust EFI pairs and one-way state generators (OWSGs). Our results establish a new paradigm of quantum information processing with weaker computational assumptions.