Simultaneous Haar Indistinguishability with Applications to Unclonable Cryptography

TL;DR

This paper introduces a new quantum indistinguishability problem called simultaneous Haar indistinguishability and uses it to construct the first unclonable encryption scheme with quantum keys in the plain model, advancing quantum cryptography.

Contribution

It presents a novel reduction from unclonable encryption to a quantum state discrimination problem, providing the first such construction in the plain model.

Findings

Proves that non-communicating entangled players cannot distinguish certain Haar random states.

Constructs unclonable encryption with quantum decryption keys in the plain model.

Implications for single-decryptor encryption and leakage-resilient secret sharing.

Abstract

Unclonable cryptography is concerned with leveraging the no-cloning principle to build cryptographic primitives that are otherwise impossible to achieve classically. Understanding the feasibility of unclonable encryption, one of the key unclonable primitives, satisfying indistinguishability security in the plain model has been a major open question in the area. So far, the existing constructions of unclonable encryption are either in the quantum random oracle model or are based on new conjectures. We present a new approach to unclonable encryption via a reduction to a novel question about nonlocal quantum state discrimination: how well can non-communicating -- but entangled -- players distinguish between different distributions over quantum states? We call this task simultaneous state indistinguishability. Our main technical result is showing that the players cannot distinguish between each player receiving independently-chosen Haar random states versus all players receiving the same Haar random state. We leverage this result to present the first construction of unclonable encryption satisfying indistinguishability security, with quantum decryption keys, in the plain model. We also show other implications to single-decryptor encryption and leakage-resilient secret sharing.