Cryptography in the Common Haar State Model: Feasibility Results and Separations

TL;DR

This paper explores the quantum analogue of the common random string model, called the common Haar state model, demonstrating new cryptographic constructions and fundamental separations between different quantum primitives.

Contribution

It introduces pseudorandom function-like states secure against unbounded adversaries with bounded copies and establishes separations between these states and other quantum cryptographic primitives.

Findings

Constructed pseudorandom function-like states secure against unbounded adversaries.

Established new separations between pseudorandom states and quantum cryptographic primitives.

Proved indistinguishability results for Haar states against LOCC adversaries.

Abstract

Common random string model is a popular model in classical cryptography. We study a quantum analogue of this model called the common Haar state (CHS) model. In this model, every party participating in the cryptographic system receives many copies of one or more i.i.d Haar random states. We study feasibility and limitations of cryptographic primitives in this model and its variants: - We present a construction of pseudorandom function-like states with security against computationally unbounded adversaries, as long as the adversaries only receive (a priori) bounded number of copies. By suitably instantiating the CHS model, we obtain a new approach to construct pseudorandom function-like states in the plain model. - We present separations between pseudorandom function-like states (with super-logarithmic length) and quantum cryptographic primitives, such as interactive key agreement and bit commitment, with classical communication. To show these separations, we prove new results on the indistinguishability of identical versus independent Haar states against LOCC (local operations, classical communication) adversaries.