Quantum Unpredictability

TL;DR

This paper introduces quantum unpredictability primitives called UPSGs, which can replace classical pseudorandom functions in cryptographic applications, showing that quantum unpredictability suffices for many cryptographic tasks.

Contribution

The paper defines UPSGs as a quantum analog of UPFs, explores their relation to PRFSs, and demonstrates their applicability in cryptographic protocols.

Findings

UPSGs can implement secure encryption and MACs.

All known PRFS applications are achievable with UPSGs.

Quantum unpredictability may be sufficient for cryptographic security.

Abstract

Unpredictable functions (UPFs) play essential roles in classical cryptography, including message authentication codes (MACs) and digital signatures. In this paper, we introduce a quantum analog of UPFs, which we call unpredictable state generators (UPSGs). UPSGs are implied by pseudorandom function-like states generators (PRFSs), which are a quantum analog of pseudorandom functions (PRFs), and therefore UPSGs could exist even if one-way functions do not exist, similar to other recently introduced primitives like pseudorandom state generators (PRSGs), one-way state generators (OWSGs), and EFIs. In classical cryptography, UPFs are equivalent to PRFs, but in the quantum case, the equivalence is not clear, and UPSGs could be weaker than PRFSs. Despite this, we demonstrate that all known applications of PRFSs are also achievable with UPSGs. They include IND-CPA-secure secret-key encryption and EUF-CMA-secure MACs with unclonable tags. Our findings suggest that, for many applications, quantum unpredictability, rather than quantum pseudorandomness, is sufficient.