Signatures From Pseudorandom States via $\bot$-PRFs

TL;DR

This paper introduces $ot$-PRG and $ot$-PRF, new cryptographic primitives based on quantum pseudorandomness, enabling quantum digital signatures with classical keys and tamper-resilient encryption.

Contribution

It defines $ot$-PRG and $ot$-PRF, constructs them from pseudo-deterministic PRGs, and applies these to create quantum digital signatures with classical keys and secure encryption.

Findings

Constructed $ot$-PRG from pseudo-deterministic PRG

Built $ot$-PRF from $ot$-PRG

Achieved quantum digital signatures with classical keys

Abstract

Different flavors of quantum pseudorandomness have proven useful for various cryptographic applications, with the compelling feature that these primitives are potentially weaker than post-quantum one-way functions. Ananth, Lin, and Yuen (2023) have shown that logarithmic pseudorandom states can be used to construct a pseudo-deterministic PRG: informally, for a fixed seed, the output is the same with $1-1/poly$ probability. In this work, we introduce new definitions for $\bot$-PRG and $\bot$-PRF. The correctness guarantees are that, for a fixed seed, except with negligible probability, the output is either the same (with probability $1-1/poly$) or recognizable abort, denoted $\bot$. Our approach admits a natural definition of multi-time PRG security, as well as the adaptive security of a PRF. We construct a $\bot$-PRG from any pseudo-deterministic PRG and, from that, a $\bot$-PRF. Even though most mini-crypt primitives, such as symmetric key encryption, commitments, MAC, and length-restricted one-time digital signatures, have been shown based on various quantum pseudorandomness assumptions, digital signatures remained elusive. Our main application is a (quantum) digital signature scheme with classical public keys and signatures, thereby addressing a previously unresolved question posed in Morimae and Yamakawa's work (Crypto, 2022). Additionally, we construct CPA secure public-key encryption with tamper-resilient quantum public keys.