Conditional disclosure of secrets with quantum resources

TL;DR

This paper introduces and analyzes the quantum analogue of the classical conditional disclosure of secrets (CDS) primitive, called CDQS, exploring how quantum resources like entanglement impact privacy and communication complexity.

Contribution

It systematically studies CDQS, establishing fundamental properties, lower bounds, and its relation to quantum position-verification schemes, advancing understanding of quantum cryptographic primitives.

Findings

Established lower bounds on entanglement and communication for CDQS.

Derived quantum analogues of classical CDS results.

Linked CDQS properties to the security of quantum position-verification.

Abstract

The conditional disclosure of secrets (CDS) primitive is among the simplest cryptographic settings in which to study the relationship between communication, randomness, and security. CDS involves two parties, Alice and Bob, who do not communicate but who wish to reveal a secret $z$ to a referee if and only if a Boolean function $f$ has $f(x,y)=1$. Alice knows $x,z$, Bob knows $y$, and the referee knows $x,y$. Recently, a quantum analogue of this primitive called CDQS was defined and related to $f$-routing, a task studied in the context of quantum position-verification. CDQS has the same inputs, outputs, and communication pattern as CDS but allows the use of shared entanglement and quantum messages. We initiate the systematic study of CDQS, with the aim of better understanding the relationship between privacy and quantum resources in the information theoretic setting. We begin by looking for quantum analogues of results already established in the classical CDS literature. Doing so we establish a number of basic properties of CDQS, including lower bounds on entanglement and communication stated in terms of measures of communication complexity. Because of the close relationship to the $f$-routing position-verification scheme, our results have relevance to the security of these schemes.