Local contextuality-based self-tests are sufficient for randomness expansion secure against quantum adversaries

TL;DR

This paper introduces a quantum randomness expansion protocol based on local contextuality self-tests, which is secure against quantum adversaries and semi-device-independent, advancing quantum cryptography security.

Contribution

It demonstrates that local contextuality-based self-tests are sufficient for secure randomness expansion against quantum adversaries, with proven asymptotic security guarantees.

Findings

Protocol produces randomness close to uniform and private

Security is asymptotic with respect to the number of bits generated

Scheme is semi-device-independent, relying on self-test assumptions

Abstract

In quantum cryptography, secure randomness expansion involves using a short private string of random bits to generate a longer one, even in the presence of an adversary who may have access to quantum resources. In this work, we demonstrate that local contextuality-based self-tests are sufficient to construct a randomness expansion protocol that is secure against computationally unbounded quantum adversaries. Our protocol is based on self-testing from non-contextuality inequalities and we prove that our scheme asymptotically produces secure random numbers which are $\mathcal{O}(m\sqrt{\epsilon})$-close to uniformly distributed and private, where $\epsilon$ is the robustness parameter of the self-test and $m$ is the length of the generated random bit string. Our protocol is semi-device-independent in the sense that it inherits any assumptions necessary for the underlying self-test.