Certified Randomness with Optimal Rate

2026-09-30

AI Summary

This study addresses the limitations of existing quantum randomness certification protocols, which suffer from low generation rates or reliance on trusted seeds. To overcome these constraints, this work proposes a novel quantum protocol that eliminates the need for trusted seeds. By leveraging the Quantum Random Oracle Model (QROM) and unconditionally secure cryptographic techniques, it achieves, for the first time, an optimal entropy rate approaching unity without requiring a trusted randomness source, accompanied by a rigorous proof of the conditional min-entropy. This contribution significantly improves upon the weak randomness results established by Coladangelo et al. and resolves an open problem posed by Aaronson, thereby realizing the certification of random bits at an optimal rate.

Abstract

The generation of certified random bits is an emerging near-term application of quantum computers. Potential applications, such as randomness beacons and CRS generation, require nearly uniform randomness, whose rate (the ratio of min-entropy to bitlength) is ~ 1. However, existing protocols for certified randomness either produce weakly random strings with rate o(1), or they require a trusted random seed. We show how to certify randomness with the optimal rate ~ 1 without requiring any trusted randomness from the verifier. Our protocol is secure unconditionally in the quantum random oracle model (QROM). This improves the result of Coladangelo et al., who certified weakly random strings unconditionally in the QROM, and answers a question posed by Aaronson and Hung. We also define and construct a proof of conditional min-entropy, which certifies optimal min-entropy even conditioned on an adversarially chosen transcript. We show an application of this primitive to randomness beacons, where each pulse should have high min-entropy conditioned on all previous messages.

Problem

• certified randomness
• optimal rate
• min-entropy
• quantum random oracle model
• randomness beacon

Innovation

• Certified Randomness
• Quantum Random Oracle Model
• Optimal Rate
• Conditional Min-Entropy
• Randomness Beacons