Certified Randomness without Structure Against Shallow-Query Adversaries

2026-08-25

AI Summary

本文无条件证明了Yamakawa-Zhandry认证随机性协议的安全性，对抗低查询深度的量子对手，无需依赖未证实的Aaronson-Ambainis猜想。

Abstract

In a recent breakthrough, Yamakawa and Zhandry (J. ACM 2024) constructed a proof of quantumness in the quantum random oracle model (QROM) in which the quantum prover samples a codeword preimage of a publicly computable function H. They conjectured that given any H, a successful prover must sample their preimage from a high-entropy distribution over possible answers. If true, this would give a certifiable randomness protocol in the quantum random oracle model. As partial evidence for their conjecture, Yamakawa and Zhandry proved the security of their certifiable randomness protocol assuming the Aaronson-Ambainis conjecture. We prove the security of the certifiable randomness protocol of Yamakawa-Zhandry unconditionally, without relying on the unproven Aaronson-Ambainis conjecture, against low query-depth quantum adversaries: specifically, adversaries that make up to o(\log λ) adaptive quantum queries to the random oracle.

Problem

• Certifiable Randomness
• Quantum Adversaries
• Query Depth
• Random Oracle Model

Innovation

• Certified Randomness
• Quantum Random Oracle Model (QROM)
• Low Query-Depth Quantum Adversaries