Unclonable encryption from BB84 states: a simultaneous Goldreich-Levin reduction

2026-08-18

AI Summary

研究通过同时Goldreich-Levin归约方法，将基于BB84态的不可克隆加密方案从搜索安全提升至不可克隆不可区分性安全。

Abstract

Goldreich-Levin reductions are ubiquitous in cryptography: they convert an algorithm capable of guessing $\langle r, m \rangle$ (mod $2$) for a hidden string $m$ and a random challenge $r$, to one that is capable of extracting the entirety of $m$. Here, we describe a "simultaneous" Goldreich-Levin reduction for two entangled parties who are capable of guessing $\langle r, m \rangle$ given uniformly random identical challenges $r$. This allows to upgrade any unclonable encryption scheme satisfying "search" security to one satisfying the gold standard of unclonable "indistinguishability". As a corollary, we show that the simplest candidate unclonable encryption scheme from BB84 states satisfies unclonable indistinguishability. This result was discovered by GPT-5.6 Ultra after a few interactions. Our prompts included recent results on unclonable encryption by Ananth and Sahai, and Ragavan.

Problem

• unclonable encryption
• Goldreich-Levin reduction
• indistinguishability

Innovation

• simultaneous Goldreich-Levin reduction
• unclonable encryption
• BB84 states
• indistinguishability