F2上的非局部搜索到决策归约

中文摘要 AI 辅助

非局部搜索到决策问题是指：两个非通信方获得均匀随机字符串x∈F₂ⁿ的二分编码的两个份额后，能否在无需本地测量即可共同恢复x的情况下，共同预测同一随机内积奇偶性⟨r,x⟩。我们证明，若双方通过本地测量共同恢复x的最优概率为p，则他们共同回答同一奇偶性挑战的概率至多为min{1,1/2 +5p^(1/22)}。该结果由不可克隆加密和量子拷贝保护的应用驱动，证明是信息论性质的，未提供高效提取器，证明与阐述过程得到了ChatGPT（使用GPT-5.6 Sol Pro及Ultra推理模式下的Codex）的协助。

英文摘要

Non-local search-to-decision asks whether the difficulty of two non-communicating (non-local) parties both predicting x given a bipartite state (that possibly depends on x) implies the difficulty of non-local parties both predicting the inner product <r,x>, for a uniformly random r. This problem and its variants have been extensively studied and are motivated by applications to unclonable cryptographic primitives such as unclonable encryption and copy-protection. We study the identical-challenge setting, in which both parties receive the same uniformly random vector r, in contrast to the independently sampled challenges considered in prior works. We demonstrate positive results for the cases when $x$ and r are vectors over F_2 and over large finite fields. As a consequence, we obtain a conceptually different proof of indistinguishability-secure unclonable encryption.

发表机构

• UCSB（加州大学圣塔芭芭拉分校）

机构由 AI 辅助整理，请以论文原文为准。