论文标题
路由：对位置验证的新攻击
Code-routing: a new attack on position verification
论文作者
论文摘要
位置验证的加密任务试图通过利用量子信息和相对论因果关系的约束来验证一方在时空中的位置。一种流行的验证方案称为$ f $ -routing，涉及要求谚语根据布尔函数$ f $的价值重定向量子系统。 $ f $ - 散布计划的作弊策略需要供奉献者使用前共享的纠缠，而该计划的安全基于假设供者可以操纵多少纠缠。在这里，我们提供了一种新的作弊策略，其中量子系统被编码为秘密共享计划，并利用了秘密共享方案的授权结构来适当地指导系统。此策略使用$ O（sp_p（f））$ epr对完成了$ f $ -routing任务，其中$ sp_p（f）$是字段$ \ mathbb {z} _p $ cumputing $ f $的跨度程序的最小尺寸。这表明我们可以在允许本地预处理后的复杂性类别$ \ text {mod} _p \ text {l} $中有效地攻击$ f $ -routing方案。最好的早期结构实现了L类，据信它严格在$ \ text {mod} _p \ text {l} $的内部。我们还表明，具有指标功能的量子秘密共享方案的大小$ f_i $上界的纠缠成本为$ f $ -routing $ f_i $。
The cryptographic task of position verification attempts to verify one party's location in spacetime by exploiting constraints on quantum information and relativistic causality. A popular verification scheme known as $f$-routing involves requiring the prover to redirect a quantum system based on the value of a Boolean function $f$. Cheating strategies for the $f$-routing scheme require the prover use pre-shared entanglement, and security of the scheme rests on assumptions about how much entanglement a prover can manipulate. Here, we give a new cheating strategy in which the quantum system is encoded into a secret-sharing scheme, and the authorization structure of the secret-sharing scheme is exploited to direct the system appropriately. This strategy completes the $f$-routing task using $O(SP_p(f))$ EPR pairs, where $SP_p(f)$ is the minimal size of a span program over the field $\mathbb{Z}_p$ computing $f$. This shows we can efficiently attack $f$-routing schemes whenever $f$ is in the complexity class $\text{Mod}_p\text{L}$, after allowing for local pre-processing. The best earlier construction achieved the class L, which is believed to be strictly inside of $\text{Mod}_p\text{L}$. We also show that the size of a quantum secret sharing scheme with indicator function $f_I$ upper bounds entanglement cost of $f$-routing on the function $f_I$.
