We explore the cryptographic power of arbitrary shared physical resources. The most general such resource is access to a fresh entangled quantum state at the outset of each protocol execution. We call this the Common Reference Quantum State (CRQS) model, in analogy to the well-known Common Reference String (CRS). The CRQS model is a natural generalization of the CRS model but appears to be more powerful: in the two-party setting, a CRQS can sometimes exhibit properties associated with a Random Oracle queried once by measuring a maximally entangled state in one of many mutually unbiased bases. We formalize this notion as a Weak One-Time Random Oracle (WOTRO), where we only ask of the $m$--bit output to have some randomness when conditioned on the $n$--bit input. We show that when $n-m\in\omega(\lg n)$, any protocol for WOTRO in the CRQS model can be attacked by an (inefficient) adversary. Moreover, our adversary is efficiently simulatable, which rules out the possibility of proving the computational security of a scheme by a black-box reduction to a cryptographic game assumption. On the other hand, we introduce a non-game quantum assumption for hash functions that implies WOTRO in the CRQ\$ model (where the CRQS consists only of EPR pairs). We first build a statistically secure WOTRO protocol where $m=n$, then hash the output. The impossibility of WOTRO has the following consequences. First, we show the black-box impossibility of a quantum Fiat-Shamir transform, extending the impossibility result of Bitansky et al. (TCC '13) to the CRQS model. Second, we show a black-box impossibility result for a strenghtened version of quantum lightning (Zhandry, Eurocrypt '19) where quantum bolts have an additional parameter that cannot be changed without generating new bolts.
翻译:我们探索了任意共享物理资源的加密能力。 最一般的这种资源是在每次执行协议时, 在每次协议执行开始时, 进入一个新缠绕的量子状态。 我们称之为“ 共同参考量量量子( CRQS ) ” 模式, 类似于众所周知的“ 共同参考值字符串( CRS ) ” 。 CRQS 模式是CRS 模式的自然概括化, 但似乎更强大: 在两方环境下, CRQS 有时会显示与随机 Oracle 相关的属性, 在一个相互不偏倚的基地中, 测量一个最深的状态。 我们把这个概念正式化为“WOright- Oright Ormal Ormal ” (WO) (WO) 。 我们只要求以 $- bitm 输出量子( CRQR) 模式为条件时, 将Oright Ormal Oral 的数值值变成另一个版本。 我们显示的是“ RO ” (WQQQR ) 的“Oral- ” 模式” 。 我们的“ Oral- dal- dalal 的数值” 格式” 版本, 变换了一个“Odal- 。