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 fully 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 CRQS 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 fully-black-box impossibility of a quantum Fiat-Shamir transform, extending the impossibility result of Bitansky et al. (TCC 2013) to the CRQS model. Second, we show a fully-black-box impossibility result for a strenghtened version of quantum lightning (Zhandry, Eurocrypt 2019) where quantum bolts have an additional parameter that cannot be changed without generating new bolts. Our results also apply to $2$-message protocols in the plain model.

翻译：我们探讨了任意共享物理资源的密码学能力。最一般的此类资源是每次协议执行开始时访问一个全新的纠缠量子态。我们将此模型称为公共参考量子态（CRQS）模型，类比于众所周知的公共参考串（CRS）模型。CRQS模型是CRS模型的自然推广，但似乎更强大：在双方设定中，CRQS有时能表现出与随机预言机（Random Oracle）相关的性质——该随机预言机通过测量最大纠缠态在多个互无偏基中的一个基上的结果，被查询一次。我们将此概念形式化为弱一次性随机预言机（WOTRO），其中仅要求当条件于$n$-比特输入时，$m$-比特输出具有一定的随机性。我们证明，当$n-m\in\omega(\lg n)$时，CRQS模型中的任何WOTRO协议都可被（非有效）对手攻击。此外，我们的对手是可有效模拟的，这排除了通过完全黑盒归约到密码学游戏假设来证明方案计算安全性的可能性。另一方面，我们引入了一个针对哈希函数的非游戏量子假设，该假设在CRQS模型（其中CRQS仅由EPR对组成）中蕴含WOTRO。我们首先构建了一个统计安全的WOTRO协议（其中$m=n$），然后对输出进行哈希。WOTRO的不可行性具有以下后果。首先，我们证明了量子Fiat-Shamir变换的完全黑盒不可行性，将Bitansky等人（TCC 2013）的不可行性结果扩展到CRQS模型。其次，我们证明了量子闪电（Zhandry, Eurocrypt 2019）强化版本的完全黑盒不可行性结果，其中量子螺栓具有一个额外参数，该参数在未生成新螺栓的情况下无法更改。我们的结果也适用于普通模型中的2-消息协议。