A card-based secure computation protocol is a method for $n$ parties to compute a function $f$ on their private inputs $(x_1,\ldots,x_n)$ using physical playing cards, in such a way that the suits of revealed cards leak no information beyond the value of $f(x_1,\ldots,x_n)$. A \textit{single-shuffle full-open} protocol is a minimal model of card-based secure computation in which, after the parties place face-down cards representing their inputs, a single shuffle operation is performed and then all cards are opened to derive the output. Despite the simplicity of this model, the class of functions known to admit single-shuffle full-open protocols has been limited to a few small examples. In this work, we prove for the first time that every function admits a single-shuffle full-open protocol. We present two constructions that offer a trade-off between the number of cards and the complexity of the shuffle operation. These feasibility results are derived from a novel connection between single-shuffle full-open protocols and a cryptographic primitive known as \textit{Private Simultaneous Messages} protocols, which has rarely been studied in the context of card-based cryptography. We also present variants of single-shuffle protocols in which only a subset of cards are revealed. These protocols reduce the complexity of the shuffle operation compared to existing protocols in the same setting.

翻译：卡牌安全计算协议是一种利用实体扑克牌使$n$方计算其私有输入$(x_1,\ldots,x_n)$上函数$f$的方法，该方法确保公开牌的花色除$f(x_1,\ldots,x_n)$的值外不泄露任何信息。\textit{单次洗牌全公开}协议是卡牌安全计算的一种极简模型：参与方放置代表其输入的牌面朝下的卡牌后，仅执行一次洗牌操作，随后翻开所有卡牌以推导输出。尽管该模型结构简单，已知适用于单次洗牌全公开协议的函数类此前仅限于少数小型示例。本研究中，我们首次证明所有函数均存在单次洗牌全公开协议。我们提出两种构造方案，在卡牌数量与洗牌操作复杂度之间实现权衡。这些可行性结论源于单次洗牌全公开协议与密码学原语\textit{私有同步消息}协议之间的新颖关联，该关联在卡牌密码学领域鲜有研究。我们还提出了仅公开部分卡牌的单次洗牌协议变体。相较于同场景下的现有协议，这些协议降低了洗牌操作的复杂度。