Card-based cryptography uses physical playing cards to construct protocols for secure multi-party computation. Existing card-based protocols employ various types of shuffles, some of which are easy to implement in practice while others are considerably more complex. In this paper, we classify shuffle operations into several levels according to their implementation complexity. We motivate this hierarchy from both practical and theoretical perspectives, and prove separation results between several levels by showing that certain shuffles cannot be realized using only operations from lower levels. Finally, we propose a new complexity measure for evaluating card-based protocols based on this hierarchy.

翻译：纸牌密码学利用实体扑克牌构建安全多方计算的协议。现有纸牌协议采用了多种洗牌操作，其中部分在实际应用中易于实现，而另一些则复杂得多。本文根据实现复杂度将洗牌操作划分为若干层级。我们从实践与理论双重角度论证该层级划分的合理性，并通过证明特定洗牌操作无法仅由低层级操作实现，揭示层级间的分离关系。最终，我们基于此层级提出一种评估纸牌协议的新复杂度度量标准。