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：卡牌密码学利用实体扑克牌构造用于安全多方计算的协议。现有卡牌协议采用多种类型的洗牌操作，其中部分在实际中易于实现，而另一些则相当复杂。本文根据洗牌操作的实现复杂度将其划分为若干层级。我们从实践与理论两个角度论证该层级的必要性，并通过证明某些洗牌无法仅用低层级操作实现，得出层级间的分离结果。最后，我们基于该层级提出一种评估卡牌协议的新复杂度度量指标。