Consider a group of people who want to know the “rich list” among them, namely the ranking in terms of their total assets, without revealing any information about the actual value of their assets. This can be achieved by a “secure ranking computation,” which was first considered by Jiang and Gong (CT-RSA 2006); they constructed a secure ranking computation protocol based on a public-key cryptosystem. In this paper, instead of using a public-key cryptosystem, we use a deck of physical cards to provide secure ranking computation protocols. Therefore, our card-based protocols do not rely on computers, and they are simple and easy for humans to implement. Specifically, we design four protocols considering tradeoffs between the number of cards and the number of shuffles required to execute the protocols. We also present a guide to choose an appropriate protocol according to the number of people participating in the protocol and the size of the input range. To be precise, whereas our protocols make all players know the rich list, the Jiang–Gong scheme makes each player know his/her rank only; to achieve the same task (as the Jiang–Gong scheme) using a deck of cards is an intriguing open problem.

考虑一群想知道其中的“富豪榜”的人，即以总资产计的排名，而又不透露其资产实际价值的任何信息。这可以通过“安全排名计算”来实现，这是江和龚首先考虑的（CT-RSA，2006年）。他们构建了基于公共密钥密码系统的安全排名计算协议。在本文中，我们使用一副物理卡来提供安全的排名计算协议，而不是使用公共密钥密码系统。因此，我们的基于卡的协议不依赖于计算机，并且对于人类而言，它们是简单易行的。具体来说，我们设计了四种协议，其中考虑了卡数和执行协议所需的随机播放次数之间的折衷。我们还提供了根据参与协议的人数和输入范围的大小来选择合适的协议的指南。确切地说，尽管我们的协议使所有玩家都知道了富翁名单，但江公计划却使每个玩家仅知道自己的排名；使用一副扑克牌来完成相同的任务（如江公计划）是一个有趣的开放问题。