Another Use of the Five-Card Trick: Card-Minimal Secure Three-Input Majority Function Evaluation

Starting from the five-card trick proposed by Den Boer (EUROCRYPT’ 89), many card-based protocols performing secure multiparty computations with a deck of physical cards have been devised. However, the five-card trick is considered to be still the most elegant, easy-to-understand and practical protocol, which enables two players to securely evaluate the AND value of their private inputs using five cards. In other words, for more than thirty years, in the research area of card-based cryptography, we have not discovered any protocols that are as simple and beautiful as the five-card trick. In this study, making use of the five-card trick, we design a novel easy-to-understand protocol which securely evaluates the three-input majority function using six cards. That is, by applying a simple shuffle, we reduce a secure three-input majority computation to evaluating the AND value. By virtue of a direct application of the five-card trick, our proposed majority protocol is extremely simple enough for lay-people to execute. In addition, one advantage is that ordinary people such as high school students will be able to learn the concept of logical AND/OR operations and the majority function as well as their relationship through our majority protocol, providing a nice tool of pedagogical significance. Thus, we believe that our new protocol is no less practical and beautiful than the five-card trick.