How to Play Mastermind Without Game Master
摘要
Mastermind is a classic code-guessing game in which a game master secretly selects a multi-digit code with no duplicates and a codebreaker iteratively submits candidate codes. For each submission, the game master compares it to the secret code and tells the number of “hits” and “blows” as feedback. In this paper, we design a novel method to play Mastermind without a game master using card-based cryptographic techniques. In particular, we design feedback protocols and a code generation protocol, where the former outputs the number of hits and blows without revealing the code itself, and the latter outputs a sequence of cards representing a code chosen uniformly at random. By using these protocols, we can enjoy Mastermind without the need for a game master. All of the proposed protocols are extremely simple and can be executed in real gameplay. This enables people to learn fundamental principles of cryptography through playing Mastermind.