This paper introduces mathematical optimization as a new method for proving impossibility results in the field of card-based cryptography. While previous impossibility proofs were often limited to cases involving a small number of cards, this new approach establishes results that hold for a large number of cards. The research focuses on single-cut full-open (SCFO) protocols, which consist of performing one random cut and then revealing all cards. The main contribution is that for any three-variable Boolean function, no new SCFO protocols exist beyond those already known, under the condition that all additional cards have the same color. The significance of this work is that it provides a new framework for proving impossibility results and delivers a proof that is valid for any number of cards, as long as all additional cards have the same color.

翻译：本文引入数学优化作为证明卡牌密码学领域不可行性结果的新方法。以往的不可能性证明通常局限于涉及少量卡牌的情形，而这一新方法建立了适用于大量卡牌的结果。研究聚焦于单切全开协议，该协议包含执行一次随机切牌并随后揭示所有卡牌。主要贡献在于：对于任意三变量布尔函数，在附加卡牌均为同色的条件下，除已知协议外不存在新的单切全开协议。本工作的意义在于提供了证明不可行性结果的新框架，并给出了在附加卡牌同色条件下对任意数量卡牌均有效的证明。