In 2009, Gradwohl, Naor, Pinkas, and Rothblum proposed physical zero-knowledge proof protocols for Sudoku. That is, for a puzzle instance of Sudoku, their excellent protocols allow a prover to convince a verifier that there is a solution to the Sudoku puzzle and the prover knows it, without revealing any information about the solution. The possible drawback is that the existing protocols have an extractability error with a non-zero probability, or need special cards (such as scratch-off cards). Thus, in this study, we propose new protocols to perform zero-knowledge proof of knowledge for Sudoku using a normal deck of playing cards with no extractability error. Our protocols can be easily implemented by humans with a reasonable number of playing cards.

在2009年，Gradwohl，Naor，Pinkas和Rothblum为Sudoku提出了物理零知识证明协议。也就是说，对于Sudoku的拼图实例，其出色的协议允许证明者说服验证者该Sudoku拼图有解决方案，并且证明者知道该解决方案，而无需透露有关该解决方案的任何信息。可能的缺点是现有协议具有非零概率的可提取性错误，或者需要特殊的卡（例如刮刮卡）。因此，在这项研究中，我们提出了一种新协议，可以使用无抽取错误的普通扑克牌对Sudoku执行知识的零知识证明。我们的协议可以很容易地由人类以合理数量的扑克牌实现。