Akari、Takuzu、Kakuro和KenKen的物理零知识证明
Physical Zero-Knowledge Proofs for Akari, Takuzu, Kakuro and KenKen
摘要：
Akari，Takuzu，Kakuro和KenKen是类似于Sudoku的逻辑游戏。在Akari，网格上的迷宫必须通过放置灯笼来照亮，尊重各种限制。在Takuzu中，网格必须填充0和1，同时遵守某些约束。在Kakuro中，网格必须用数字填充，使得每行和每列的总和与给定值相匹配;类似地，在KenKen中，网格必须用数字填充，使得在给定区域中，积、和、差或商等于给定值。我们给出了实现这些博弈的零知识证明的物理算法，这些算法允许玩家在不透露答案的情况下表明他知道答案。这些交互式证明可以用简单的办公材料来实现，因为它们只依赖于卡片和信封。此外，我们形式化我们的算法，并证明其安全性。
英文摘要：
Akari, Takuzu, Kakuro and KenKen are logic games similar to Sudoku. In Akari, a labyrinth on a grid has to be lit by placing lanterns, respecting various constraints. In Takuzu a grid has to be filled with 0's and 1's, while respecting certain constraints. In Kakuro a grid has to be filled with numbers such that the sums per row and column match given values; similarly in KenKen a grid has to be filled with numbers such that in given areas the product, sum, difference or quotient equals a given value. We give physical algorithms to realize zero-knowledge proofs for these games which allow a player to show that he knows a solution without revealing it. These interactive proofs can be realized with simple office material as they only rely on cards and envelopes. Moreover, we formalize our algorithms and prove their security.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
