Research in secure multi-party computation using a deck of playing cards, often called card-based cryptography, dates back to 1989 when Den Boer introduced the "five-card trick" to compute the logical AND function. Since then, many protocols to compute different functions have been developed. In this paper, we propose a new encoding scheme using five cards to encode each integer in $\mathbb{Z}/6\mathbb{Z}$. Using this encoding scheme, we develop protocols that can copy a commitment with 13 cards, add two integers with 10 cards, and multiply two integers with 16 cards. All of our protocols are the currently best known protocols in terms of the required number of cards. Our encoding scheme can also be generalized to encode integers in $\mathbb{Z}/n\mathbb{Z}$ for other values of $n$ as well.
翻译:使用牌牌(通常称为纸牌加密)的安全多党计算研究始于1989年,当时Den Boer引入了计算逻辑和函数的“五张牌把戏”来计算逻辑和函数。从那时以来,已经制定了许多计算不同函数的规程。在本文中,我们提出一个新的编码方案,使用五张卡来编码每个整数,以$\mathb ⁇ /6\mathb ⁇ $。使用这个编码方案,我们制定程序,可以复制13张牌的承诺,增加两个整数,10张,并乘两个整数加上16张卡。我们的所有协议都是目前最已知的关于所需牌数的规程。我们的编码方案也可以普遍化为$\mathb ⁇ /n\mathb ⁇ $的其他值编码整数。