Research in the area of secure multi-party computation using a deck of playing cards, often called card-based cryptography, started from the introduction of the five-card trick protocol to compute the logical AND function by den Boar in 1989. Since then, many card-based protocols to compute various functions have been developed. In this paper, we propose two new protocols that securely compute the $n$-variable equality function (determining whether all inputs are equal) $E: \{0,1\}^n \rightarrow \{0,1\}$ using $2n$ cards. The first protocol can be generalized to compute any doubly symmetric function $f: \{0,1\}^n \rightarrow \mathbb{Z}$ using $2n$ cards, and any symmetric function $f: \{0,1\}^n \rightarrow \mathbb{Z}$ using $2n+2$ cards. The second protocol can be generalized to compute the $k$-candidate $n$-variable equality function $E: (\mathbb{Z}/k\mathbb{Z})^n \rightarrow \{0,1\}$ using $2 \lceil \lg k \rceil n$ cards.
翻译:使用牌牌牌(通常称为基于纸牌的密码学)进行安全多党计算领域的研究, 通常称为基于纸牌的密码学, 始于1989年引入五张牌的游戏游戏游戏程序, 以便用 den Boar 来计算逻辑和函数。 从那时以来, 已经开发了许多基于纸牌的计算各种函数的协议。 在本文中, 我们提议了两个新的协议, 安全地计算$- $- 变量平等功能( 确定所有输入是否相等) $ : 0. 1 ⁇ n \ rightrow ⁇ 0. 1, 美元 美元 美元 。 第一个协议可以被普遍化, 用来计算任何双重对称功能 $ : 0. 1\\\\\\\\ right\ mathb} 美元, 使用 $2n+2 card 。 第二个协议可以被普遍化为 $- carddate $- cardate $n- valable eqreal 函数 $ E: (\\mathbl_\\\\\\\ ral card * k_\ k_\ k_\\\ card * *) card_ k_ k_ * * * * * * *