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Research in the area of secure multi-party computation using a deck ofplaying cards, often called card-based cryptography, started from theintroduction of the five-card trick protocol to compute the logical ANDfunction by den Boer in 1989. Since then, many card-based protocols to computevarious functions have been developed. In this paper, we propose two newprotocols that securely compute the $n$-variable equality function (determiningwhether all inputs are equal) $E: \{0,1\}^n \rightarrow \{0,1\}$ using $2n$cards. The first protocol can be generalized to compute any doubly symmetricfunction $f: \{0,1\}^n \rightarrow \mathbb{Z}$ using $2n$ cards, and anysymmetric 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.

Securely Computing the $n$-Variable Equality Function with $2n$ Cards