Using Five Cards to Encode Each Integer in $\mathbb{Z}/6\mathbb{Z}$
This work addresses the problem of improving efficiency in card-based cryptography for secure computation, offering incremental advancements in protocol optimization for researchers in cryptography.
The paper tackles the problem of secure multi-party computation using card-based cryptography by proposing a new encoding scheme that uses five cards to encode each integer in Z/6Z, resulting in protocols for copying, addition, and multiplication with 13, 10, and 14 cards respectively, which are currently the best known in terms of card count.
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 that uses 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 14 cards. All of our protocols are the currently best known protocols in terms of the required number of cards. Our encoding scheme can be generalized to encode integers in $\mathbb{Z}/n\mathbb{Z}$ for other values of $n$ as well.