June 18, 2021

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Using Five Cards to Encode Each Integer in $mathbb{Z}/6mathbb{Z}$. (arXiv:2011.02980v3 [cs.CR] UPDATED)

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 $mathbb{Z}/6mathbb{Z}$. 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
$mathbb{Z}/nmathbb{Z}$ for other values of $n$ as well.