Secure Grouping Protocol Using a Deck of Cards

We consider a problem, which we call secure grouping, of dividing a number of parties into some subsets (groups) in the following manner: Each party has to know the other members of his/her group, while he/she may not know anything about how the remaining parties are divided (except for certain public predetermined constraints, such as the number of parties in each group). In this paper, we construct an information-theoretically secure protocol using a deck of physical cards to solve the problem, which is jointly executable by the parties themselves without a trusted third party. Despite the non-triviality and the potential usefulness of the secure grouping, our proposed protocol is fairly simple to describe and execute. Our protocol is based on algebraic properties of conjugate permutations. A key ingredient of our protocol is our new techniques to apply multiplication and inverse operations to hidden permutations (i.e., those encoded by using face-down cards), which would be of independent interest and would have various potential applications

Using Five Cards to Encode Each Integer in Z/6Z\mathbb{Z}/6\mathbb{Z}

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

Card-Based Protocols Using Regular Polygon Cards

Cryptographic protocols enable participating parties to compute any function of their inputs without leaking any information beyond the output. A card-based protocol is a cryptographic protocol implemented by physical cards. In this paper, for constructing protocols with small numbers of shuffles, we introduce a new type of cards, regular polygon cards, and a new protocol, oblivious conversion. Using our cards, we construct an addition protocol on non-binary inputs with only one shuffle and two cards. Furthermore, using our oblivious conversion protocol, we construct the first protocol for general functions in which the number of shuffles is linear in the number of inputs