Card-Based Cryptographic Protocols with a Standard Deck of Cards Using Private Operations

Abstract

This paper shows new kinds of card-based cryptographic protocols with a standard deck of cards using private operations. They are multi-party secure computations executed by multiple players without computers. Most card-based cryptographic protocols use a special deck of cards that consists of many cards with two kinds of marks. Though these protocols are simple and efficient, the users need to prepare such special cards. Few protocols were shown that use a standard deck of playing cards. Though the protocols with a standard deck of cards can be easily executed in our daily life, the numbers of cards used by these protocols are larger than the ones that use the special deck of cards. This paper shows logical AND, logical XOR, and copy protocols for a standard deck of cards that use the minimum number of cards. Any Boolean functions can be calculated with a combination of the above protocols. The new protocols use private operations that are executed by a player where the other players cannot see. The results show the effectiveness of private operations in card-based cryptographic protocols.