On the Number of Rounds by Card-based Cryptographic Protocols Using Private Operations

摘要

This paper discusses the number of rounds by card-based cryptographic protocols using private operations. Operations that a player executes where the other players cannot see are called private operations. Using private operations, xor, logical and, logical or, and copy operations can be realized with the minimum number of cards. Though the number of cards is discussed, efficiency of these protocols is not discussed. The number of rounds is used to evaluate the efficiency of the protocols using private operations. Most of meaningful calculations using private operations need at least two rounds. This paper shows two round xor protocol using four cards. Then we show two round logical and, logical or, and copy protocols using six cards. This paper then shows that if the private operations are restricted to private random bisection cuts and private reverse cuts, logical and, logical or, xor, and copy operations can be executed with the minimum number of cards in three rounds.