Secure implementations of a random bisection cut

By using a deck of cards, it is possible to realize a secure multiparty computation. In particular, since a new shuffling operation, called a random bisection cut, was devised in 2009, many efficient card-based protocols have been designed. The random bisection cut functions in the following manner. A sequence of cards is bisected, and the two halves are shuffled. This results in two possible cases depending on whether the two halves of the card sequence are swapped. As only two possibilities exist when a random bisection cut is performed, it has been suggested that information regarding the outcome of the shuffle could sometimes be leaked visually. Thus, in this paper we propose some methods for securely implementing a random bisection cut without leaking such information.