The Asymmetric five-card trick: working with variable encoding in card-based protocols

Abstract

Recently, card-based protocols have been extensively explored to illustrate relatively complex cryptographic concepts, such as Secure Multiparty Computations, so that even non-specialists can understand them. These protocols rely on three elements: a given alphabet with a set number of physical cards, encoding those cards, and shuffling operations. However, the execution is becoming over-complicated, as most follow the same encoding: fixed uniform disclosed encoding, which constrains other elements and decreases their expressiveness. This paper introduces the asymmetric five-card trick, a generalization of the five-card trick (a seminal work in the field of card-based cryptography) with the added feature of allowing variable encoding. To do so, we propose a pre-process called “handshake” that allows protocols to adapt operations based on players’ encoding. The protocol handshake is included as part of the protocol’s production phase in the proposed general framework, which is negotiated before its execution. Finally, this paper also introduces the notion of time and space complexity in card-based protocols to assess their production and execution’s lower bounds.