Graph Automorphism Shuffles from Pile-Scramble Shuffles

09/01/2021

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by   Kengo Miyamoto, et al.

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A pile-scramble shuffle is one of the most effective shuffles in card-based cryptography. Indeed, many card-based protocols are constructed from pile-scramble shuffles. This article aims to study the power of pile-scramble shuffles. In particular, for any directed graph G, we introduce a new protocol called "a graph shuffle protocol for G", and show that it is realized by using pile-scramble shuffles only. Our proposed protocol requires 2(n+m) cards, where n and m are the numbers of vertices and arrows of G, respectively. The number of pile-scramble shuffles is k+1, where 1 ≤ k ≤ n is the number of distinct degrees of vertices in G. As an application, a random cut for n cards, which is also an important shuffle, can be realized by 2n cards and 2 pile-scramble shuffles.