Graph automorphism shuffles from pile-scramble shuffles

K Miyamoto, K Shinagawa - New Generation Computing, 2022 - Springer
K Miyamoto, K Shinagawa
New Generation Computing, 2022Springer
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 paper
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 can be
implemented using pile-scramble shuffles only. Our proposed protocol requires 2 (n+ m)
cards, where n and m are the numbers of vertices and edges of G, respectively. The number …
Abstract
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 paper 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 can be implemented using pile-scramble shuffles only. Our proposed protocol requires cards, where n and m are the numbers of vertices and edges of G, respectively. The number of pile-scramble shuffles is , where is the number of distinct degrees of vertices of G. As an application, a random cut for n cards, which is also an important shuffle, can be implemented by 3n cards and two pile-scramble shuffles.
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