Graph Automorphism Shuffles from Pile-Scramble Shuffles

A pile-scramble shuffle is one of the most effective shuffles in card-based cryptography. Indeed, many protocols are constructed from shuffles. This paper aims to study power In particular, for any directed graph G, we introduce a new protocol called “a G”, and show that it can be implemented using only. Our proposed requires $$2(n+m)$$ cards, where n m numbers vertices edges respectively. The number $$k+1$$ , $$1 \le k n$$ distinct degrees G. As an application, random cut which also important shuffle, by 3n cards two