Graph Automorphism Shuffles from PileScramble Shuffles
Abstract
A pilescramble shuffle is one of the most effective shuffles in cardbased cryptography. Indeed, many cardbased protocols are constructed from pilescramble shuffles. This article aims to study the power of pilescramble 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 by using pilescramble 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 of pilescramble shuffles is $k+1$, where $1 \leq k \leq n$ 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 realized by $3n$ cards and two pilescramble shuffles.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.00397
 Bibcode:
 2021arXiv210900397M
 Keywords:

 Computer Science  Cryptography and Security;
 Mathematics  Combinatorics;
 94A60;
 05C20
 EPrint:
 16 pages. We have corrected some typos and added Subsections 1.3, 3.6, Section 5, and proofs of correctness and security of protocols in Subsections 4.1. 4.2