A Complexity Hierarchy of Shuffles in Card-Based Protocols

Computer Science > Cryptography and Security [Submitted on 19 Mar 2026] A Complexity Hierarchy of Shuffles in Card-Based Protocols Tomoki Ono, Suthee Ruangwises Card-based cryptography uses physical playing cards to construct protocols for secure multi-party computation. Existing card-based protocols employ various types of shuffles, some of which are easy to implement in practice while others are considerably more complex. In this paper, we classify shuffle operations into several levels according to their implementation complexity. We motivate this hierarchy from both practical and theoretical perspectives, and prove separation results between several levels by showing that certain shuffles cannot be realized using only operations from lower levels. Finally, we propose a new complexity measure for evaluating card-based protocols based on this hierarchy. Subjects: Cryptography and Security (cs.CR) Cite as: arXiv:2603.18608 [cs.CR]   (or arXiv:2603.18608v1 [cs.CR] for this version)   https://doi.org/10.48550/arXiv.2603.18608 Focus to learn more Submission history From: Suthee Ruangwises [view email] [v1] Thu, 19 Mar 2026 08:27:02 UTC (52 KB) Access Paper: HTML (experimental) view license Current browse context: cs.CR < prev   |   next > new | recent | 2026-03 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)