In this paper we study the computational complexity of functions that have efficient card-based protocols. A study of card-based protocols was initiated by den Boer [den Boer, 1990] as a means for secure two-party computation. Our contribution is two-fold: We classify a large class of protocols with respect to the computational complexity of functions they compute, and we propose other encodings of inputs which require fewer cards than the usual 2-card representation.
@InProceedings{dvorak_et_al:LIPIcs.STACS.2021.26, author = {Dvo\v{r}\'{a}k, Pavel and Kouck\'{y}, Michal}, title = {{Barrington Plays Cards: The Complexity of Card-Based Protocols}}, booktitle = {38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)}, pages = {26:1--26:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-180-1}, ISSN = {1868-8969}, year = {2021}, volume = {187}, editor = {Bl\"{a}ser, Markus and Monmege, Benjamin}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.26}, URN = {urn:nbn:de:0030-drops-136715}, doi = {10.4230/LIPIcs.STACS.2021.26}, annote = {Keywords: Efficient card-based protocol, Branching program, Turing machine} }
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