@inbook{edf7e8b122ba413b8d83a89e2902debe,
title = "Multi-party computation with small shuffle complexity using regular polygon cards",
abstract = "It is well-known that a protocol for any function can be constructed using only cards and various shuffling techniques (this is referred to as a card-based protocol). In this paper, we propose a new type of cards called regular polygon cards. These cards enable a new encoding for multi-valued inputs while the previous works can only handle binary inputs. We furthermore propose a new technique for constructing a card-based protocol for any n-ary function with small shuffle complexity. This is the first general construction in which the shuffle complexity is independent of the complexity (size/depth) of the desired functionality, although being directly proportional to the number of inputs. The construction furthermore supports a wide range of cards and encodings, including previously proposed types of cards. Our techniques provide a method for reducing the number of shuffles in card-based protocols.",
author = "Kazumasa Shinagawa and Takaaki Mizuki and Schuldt, {Jacob C.N.} and Koji Nuida and Naoki Kanayama and Takashi Nishide and Goichiro Hanaoka and Eiji Okamoto",
note = "Funding Information: The authors would like to thank members of the study group “Shin-Akarui-Angou-Benkyou-Kai” for the valuable discussions and helpful comments, and thank the anonymous reviewers for their comments. This work was partially supported by JSPS KAKENHI Grant Numbers 26330001 and 26330151, Kurata Grant from The Kurata Memorial Hitachi Science and Technology Foundation, and JSPS A3 Foresight Program. Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2015.",
year = "2015",
doi = "10.1007/978-3-319-26059-4_7",
language = "English",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "127--146",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
address = "Germany",
}