TY - JOUR
T1 - Secure computation protocols using polarizing cards
AU - Shinagawa, Kazumasa
AU - Mizuki, Takaaki
AU - Schuldt, Jacob C.N.
AU - Nuida, Koji
AU - Kanayama, Naoki
AU - Nishide, Takashi
AU - Hanaoka, Goichiro
AU - Okamoto, Eiji
N1 - 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. 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:
Copyright © 2016 The Institute of Electronics, Information and Communication Engineers.
PY - 2016/6
Y1 - 2016/6
N2 - It is known that, using just a deck of cards, an arbitrary number of parties with private inputs can securely compute the output of any function of their inputs. In 2009, Mizuki and Sone constructed a six-card COPY protocol, a four-card XOR protocol, and a six-card AND protocol, based on a commonly used encoding scheme in which each input bit is encoded using two cards. However, up until now, there are no known results to construct a set of COPY, XOR, and AND protocols based on a two-card-per-bit encoding scheme, which all can be implemented using only four cards. In this paper, we show that it is possible to construct four-card COPY, XOR, and AND protocols using polarizing plates as cards and a corresponding two-card-per-bit encoding scheme. Our protocols use a minimum number of cards in the setting of two-card-per-bit encoding schemes since four cards are always required to encode the inputs. Moreover, we show that it is possible to construct two-card COPY, two-card XOR, and three-card AND protocols based on a one-card-per-bit encoding scheme using a common reference polarizer which is a polarizing material accessible to all parties.
AB - It is known that, using just a deck of cards, an arbitrary number of parties with private inputs can securely compute the output of any function of their inputs. In 2009, Mizuki and Sone constructed a six-card COPY protocol, a four-card XOR protocol, and a six-card AND protocol, based on a commonly used encoding scheme in which each input bit is encoded using two cards. However, up until now, there are no known results to construct a set of COPY, XOR, and AND protocols based on a two-card-per-bit encoding scheme, which all can be implemented using only four cards. In this paper, we show that it is possible to construct four-card COPY, XOR, and AND protocols using polarizing plates as cards and a corresponding two-card-per-bit encoding scheme. Our protocols use a minimum number of cards in the setting of two-card-per-bit encoding schemes since four cards are always required to encode the inputs. Moreover, we show that it is possible to construct two-card COPY, two-card XOR, and three-card AND protocols based on a one-card-per-bit encoding scheme using a common reference polarizer which is a polarizing material accessible to all parties.
KW - Boolean circuits
KW - Card-based protocols
KW - Polarizing cards
KW - Recreational cryptography
KW - Secure computation
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U2 - 10.1587/transfun.E99.A.1122
DO - 10.1587/transfun.E99.A.1122
M3 - Article
AN - SCOPUS:85009401659
SN - 0916-8508
VL - E99A
SP - 1122
EP - 1131
JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
IS - 6
ER -