TY - GEN
T1 - A Card-Minimal Three-Input AND Protocol Using Two Shuffles
AU - Isuzugawa, Raimu
AU - Toyoda, Kodai
AU - Sasaki, Yu
AU - Miyahara, Daiki
AU - Mizuki, Takaaki
N1 - Funding Information:
Acknowledgements. We thank the anonymous referees, whose comments have helped us improve the presentation of the paper. We would like to thank Hideaki Sone for his cooperation in preparing a Japanese draft version at an earlier stage of this work. This work was supported in part by JSPS KAKENHI Grant Numbers JP19J21153 and JP21K11881.
Publisher Copyright:
© 2021, Springer Nature Switzerland AG.
PY - 2021
Y1 - 2021
N2 - Card-based cryptography typically uses a physical deck comprising black and red cards to perform secure computations, where a one-bit value is encoded using a pair of cards with different colors such that the order of black to red represents 0 and red to black represents 1. One of the most fundamental classes of card-based protocols is the class of “card-minimal” n-input AND protocols, which require 2n face-down cards as input to securely evaluate the AND value after applying a number of shuffles; here, the 2n cards are minimally required to describe an n-bit input. The best n-input AND protocols currently known use two shuffles for n= 2, five shuffles for n= 3, and n+ 1 shuffles for n> 3. These upper bounds on the numbers of shuffles have not been improved for several years. In this work, we present a better upper bound for the n= 3 case by designing a new card-minimal three-input AND protocol using only two shuffles. Therefore, our proposed protocol reduces the number of required shuffles from five to two; we believe that this is a significant improvement.
AB - Card-based cryptography typically uses a physical deck comprising black and red cards to perform secure computations, where a one-bit value is encoded using a pair of cards with different colors such that the order of black to red represents 0 and red to black represents 1. One of the most fundamental classes of card-based protocols is the class of “card-minimal” n-input AND protocols, which require 2n face-down cards as input to securely evaluate the AND value after applying a number of shuffles; here, the 2n cards are minimally required to describe an n-bit input. The best n-input AND protocols currently known use two shuffles for n= 2, five shuffles for n= 3, and n+ 1 shuffles for n> 3. These upper bounds on the numbers of shuffles have not been improved for several years. In this work, we present a better upper bound for the n= 3 case by designing a new card-minimal three-input AND protocol using only two shuffles. Therefore, our proposed protocol reduces the number of required shuffles from five to two; we believe that this is a significant improvement.
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U2 - 10.1007/978-3-030-89543-3_55
DO - 10.1007/978-3-030-89543-3_55
M3 - Conference contribution
AN - SCOPUS:85118156620
SN - 9783030895426
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 668
EP - 679
BT - Computing and Combinatorics - 27th International Conference, COCOON 2021, Proceedings
A2 - Chen, Chi-Yeh
A2 - Hon, Wing-Kai
A2 - Hung, Ling-Ju
A2 - Lee, Chia-Wei
PB - Springer Science and Business Media Deutschland GmbH
T2 - 27th International Conference on Computing and Combinatorics, COCOON 2021
Y2 - 24 October 2021 through 26 October 2021
ER -