TY - GEN

T1 - Necessary and sufficient numbers of cards for securely computing two-bit output functions

AU - Francis, Danny

AU - Aljunid, Syarifah Ruqayyah

AU - Nishida, Takuya

AU - Hayashi, Yu Ichi

AU - Mizuki, Takaaki

AU - Sone, Hideaki

N1 - Funding Information:
We thank the anonymous referees, whose comments have helped us to improve the presentation of the paper. This work was supported by JSPS KAKENHI Grant Number 26330001.
Publisher Copyright:
© Springer International Publishing AG 2017.

PY - 2017

Y1 - 2017

N2 - In 2015, Koch et al. proposed a five-card finite-runtime committed protocol to compute securely the AND function, showing that their protocol was optimal: there is no protocol computing the AND function with four cards in finite-runtime fashion and committed format. Thus, necessary and sufficient numbers of cards for computing single-bit output functions are known. However, as for two-bit output functions, such an exact characterization is unknown. This paper gives a six-card (or less) protocol for each of all two-bit output functions and proves that our finite-runtime committed protocols are optimal by providing a lower bound. In other words, we give the necessary and sufficient number of cards for any two-bit output function to be computed by a finite-runtime committed protocol. Our lower bound can also be applied to any function which outputs more than two bits.

AB - In 2015, Koch et al. proposed a five-card finite-runtime committed protocol to compute securely the AND function, showing that their protocol was optimal: there is no protocol computing the AND function with four cards in finite-runtime fashion and committed format. Thus, necessary and sufficient numbers of cards for computing single-bit output functions are known. However, as for two-bit output functions, such an exact characterization is unknown. This paper gives a six-card (or less) protocol for each of all two-bit output functions and proves that our finite-runtime committed protocols are optimal by providing a lower bound. In other words, we give the necessary and sufficient number of cards for any two-bit output function to be computed by a finite-runtime committed protocol. Our lower bound can also be applied to any function which outputs more than two bits.

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U2 - 10.1007/978-3-319-61273-7_10

DO - 10.1007/978-3-319-61273-7_10

M3 - Conference contribution

AN - SCOPUS:85026777593

SN - 9783319612720

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 193

EP - 211

BT - Paradigms in Cryptology – Mycrypt 2016

A2 - Phan, Raphael C.-W.

A2 - Yung, Moti

PB - Springer Verlag

T2 - 2nd International Conference on Cryptology and Malicious Security, Mycrypt 2016

Y2 - 1 December 2016 through 2 December 2016

ER -