Abstract
It is known that secure computation can be done by using a deck of physical cards. This area is called card-based cryptography. Shinagawa et al. (in: Provable security—9th international conference, ProvSec 2015, Kanazawa, Japan, 2015) proposed regular n-sided polygon cards that enable to compute functions over {mathbb {Z}}/n{mathbb {Z}}. In particular, they designed efficient protocols for linear functions (e.g. addition and constant multiplication) over {mathbb {Z}}/n{mathbb {Z}}. Here, efficiency is measured by the number of cards used in the protocol. In this paper, we propose a new type of cards, dihedral cards, as a natural generalization of regular polygon cards. Based on them, we construct efficient protocols for various interesting functions such as carry of addition, equality, and greater-than, whose efficient construction has not been known before. Beside this, we introduce a new protocol framework that captures a wide class of card types including binary cards, regular polygon cards, dihedral cards, and so on.
Highlights
Keywords Secure computation · Card-based cryptography · Invisible ink Secure computation enables a set of parties each having inputs to jointly compute a predetermined function of their inputs without revealing their inputs beyond the output
Card-based cryptography is secure computation that can be done by using a deck of physical cards, instead of computer devices
Dihedral cards We design a new type of cards, dihedral cards, which is based on the use of invisible ink
Summary
Secure computation enables a set of parties each having inputs to jointly compute a predetermined function of their inputs without revealing their inputs beyond the output. In order to compute multi-valued functions efficiently, Shinagawa et al [15] proposed a deck of regular polygon cards, whose shape is a regular n-sided polygon for the base number n. They proposed a two-card addition protocol that outputs x + y mod n given two cards having x, y ∈ Z∕nZ. Does a deck of regular polygon cards realize sufficiently efficient secure computation for multi-valued functions? Dihedral cards We design a new type of cards, dihedral cards, which is based on the use of invisible ink It enables to construct several efficient protocols. We left to give concrete definitions for other cards as future works
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