Article

Zero-Knowledge Proof Protocol for Cryptarithmetic Using Dihedral Cards

Authors:

Raimu Isuzugawa,

Daiki Miyahara,

Takaaki MizukiAuthors Info & Claims

Unconventional Computation and Natural Computation: 19th International Conference, UCNC 2021, Espoo, Finland, October 18–22, 2021, Proceedings

Pages 51 - 67

https://doi.org/10.1007/978-3-030-87993-8_4

Published: 18 October 2021 Publication History

Abstract

Cryptarithmetic, also known as Verbal Arithmetic or Word Addition, is a popular pencil puzzle in which the aim is to deduce which letter corresponds to which numeral, given a mathematical equation in which each numeral (from 0 to 9) has been replaced with a unique letter. The most famous instance of this puzzle is probably “SEND + MORE = MONEY", whose solution is “9567 + 1085 = 10652", i.e., S = 9, E = 5, N = 6, D = 7, M = 1, O = 0, R = 8, and Y = 2. In this study, we construct a physical zero-knowledge proof protocol for a Cryptarithmetic puzzle: That is, our protocol enables a prover who knows a solution to the puzzle to convince a verifier that he/she knows the solution without revealing any information about it. The proposed protocol uses a physical deck of “dihedral cards,” which were developed by Shinagawa in 2019.

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cover image Guide Proceedings

Unconventional Computation and Natural Computation: 19th International Conference, UCNC 2021, Espoo, Finland, October 18–22, 2021, Proceedings

Oct 2021

214 pages

ISBN:978-3-030-87992-1

DOI:10.1007/978-3-030-87993-8

Editors:
Irina Kostitsyna
TU Eindhoven, Eindhoven, The Netherlands
,
Pekka Orponen
Aalto University, Espoo, Finland

© Springer Nature Switzerland AG 2021.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 18 October 2021

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Cited By

Tamura YSuzuki AMizuki T(2024)Card-Based Zero-Knowledge Proof Protocols for the 15-Puzzle and the Token Swapping ProblemProceedings of the 11th ACM Asia Public-Key Cryptography Workshop10.1145/3659467.3659905(11-22)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1145/3659467.3659905
Komano YMizuki T(2024)Physical Zero-Knowledge Proof Protocols for Topswops and BotdropsNew Generation Computing10.1007/s00354-024-00272-342:3(399-428)Online publication date: 1-Sep-2024
https://dl.acm.org/doi/10.1007/s00354-024-00272-3
Kaneko SLafourcade PMallordy LMiyahara DPuys MSakiyama K(2024)Balance-Based ZKP Protocols for Pencil-and-Paper PuzzlesInformation Security10.1007/978-3-031-75757-0_11(211-231)Online publication date: 24-Oct-2024
https://dl.acm.org/doi/10.1007/978-3-031-75757-0_11
Robert LMiyahara DLafourcade PMizuki T(2023)Physical ZKP protocols for Nurimisaki and KurodokoTheoretical Computer Science10.1016/j.tcs.2023.114071972:COnline publication date: 13-Sep-2023
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Hand SKoch ALafourcade PMiyahara DRobert L(2023)Check Alternating Patterns: A Physical Zero-Knowledge Proof for Moon-or-SunAdvances in Information and Computer Security10.1007/978-3-031-41326-1_14(255-272)Online publication date: 29-Aug-2023
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Robert LMiyahara DLafourcade PMizuki T(2022)Card-Based ZKP for Connectivity: Applications to Nurikabe, Hitori, and HeyawakeNew Generation Computing10.1007/s00354-022-00155-540:1(149-171)Online publication date: 14-Mar-2022
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Komano YMizuki T(2022)Card-Based Zero-Knowledge Proof Protocol for Pancake SortingInnovative Security Solutions for Information Technology and Communications10.1007/978-3-031-32636-3_13(222-239)Online publication date: 8-Dec-2022
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Robert LMiyahara DLafourcade PMizuki T(2022)Card-Based ZKP Protocol for NurimisakiStabilization, Safety, and Security of Distributed Systems10.1007/978-3-031-21017-4_19(285-298)Online publication date: 15-Nov-2022
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