A formalization of card-based cryptographic protocols via abstract machine

Takaaki Mizuki; Hiroki Shizuya

doi:10.1007/s10207-013-0219-4

A formalization of card-based cryptographic protocols via abstract machine

Takaaki Mizuki, Hiroki Shizuya

Research and Development Divisions

Research output: Contribution to journal › Article › peer-review

41 Citations (Scopus)

Abstract

Consider a face-down card lying on the table such that we do not know whether its suit color is black or red. Then, how do we make identical copies of the card while keeping its color secret? A partial solution has been devised: using a number of additional black and red cards, Niemi and Renvall proposed an excellent protocol which can copy a face-down card while allowing only a small probability of revealing its color. In contrast, this paper shows the nonexistence of a perfect solution, namely, the impossibility of copying a face-down card with perfect secrecy. To prove such an impossibility result, we construct a rigorous mathematical model of card-based cryptographic protocols; giving this general computational model is the main result of this paper.

Original language	English
Pages (from-to)	15-23
Number of pages	9
Journal	International Journal of Information Security
Volume	13
Issue number	1
DOIs	https://doi.org/10.1007/s10207-013-0219-4
Publication status	Published - 2014 Feb

Keywords

Card games
Card-based protocols
Cryptography without computers
Recreational cryptography
Secure computations

ASJC Scopus subject areas

Software
Information Systems
Safety, Risk, Reliability and Quality
Computer Networks and Communications

Access to Document

10.1007/s10207-013-0219-4

Fingerprint Dive into the research topics of 'A formalization of card-based cryptographic protocols via abstract machine'. Together they form a unique fingerprint.

Cite this

@article{bcdc2d291b76477aac91f6089860408a,

title = "A formalization of card-based cryptographic protocols via abstract machine",

abstract = "Consider a face-down card lying on the table such that we do not know whether its suit color is black or red. Then, how do we make identical copies of the card while keeping its color secret? A partial solution has been devised: using a number of additional black and red cards, Niemi and Renvall proposed an excellent protocol which can copy a face-down card while allowing only a small probability of revealing its color. In contrast, this paper shows the nonexistence of a perfect solution, namely, the impossibility of copying a face-down card with perfect secrecy. To prove such an impossibility result, we construct a rigorous mathematical model of card-based cryptographic protocols; giving this general computational model is the main result of this paper.",

keywords = "Card games, Card-based protocols, Cryptography without computers, Recreational cryptography, Secure computations",

author = "Takaaki Mizuki and Hiroki Shizuya",

year = "2014",

month = feb,

doi = "10.1007/s10207-013-0219-4",

language = "English",

volume = "13",

pages = "15--23",

journal = "International Journal of Information Security",

issn = "1615-5262",

publisher = "Springer Verlag",

number = "1",

}

TY - JOUR

T1 - A formalization of card-based cryptographic protocols via abstract machine

AU - Mizuki, Takaaki

AU - Shizuya, Hiroki

PY - 2014/2

Y1 - 2014/2

N2 - Consider a face-down card lying on the table such that we do not know whether its suit color is black or red. Then, how do we make identical copies of the card while keeping its color secret? A partial solution has been devised: using a number of additional black and red cards, Niemi and Renvall proposed an excellent protocol which can copy a face-down card while allowing only a small probability of revealing its color. In contrast, this paper shows the nonexistence of a perfect solution, namely, the impossibility of copying a face-down card with perfect secrecy. To prove such an impossibility result, we construct a rigorous mathematical model of card-based cryptographic protocols; giving this general computational model is the main result of this paper.

AB - Consider a face-down card lying on the table such that we do not know whether its suit color is black or red. Then, how do we make identical copies of the card while keeping its color secret? A partial solution has been devised: using a number of additional black and red cards, Niemi and Renvall proposed an excellent protocol which can copy a face-down card while allowing only a small probability of revealing its color. In contrast, this paper shows the nonexistence of a perfect solution, namely, the impossibility of copying a face-down card with perfect secrecy. To prove such an impossibility result, we construct a rigorous mathematical model of card-based cryptographic protocols; giving this general computational model is the main result of this paper.

KW - Card games

KW - Card-based protocols

KW - Cryptography without computers

KW - Recreational cryptography

KW - Secure computations

UR - http://www.scopus.com/inward/record.url?scp=84893647951&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893647951&partnerID=8YFLogxK

U2 - 10.1007/s10207-013-0219-4

DO - 10.1007/s10207-013-0219-4

M3 - Article

AN - SCOPUS:84893647951

VL - 13

SP - 15

EP - 23

JO - International Journal of Information Security

JF - International Journal of Information Security

SN - 1615-5262

IS - 1

ER -

A formalization of card-based cryptographic protocols via abstract machine

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Cite this