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A discussion of a cryptographical scheme based in F-critical sets of a Latin square

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Date
31/01/2021
Author
Johnson, Laura M.
Perkins, Stephanie
Keywords
F-critical sets
Latin squares
Latin subsquare
Intercalate
Secret sharing scheme
QA Mathematics
T-NDAS
NIS
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Abstract
This communication provides a discussion of a scheme originally proposed by Falcón in a paper entitled “Latin squares associated to principal autotopisms of long cycles. Applications in cryptography”. Falcón outlines the protocol for a cryptographical scheme that uses the F-critical sets associated with a particular Latin square to generate access levels for participants of the scheme. Accompanying the scheme is an example, which applies the protocol to a particular Latin square of order six. Exploration of the example itself, revealed some interesting observations about both the structure of the Latin square itself and the autotopisms associated with the Latin square. These observations give rise to necessary conditions for the generation of the F-critical sets associated with certain autotopisms of the given Latin square. The communication culminates with a table which outlines the various access levels for the given Latin square in accordance with the scheme detailed by Falcón.
Citation
Johnson , L M & Perkins , S 2021 , ' A discussion of a cryptographical scheme based in F -critical sets of a Latin square ' , Mathematics , vol. 9 , no. 3 , 285 . https://doi.org/10.3390/math9030285
Publication
Mathematics
Status
Peer reviewed
DOI
https://doi.org/10.3390/math9030285
ISSN
2227-7390
Type
Journal article
Rights
Copyright:© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and con-ditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/21352

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