A Discussion of a Cryptographical Scheme Based in <inline-formula><math display="inline"><semantics><mi mathvariant="fraktur">F</mi></semantics></math></inline-formula>-Critical Sets of a Latin Square

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.

Keywords

• F -critical sets%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <named-content content-type="inline"><inline-formula> <mml:math id="mm2222" display="block"> <mml:semantics> <mml:mi mathvariant="fraktur">F</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-critical sets
• Latin square
• Latin subsquare
• intercalate
• secret sharing scheme