Magic Squares and Cubes Constructions properties and applications

Abstract

Title : Magic Squares and Cubes : Constructions, properties and applications newline newlineAbstract: With the growing demands it is necessary to focus on some techniques that havenot yet been investigated. Despite their intriguing features, the magic squaresand cubes are the techniques that have not been widely explored. Additionally, it isnoted that mathematically sophisticated ways for creating magic squares and cubesare less frequently available. Also, magic cubes symmetry is a key feature from theperspective of their practical use. The uniqueness of all the elements facilitate theiruse in game theory, cryptography, etc. The magic cubes created with the techniquesat hand aren t necessarily symmetric and could have unique entries. Besides this,this thesis work opens the path of a magic cube with unique entries but havinga flexible range by removing the restriction on the entries of magic cubes rangingfrom 1 to n^3 (where n is the order of magic cubes). Moreover, it has been deducedfrom the literature that the generalised formula for compounding magic cubes isinapplicable to the creation of higher order magic cubes. The complexity and securityof cryptographic algorithms have improved as a result of the magic square/cubetransformations. Additionally, the magic cube or square based image cryptographymodels increase in complexity and are hence more reliable.The magic cubes and squares are the methods that can give encrypted data bit-leveland position-level privacy. We thus propose an image/text encryption model employingthe notions of magic square or magic cube in response to the benchmark models shortcomings. By using its components, the introduction of new magic squares orcubes improve the level of intricacy and security. Additionally, the combinationof the magic square and magic cube with other elements like differential encoding,chaotic maps, and scrambling techniques in the suggested encryption modelseffectively ignores all the significant drawbacks of the existing models.