The Construction and Applications of Latin k-hypercube and Its Critical Sets

• Main Authors: Shu-Mei Chen, 陳淑美
• Other Authors: Tso, Ray-Lin
• Format: Others
• Language: zh-TW
• Published: 2018
• Online Access: http://ndltd.ncl.edu.tw/handle/q2btcs

碩士 === 國立政治大學 === 資訊科學系碩士在職專班 === 106 === Researches related to "information security" such as Cryptography and Secret sharing schemes are usually designed and constructed using mathematical techniques. For example,in 1994 Cooper, Donovan and Seberry showed the method how to use the Latin square to design secret sharing schemes. The design of Latin squares are in the scope of the Combinatorial designs, and they have considerable contributions to Cryptography and coding theory. This thesis will develop the Latin cubes methodology based on the concepts of Latin squares and their critical sets. We will introduce how to construct a Latin cube,how to find the critical sets of the Latin cube,and how to rebuild the Latin cube using its critical sets and so on. The idea introduced here can be used to increase the complexity and diversity of the application of the Latin squares. Based on the methodology of Latin cubes,we will also develop the multi-dimensional Latin squares (called the Latin k-hypercubes) methodology,and show how it can be successfully applied to the areas of information hiding. We hope that the methodologies proposed in this thesis can be followed by more relevant applications in various fields of information security researches.