An implementation of Hill cipher and 3x3x3 rubik's cube to enhance communication security

Message security is must be managed seriously. Therefore, to maintain the confidentiality of any message, cryptography is needed. Cryptography is a science that uses mathematics to encrypt and decrypt messages. Cryptography is used as a tool to protect messages, for example, national secrets and strategies.  The method of this research is qualitative research with a literature review. This research implements a hybrid cryptographic algorithm by combining Hill cipher and 3x3x3 Rubik's cube methods with Python software simulation

The group theoretic Rubik\u27s Cube

Cyclic fads often boomerang our childhood toys, sending them back to us with renewed popularity during our adulthood. Recently, Rubik\u27s Cube has made a startling comeback and is once again a staple in most toy stores. Invented by Erno Rubik in his hometown of Budapest, Hungary, the original \Magic Cube was released in 1974. Upon its world debut in 1980, the toy named after this Hungarian architect became an instant classic. Over 350 billion Rubik\u27s Cubes have been sold worlwide [sic] over the past 30 years, making it easily the top-selling puzzle toy in documented history. This seemingly innocuous puzzle has frazzled countless children, and perhaps even more adults. The mathematical complexity of the Cube attracted group theorists and other mathematicians upon its release over three decades ago, and the many layers of its structure continue to intrigue the mathematics community. Most of us place emphasis on unscralmbing [sic] the Cube, solving the puzzle. Rather than focusing on the construction of algorithms or solutions to the Cube, we chose to take a group theoretic approach to analyzing this infamous toy. Here, treating Rubik\u27s Cube as a group, we will examine subgroups of the Cube, particularly those constructed via semidirect products. These constructions aid us in describing the possible color arrangements of the Cube

Mathematical Understandings Of A Rubik\u27s Cube

Many people are familiar with the 3x3x3 Rubik’s Cube as a puzzle or a toy. But, what most people do not realize is that the cube is a great physical visual of a group. The goal of this paper is to discuss the Rubik’s Cube as a group and dive into a specific subgroup of the cube. Through this discussion, we will also explore homomorphisms in the slice group. This paper will also give insight on permutations, commutators, and conjugates in terms of the cube, as well as “God’s number”

Semidirect products and Rubik's cube

Given two groups, there are several ways of obtaining news ones. This work focuses on three of these ways: the direct, semidirect, and wreath products. These three products can be thought of as subsequently 'building upon' each other, since the definition of semidirect product depends on the concept of direct product, and wreath products are essentially a particular example of semidirect product. The concepts above were explored both theoretically and practically, by means of several different examples as well as some digressions from the main topics for the benefit of interested readers. The most substantial and convoluted examples of semidirect and wreath products were given in the last section, where the algebraic structures of Rubik's group and of the illegal Rubik's group are introduced. These are the groups of, respectively, all legal and possible (legal or illegal) moves one can perform on Rubik's cube. An illegal move is such that it cannot be performed without taking the cube apart and reassembling it differently. Rubik's group is generated by all legal basic moves that can be performed on Rubik's cube - for example, twisting a face of the cube left or right. This extremely large-sized group contains two particular subgroups, namely the subgroups of orientation-preserving and position-preserving moves. The first is such that any of the moves in it, if applied to the cube, will leave the orientation of all the cube's 'cubies' unchanged, with respect to a labelling system priorly established on the cube itself, though they may change the position of the cubies. Similarly, the elements of the subgroup of position-preserving moves will not change the position of the cubies, but they may change their orientation. The main result proved in this work is that the legal Rubik's group is the semidirect product of the orientation-preserving and position-preserving subgroups. The method used is mainly based on, and it expands upon, that used by Charles Bandelow in his book Inside Rubik's cube and beyond. A second fact - that the illegal Rubik's group is isomorphic to a direct product of wreath products - was also proved as a secondary goal

Sustainability Relations for Innovation, Low-Carbon Principles for “Rubik’s Cube” Solution

It is very difficult to calculate in advance the positive and negative long-term impacts of an investment, or a development venture. A serious global problem arises from the fact that numerous environmental-protection oriented private and government ventures are implemented in an incorrect manner significantly impair the conditions of both the environment and the economy (market). There is a high number of innovative energy related investments, waste and water management projects, etc. in Europe, which cause more harm to the society than ever imagined. The various sustainability logics can be synchronised with the 3×3×3 Rubik’s Cube’s solution algorithms, and the relations of the cube’s sides define a planning strategy that provides a new scientific approach for investment planning. We theoretically evaluated the various solution processes, and paralell investment planning levels following the solution levels and stages of the cube. After these various level-evaluations, we made „low-carbon interpretation” summaries

Learning problem solving strategies using refinement and macro generation

In this paper we propose a technique for learning efficient strategies for solving a certain class of problems. The method, RWM, makes use of two separate methods, namely, refinement and macro generation. The former is a method for partitioning a given problem into a sequence of easier subproblems. The latter is for efficiently learning composite moves which are useful in solving the problem. These methods and a system that incorporates them are described in detail. The kind of strategies learned by RWM are based on the GPS problem solving method. Examples of strategies learned for different types of problems are given. RWM has learned good strategies for some problems which are difficult by human standards. © 1990