Rubik's Cube Research Articles

Harnessing Rubik's Cube Algorithm for Counteracting Man-in-the-Middle Attacks

Harnessing Rubik's Cube Algorithm for Counteracting Man-in-the-Middle Attacks

Application Research and Teaching Implementation of Rubik's Cube Furniture in Home Design

A diversified teaching evaluation system has been established based on the characteristics of teaching content, with more diverse evaluation subjects including enterprises, teachers, and students. The evaluation content is more diverse, including daily performance evaluation, homework evaluation, project implementation evaluation, and project achievement evaluation; The evaluation methods are more diverse, including enterprise evaluation, teacher evaluation, teacher-student mutual evaluation, questionnaire voting, and other evaluation methods.

Rubik's Encryption Combined with CNN for Biometric Authentication

In response to the rapid evolution of technology, safeguarding user data has become paramount, necessitating a robust solution against diverse cyber threats. This research project proposes a comprehensive approach that integrates biometric authentication, specifically iris and fingerprint recognition, with a sophisticated encryption system based on Rubik's Cube and facilitated by Convolutional Neural Networks (CNNs). Biometric authentication establishes an unassailable link between data records and individuals, ensuring heightened accuracy and security. To counter potential threats, the project incorporates a resilient technique known as zero-bit watermarking, embedding minimal information without compromising the original biometric data's size or quality. The integration of Rubik's Cube-based encryption adds an additional layer of complexity to data protection, employing a dynamic and visually intricate encryption algorithm. The amalgamation of iris and fingerprint authentication leverages the unique biological characteristics of individuals, creating a multi-layered security approach. The CNNs play a pivotal role as the backbone for efficient feature extraction and authentication decision-making, enhancing the overall system's accuracy and reliability. This innovative fusion of cryptographic methods and biometric authentication offers a comprehensive solution for safeguarding sensitive information across diverse applications, from secure data storage to fortified communication channels, addressing the evolving landscape of cybersecurity challenges.

Multi-level image security using modified Rubik's cube algorithm

Multi-level image security using modified Rubik's cube algorithm

Text security by using a combination of the vigenere cipher and the rubik's cube method of size 4×4×4

Background: In the current era of technology, information security is increasingly important. The growth of technology leads to a higher level of threat to the security of data and information dissemination, and cryptography is a valuable protective tool.Aim: The primary objective of this research is to enhance text security through the fusion of the Vigenere cipher and the Rubik's cube algorithm. By leveraging this novel approach, we aim to fortify the confidentiality of textual data against potential eavesdroppers and adversaries. To demonstrate the practicality of this method, we perform a simulation using the Python programming language within the Google Colab environment. Method: This study employs a qualitative research methodology supplemented by empirical simulation. The combination of the Vigenere Cipher and the Rubik's Cube algorithm in a 4×4×4 configuration is implemented to encrypt and decrypt text. The simulation is executed using the Google Colab platform, enabling a practical illustration of the encryption process.Result: The results of our research indicate the feasibility of generating ciphertext through the amalgamation of the Vigenere Cipher and the Rubik's Cube algorithm in the specified 4×4×4 configuration. The simulation conducted in Google Colab serves as concrete evidence of the effectiveness and practicality of this combined encryption method.Conclusion: In conclusion, this research offers a compelling approach to bolstering text security in the modern era of information technology. By combining the Vigenere Cipher with the Rubik's Cube algorithm in a 4×4×4 configuration, we have demonstrated the potential to significantly enhance the confidentiality of sensitive textual data. The empirical simulation conducted in Google Colab reaffirms the practicality and viability of this innovative encryption technique, highlighting its potential as a valuable tool in the realm of information security.

The Rubik's cube of doing and being: Factors influencing professional identity transition to the medical registrar.

Professional identity transitions, such as the transition to medical registrar, are challenging. How minoritised identities influence transitions during medical training requires further study. This study aimed to explore the factors influencing the transition to the medical registrar in Scotland to guide support during training. Interviews exploring this transition with internal medicine trainees were audio recorded, transcribed verbatim and double-coded using template analysis. We applied an initial coding template informed by multiple and multidimensional transition theory of individual, interpersonal, systemic and macro-level factors. Using a critical theory lens, a further template analysis specifically sought to understand how trainees' social identities interacted with the various levels. Nineteen IM trainees were interviewed between January 2021 and February 2022. Influential factors reflected a parallel process of competence (doing) and identity (being) development. The interaction of social identities, such as gender (being a woman) and country of origin (being an international medical graduate), occurred across levels. This can be conceptualised as a Rubik's cube with the interplay between doing and being from an individual to a macro level with trainees' social identities interacting at all levels. The transition to the medical registrar is multifaceted; with a challenging balance between support and independence in providing opportunities to perform (doing) whilst identity develops (being). Identity transitions involve multiple Rubik's-cube-like rotations between the facets of 'doing' and 'being,' until these align. Taking heed of influential factors and the interaction of minoritised social identities could guide a trainee-centred and smoother transition.

AlphaZero-Inspired Game Learning: Faster Training by Using MCTS Only at Test Time

Recently, the seminal algorithms AlphaGo and AlphaZero have started a new era in game learning and deep reinforcement learning. While the achievements of AlphaGo and AlphaZero - playing Go and other complex games at super human level - are truly impressive, these architectures have the drawback that they require high computational resources. Many researchers are looking for methods that are similar to AlphaZero, but have lower computational demands and are thus more easily reproducible. In this paper, we pick an important element of AlphaZero - the Monte Carlo Tree Search (MCTS) planning stage - and combine it with temporal difference (TD) learning agents. We wrap MCTS for the first time around TD n-tuple networks and we use this wrapping only at test time to create versatile agents that keep at the same time the computational demands low. We apply this new architecture to several complex games (Othello, ConnectFour, Rubik's Cube) and show the advantages achieved with this AlphaZero-inspired MCTS wrapper. In particular, we present results that this agent is the first one trained on standard hardware (no GPU or TPU) to beat the very strong Othello program Edax up to and including level 7 (where most other learning-from-scratch algorithms could only defeat Edax up to level 2).

A Lightweight Image Encryption Algorithm Based on Elliptic Curves and a 5D Logistic Map

Cryptography can be thought of as a toolbox, where potential attackers gain access to various computing resources and technologies to try to compute key values. In modern cryptography, the strength of the encryption algorithm is only determined by the size of the key. Therefore, our goal is to create a strong key value that has a minimum bit length that will be useful in light encryption. Using elliptic curve cryptography (ECC) with Rubik's cube and image density, the image colors are combined and distorted, and by using the Chaotic Logistics Map and Image Density with a secret key, the Rubik's cubes for the image are encrypted, obtaining a secure image against attacks. ECC itself is a powerful algorithm that generates a pair of public and private elements, and we generate secret key values ​​with the help of the above key pair. This algorithm is applied to smart cards, sensors, and wireless network security. Whereas, the test results indicate that the highest value for PSNR is 7.9641, while the highest values for UACI and NPCR are 35.3721 and 99.9992, respectively. The encoding and decoding speeds reach 0.1561 and 0.1532 seconds, respectively.

Group theory behind Rubiks Cube

The Rubiks Cube is a widely recognized puzzle. The mathematics behind the Rubiks Cube is group theory. Group theory studies algebraic structures in mathematics such as groups, rings, and fields. The operation of the Rubiks Cube is rotation, which can be considered an operation of a group. The combination of two rotations of the Rubiks Cube can be considered the association of two operations of a group. The rotations and the combination operation of two rotations form a group called the Rubiks Cube group, and this paper presents the order of this group which is also the quantity of possible valid configurations of the Rubiks Cube. The valid configurations are the configurations that can be reached by a series of rotations from the starting configuration. This paper presents a method to illustrate the configurations of the Rubiks Cube, the requirements for making the configurations valid, and calculate the quantity of possible valid configurations.

Research on the group theory based on the perspective of the Rubiks Cube

With the development of mathematics, more and more fields of study have been created and progressed, it is worth to implement the knowledge into the real life. There is a well-known puzzle called the Rubiks Cube, has many connections to a branch of abstract algebra group theory. Therefore, this paper will discuss how the Rubiks Cube showing the properties from group theory, by introducing basic knowledges of group theory, followed by examples in terms of this intelligent toy. This paper will first introduce the properties of the Rubiks Cube, then move to the construction of its group. Subsequently, the four axioms that form a group are explained. After that, the reasons why the operations of the Rubiks Cube are able to form a group are explained as the examples of those four axioms. It is followed by the concepts in group theory, and provisions of the exemplifications in terms of the Rubiks Cube, such as closure, cyclicity, Cayleys graph. Explaining the group theory from the perspective of the Rubiks Cube provides a tangible channel to learn the intangible knowledges effectively. Learners are able to study these hard knowledges easily by rotating a simple toy and observing the conclusions.

Applications of Hypergroup Theory in Solving the Rubik's Cube

Rubik küpünün çözümünün hiper gruplar yardımıyla literatürde var olan grup cebirsel yapısından farklı bir cebirsel yapıyla tasarımı sağlanmıştır. Rubik küp çözümünün stratejisinin gelişim kaydedeceği yöntem olarak genelleştirilmiş permütasyon hiper grup kavramı benimsenmiş olup; grup teoride uygulanan yöntemlerin geliştirilmesi ile gerçekleştirilmiştir. Soyut cebir çalışmalarının uygulama bulması konusunda tüm dünyada yetersizlikler mevcut olmasına rağmen bu çalışma ile Rubik küpün hiper gruplar yardımıyla çözümleme esası elde edilmiş; böylece ulusal ve uluslararası akademik araştırmalara, ülkemizdeki soyut cebir alanında yürütülen çalışmaların uygulaması olması hususunda katkı sunulmuştur. Dolayısıyla Rubik küp yardımıyla literatürde var olan cebir çalışmalarının uygulamaya dönüştürülebilir olduğu kanıtlanmıştır.

Ultra-sensitive self-powered sensor based on the hollow Rubik's cube substrate and multiple signal amplification strategy for real-time heavy metal detection

As a common heavy metal pollutants, lead ion (Pb2+) content monitoring has always been the focus of environmental protection. The rapid development of self-powered electrochemical biosensors open up the broad application prospects for Pb2+ detection. In this work, we innovatively design three-dimensional (3D) hollow cube bimetallic sulfide heterojunction microparticles combine with DNAzyme functional nucleic acid mediated by hybridization chain reaction (HCR) strategy to construct the ultra-sensitive self-powered sensor. The multiple amplification technology synergically enhanced the sensitivity. The electrochemical data show that the sensor has a wide linear response in the range of 0.0010–25 ng·mL−1 with the low detection limit is 3.10 pg·mL−1 (S / N = 3). The most special feature is that the introduction of commercial smart phone APP can effectively reduce cost, simplify process, and realize rapid on-site detection. In conclusion, the work can provide a feasible strategy for monitoring other hazardous substances, and advance the determination of environmental pollutants in the field.

Artificial Intelligence as a tool for analyzing cognitive and thinking problems: Rubik's Cube

There is a wide variety of artificial intelligence (AI) algorithms today. The use of these algorithms can be carried out in different areas or fields of action, in turn, with different levels of efficiency. The objective of this article is to carry out an analysis of the impact of artificial intelligence algorithms and the various implementation mechanisms that can be used specifically in problem solving. The study proposes a documentary investigation, exhibiting a problem-solving case study known as Rubik's Cube, which is a mechanical puzzle that requires logical and spatial thinking skills. It is demonstrated that the application of AI algorithms is successfully used to reach a faster and more efficient resolution of the aforementioned puzzle, and that teaching its resolution contributes to the development of cognitive and logical thinking skills in students. It is expected that this contribution to the academic-scientific society will generate a new line of research in the development of cognitive skills and logical thinking with the use of AI to solve various problems in any area.

Analysis of Image Encryption and Decryption Algorithm based on Rubik’s Cube Principle

Technology is evolving today more quickly than could have been anticipated. The benefits of these quick adjustments haven't lessened worries about data security. The Rubik's cube approach is used in the article to build security measures for images. Here, the image is encrypted using XOR operations and pixel shuffles, and it is decrypted in a similar manner. Using a key, the XOR operator is used to odd rows and columns of a photograph in order to muddle the relationship between genuine and encrypted images. The same key is reversed and used to align even picture rows and columns. And we discovered that it is a lot safer approach for encryption of images. This technology makes it possible to follow a good process for guaranteeing the security of the image files, which are transmitted practically every second. The algorithm has been tested on a variety of photo types, and the results are shown.

La Cantatrice Chauve (The Bald Soprano); La Leçon (The Lesson); Les Chaises (The Chairs)

La Cantatrice Chauve (The Bald Soprano); La Leçon (The Lesson); Les Chaises (The Chairs)

A compressive sensing encryption scheme for dual color images based on discrete memristor map and Rubik’s cube scramble

The most common in practical image encryption are multiple color images, however, less attention is paid to inter-layer correlation broken in existing color image encryption algorithms. In this paper, a 2-D compressive sensing dual color images encryption algorithm based on a discrete memristor hyper-chaotic map and Rubik's cube scramble is proposed. First, we propose a new discrete memristor-Ikeda map (DM-Ikeda), the analysis result shows the DM-Ikeda map has extremely high complexity and hyper-chaotic dynamical behavior. Second, to facilitate ciphertext transmission, the images are compressed and encrypted simultaneously by DM-Ikeda map and 2D compressive sensing. Then, we design a new rubik's cube scramble algorithm, which combines the layers of two images into a cube that can be expanded in different orders, and swaps the pixels of rows, columns or faces of each image by rotating the cube to achieve image scramble. This algorithm can break the correlation not only of pixels within layers of two images but also of pixels between different layers of images. Finally, two images are further diffused with the use of hyper-chaotic sequences. The algorithm can achieve both compression and encryption of dual color images. Experimental results indicate that, our scheme has excellent compression, and can break the correlation between different images and layers, which is excellent resistance to statistical attacks and has high security.

The Rubiks Cubes in Group Theory

This paper expounds the basic concept of group theory and its application in Rubiks Cube transformation and restoration formula. The different states of the magic cube are regarded as the elements of the magic cube group, and the set generated by six basic operations is equivalent to the homomorphism of the magic cube group for analysis, from the mathematical characteristics of the permutation group to some practical examples. The collection of possible states of Rubik's Cube is a group, called Rubik's Cube Group, which can be analyzed with the knowledge of group theory. The essence of the magic cube group is the subgroup of the substitution group. There are six basic operations of the magic cube. The combination of basic operations can only produce even pairs of blocks to exchange positions or flip directions at the same time. Therefore, there are some restrictions on the transformation of the magic cube. Some practical examples give some ideas for creating the magic cube formula.

Characterisation of frailty phenotypes and analysis of the association with peri-operative/interventional complications in elderly cardiac patients

Abstract Funding Acknowledgements Type of funding sources: None. Background/Introduction Identifying the key frailty phenotypes that impact functional health outcomes in older cardiovascular patients (CVD) in clinical practice is a step towards solving the complex "Rubik's Cube" of frailty. It should be pointed out which frailty phenotypes representing the patient's physical (e.g. mobility, strength, gait speed), cognitive (e.g. dementia) or nutritional status (e.g. risk of malnutrition, protein levels) correlate with major complications (e.g. mortality, delirium) in elderly patients. Phenotypes of frailty that correlate with complications could be used to identify patients at higher risk of poor postoperative outcomes and could be addressed through preventive strategies (e.g. prehabilitation). Purpose Identification of physical, nutritional and cognitive frailty phenotypes and investigate the correlation with complications in elderly patients undergoing cardiac surgery (e.g. coronary artery bypass graft, isolated single valve) or transcatheter aortic valve implantation (TAVI). Methods Between 06/2021 and 07/2022, patients (77.6 ± 4.3) referred for elective cardiac surgery or TAVI were included in the study. At hospital admission, physical frailty was identified by the simultaneous presence of: low gait speed (5-meter Walk Test), moderate impaired mobility (Timed Up-and-Go), reduced handgrip (dynamometer) and legs strength (5-repetitions chair rise). Mild dementia (Mini-Mental State Examination) characterised cognitive frailty and risk of malnutrition (Mini Nutritional Assessment) plus low serum protein level (serum albumin) nutritional frailty. The primary outcome was the presence of perioperative complications (mortality and major morbidity, e.g. delirium, pneumonia). Additionally, the total number and type of complications and the length of hospital stay (LoS) were collected. Correlations between frailty phenotypes, complications and LoS were calculated (Spearman). Results In total, 63 patients were referred to cardiac surgery (n=34, 54%) or TAVI (n=29, 46%) and were included (Table 1). Overall, 20 patients (36%) were characterized as physically frail. 33 patients (52%) were found to be cognitively frail, and 17 patients (26%) identified as nutritionally frail; no significant differences were found between the surgical and TAVI groups (Figure 1). Altogether, 37 patients (59%) experienced ≥ 1 complication such as need of transfusion (n=24, 38%), atrial fibrillation (n=14, 22%), delirium (n=12, 19%), pneumonia (n=8, 13%) or renal failure (n=6, 10%); one patient died. Physical and nutritional frailty correlate with the presence and total number of complications and prolonged LoS, but only in TAVI patients (Figure 1). Conclusion If these results are confirmed in a multivariate analysis, preventive strategies targeting physical and nutritional frailty should be considered, especially in TAVI patients, to reduce the incidence of complications and prolonged LoS.

A Rubik's Cube Cryptosystem-based Authentication and Session Key Generation Model Driven in Blockchain Environment for IoT Security

Over the past decade, IoT has gained huge momentum in terms of technological exploration, integration, and its various applications even after having a resource-bound architecture. It is challenging to run any high-end security protocol(s) on Edge devices. These devices are highly vulnerable toward numerous cyber-attacks. IoT network nodes need peer-to-peer security, which is possible if there exists proper mutual authentication among network devices. A secure session key needs to be established among source and destination nodes before sending the sensitive data. To generate these session keys, a strong cryptosystem is required to share parameters securely over a wireless network. In this article, we utilize a Rubik's cube puzzle-based cryptosystem to exchange parameters among peers and generate session key(s). Blockchain technology is incorporated in the proposed model to provide anonymity of token transactions, on the basis of which the network devices exchange services. A session key pool randomizer is used to avoid network probabilistic attacks. Our hybrid model is capable of generating secure session keys that can be used for mutual authentication and reliable data transferring tasks. Cyber-attacks resistance and performance results were verified using standard tools, which gave industry level promising results in terms of efficiency, light weightiness, and practical applications.

Introduction of Several Special Groups and Their Applications to Rubik’s Cube

Group theory is the subject that aims to study the symmetries and structures of groups in mathematics. This work provides an introduction to group theory and explores some potential applications of group theory on complex geometric objects like the Rubik's cube. To this end, the concepts of symmetric group, permutation group, and cyclic group are introduced, and the famous Lagrange’s theorem and Cayley’s theorem are mentioned briefly. The former theorem establishes that a subgroup’s order must be a divisor of the parent group’s order. Concerning the permutation group, it is a set of permutations that form a group under composition. Hence, the various groups that can be formed by the Rubik's cube are discussed, including the group of all possible permutations of the cube's stickers, and the subgroups that are generated through permutations of the six basic movements embedded in Rubik’s cube. Overall, this essay provides an accessible introduction to group theory and its applications to the popular Rubik's cube.