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Several chaotic system-based encryption techniques have been presented in recent years to protect digital images using cryptography. The challenges of key distribution and administration make symmetric encryption difficult. The purpose of this paper is to address these concerns, the novel hybrid partial differential elliptical Rubik’s cube algorithm is developed in this study as an asymmetric image encryption approach. This novel algorithm generates a random weighted matrix, and uses the masking method on image pixels with Rubik’s cube principle. Security analysis has been conducted, it enhances and increases the reliability of the proposed algorithm against a variety of attacks including statistical and differential attacks.

In this light, a differential elliptical model is designed with two phases for image encryption and decryption. A modified image is achieved by rotating and mixing intensities of rows and columns with a masking matrix derived from the key generation technique using a unique approach based on the elliptic curve and Rubik’s cube principle.

To evaluate the security level, the proposed algorithm is tested with statistical and differential attacks on a different set of test images with peak signal-to-noise ratio, unified average changed intensity and number of pixel change rate performance metrics. These results proved that the proposed image encryption method is completely reliable and enhances image security during transmission.

The elliptic curve–based encryption is hard to break by hackers and adding a Rubik’s cube principle makes it even more complex and nearly impossible to decode. The proposed method provides reduced key size.

In the realm of education, there has been an increasing emphasis on developing analytical thinking (AT) in the past few years. This systematic review focuses on an analysis of journal publications that have explored AT within the context of science, technology, engineering and mathematics (STEM) education. This analysis investigated four primary issues: (1) the operational definition that was used; (2) the types of theories that were used; (3) the interventions that were implemented to enhance AT skills; and (4) the research designs that were used.

To ensure a comprehensive and thorough review, we used the guidelines of preferred reporting items for systematic reviews and meta-analysis.

A comprehensive review of 28 pertinent scholarly articles reveals that scholars frequently rely on the concepts proposed by Anderson (2002), Marzano and Kendall (2008), Rodrangsee and Tuntiwongwanich (2021) and Suyatman et al. (2021) to establish a framework for delineating the competencies associated with analytical thinking (AT). Quasi-experimental designs were the most frequently used research designs in the studies analysed, followed by research and development approaches and then correlational designs. Most researchers have focused on investigating the effectiveness of problem-based learning as an intervention for improving AT skills. However, most research indicates that the theories or theoretical frameworks used to guide the research must be evident.

To the extent the authors know, this study represents the initial comprehensive examination of analytical thinking in STEM education. It presents a consolidated summary of the available evidence, assessing its quality and bringing it together in a single resource.