## 1 Introduction  
Cyber security awareness has positively impacted the development of security products on the market. Most people have smartphones to communicate with, browse the Internet, read e-mails, and perform their jobs. According to predictions, the number of mobile users worldwide will likely increase to 7.26 billion by the end of 2022 [1]. Regarding the potential for cyberattacks, almost everyone in the world needs security protection [2]. Information security is crucial due to the interception and modification of data, which can lead to loss of availability, integrity, confidentiality, as well as other losses, such as loss of life, money, and assets [3]. Therefore, encryption is an important tool in security products that must be associated with the smartphone to keep the user's data safe. Most mobile encryption applications available on the market rely on conventional standard encryption algorithms, such as the AES block cipher, which has been widely implemented in various industries for more than a decade due to its security strengths [4]. Since then, numerous block cipher algorithms have been developed, using AES as the design foundation and the security benchmark. Performance evaluations of encryption algorithms in mobile devices have been conducted by comparing cryptographic algorithms, such as AES, DES, TEA, RSA, and REA [5]. The experimentation results revealed that AES recorded the fastest execution speed for the encryption process. However, a conventional algorithm, such as AES, requires huge memory and high power consumption, which is not practical to be implemented in the software encryption application [6]. Therefore, there is an important need for a lightweight algorithm design that uses simple cryptographic operations to provide sufficient security to the devices while emphasizing efficiency. Over the years, a range of lightweight algorithms have been proposed in the literature that include BRIGHT [7], CRAFT [8], ACT [9], LRBC [10], LWE [11], PriPresent [12], T-TWINE [13], LBC-IoT [14], and improved SM4 [15]. Although lightweight algorithm research has been intensively explored using multiple techniques that aim for better efficiency, their security features cannot be ignored [16]. An algorithm should offer confusion and diffusion characteristics to provide sufficient security [17]. Confusion obscures the relationship between the plaintext and ciphertext with the substitution method, while diffusion spreads the plaintext statistics through the ciphertext using the permutation method. One solution to enhance the confusion and diffusion characteristics of a cryptographic algorithm is by implementing the three-dimensional (3D) design on the block cipher. The 3D design invention was introduced by [PERSON] [18], who adopted the model on the AES algorithm. It has been experimentally demonstrated that the deployment of the 3D cipher design can strengthen the security of the AES with provided confusion and diffusion to the algorithm. An alternative 3D design approach has similarly been suggested by [PERSON] and [PERSON] [19] using a 3D rotation block cipher that produced random outputs. Later on, [PERSON] et al. [20] constructed a 3D\(-\)AES using an immune-inspired approach that passed all statistical tests. In another work, [PERSON] [21] improved the encryption acceleration of the 3D block cipher using a unified byte permutation. Next, [PERSON] and [PERSON] [22] developed a non-alternate 3D model that was immune to differential and linear attacks. In 2019, [PERSON] et al. [23] employed 3D hybrid cubes that did not correlate the input and output. Recently, [PERSON] et al. [24] increased the security strength of the RECTANGLE cipher with a 3D bit rotation function. While the security strength of the block cipher could be improved by adopting the 3D design, there is an issue that needs to be resolved for the method to be applicable. The 3D design forces the algorithm to increase the block size and enlarge the key bits, thus decreasing its efficiency.