## 1 Introduction  
The internet is a vast network of interconnected computers that enable communication between people from all over the world. It provides a cost-effective way to communicate over long distances, making it an ideal medium for businesses and organizations [1]. However, with the convenience of the internet, there is always a risk of cyber-attacks [2]. Cyber-criminals can access sensitive information transmitted over the internet, including personal data, financial information, and corporate secrets. To mitigate this risk, cryptography is one of the techniques that is used to ensure the confidentiality, integrity, and authenticity of data. It is the practice of securing data by converting it into an unreadable format called cipher text [3]. The cipher text can only be read by someone who has the decryption key to convert it back to its original format. Cryptography can be either symmetric or asymmetric. Symmetric cryptography uses the same key for both encryption and decryption. The sender and the receiver both have access to the same key, making it easier to encrypt and decrypt data. However, the symmetric approach is less secure as the key needs to be shared between the sender and receiver, making it more vulnerable to cyber-attacks [4]. Asymmetric cryptography, on the other hand, uses two different keys for encryption and decryption [5]. The sender encrypts the data with the receiver's public key, and the receiver decrypts the data with their private key. Asymmetric cryptography is more secure than symmetric cryptography as the private key is never shared, making it more difficult for cyber-criminals to intercept the data. ECC is a type of asymmetric cryptography that is gaining popularity due to its security and efficiency [6; 7]. It is more secure than RSA [8], another popular asymmetric cryptography algorithm, because it requires shorter key sizes to achieve the same level of security [9]. This means that ECC is faster and requires less storage space, making it ideal for mobile devices with limited processing power and storage capacity [10; 11]. ECC implementation can be thought of as a stack of four distinct layers [3]. The foundation of the stack is the arithmetic operations layer, which includes the fundamental building blocks of mathematics such as addition, subtraction, multiplication, and division. These operations form the basis of elliptic curve group operations, which enable ECC's security and efficiency. The second layer of the stack is the point addition and point doubling layer, which enables the construction of new points on the elliptic curve by performing operations that combine existing points. This layer is a key component in ECC's scalability, as it allows for the generation of multiple points from a single base point. The third layer of the stack is point multiplication, which involves multiplying a point on the elliptic curve by a scalar. This layer is responsible for generating the final result of ECC operations, which are new points on the curve. The fourth and final layer is the protocol layer, which includes the implementation of ECC-based protocols used for key exchange, digital signatures, and encryption. This layer is responsible for the practical application of ECC, enabling secure communication and data protection in a wide range of contexts. One of the important challenges in implementing ECC is the risk of side-channel attacks [12], where an attacker can extract information from the implementation of the algorithm rather than trying to break the mathematical problem. One way to mitigate this risk is to use the hybrid algorithms that combine multiple techniques, such as Montgomery ladder and double-and-add algorithms. It can potentially increase the resistance to SPA attacks [13; 14]. In this context, Binary Edwards curves [15], which are known for their ability to resist side-channel attacks, are being increasingly used in various high-security applications.