Mathematical Insights into Cryptographic Algorithms: Recent Analysis and Future Directions

Particularly, in the last two decades, digital technologies have rapidly grown in a walk of life such as education, finance, information technology, e-vehicles, smart-homes, health care, etc. Therefore, the involved devices in the process exchange information during communication. Hence, the security of the information is a primary concern for the research and development community. Cryptography techniques are used to provide secure communication, considering the confidentiality and integrity of the messages. Symmetric and asymmetric key cryptography plays an important role in securing the information and ensuring the characteristics of the security pyramid. Symmetric key algorithms are generally faster than asymmetric key algorithms but asymmetric key algorithms are more secure. These algorithms are complex enough and hence require a rigorous cryptanalysis to compare. In this paper, the atomic operations are computed such as addition, multiplication, subtraction, division, and shift for asymmetric key cryptography algorithms to analyze and compare their performance. According to the obtained results, the computational cost of RSA is higher than El-Gamal and Elliptic Curve Cryptography (ECC) due to the usage of very large prime numbers and large exponential calculations. ECC also offers significantly lower computational overhead, making it particularly suitable for devices where power consumption is a critical consideration.