A Comparative Study of Elliptic curve and Hyperelliptic Curve Cryptography Methods and an Overview of Their Applications

The significance of cybersecurity in today's highly technological era cannot be overstated. With the advancement of modern technologies, various security measures have been developed. However, the gap to breach that security is also widening, compelling the need for enhanced security techniques. Hyper Elliptic Curve Cryptography (HECC) distinguishes itself from previous technologies by its distinct features, including untraceability, compressibility, and notably, its finite condition and key size. This research paper investigates HECC and its improved variant, Elliptic Curve Cryptography (ECC), while also conducting a survey of real-world applications where ECC and HECC have been utilized.