Definition and usage of Elliptic Curve Cryptography

Data encryption technologies continue to advance as hackers find more sophisticated ways to access systems, programs, and communication. The Elliptic Curve Cryptography (ECC) is a data encryption algorithm that generates key pairs for public and private keys when encrypting and decrypting communication and network traffic (Singh & Singh, 2015). This algorithm applies calculations used in elliptic curves. On most occasions, ECC is associated with the Rivest–Shamir–Adleman (RSA) encryption algorithm. However, unlike RSA, ECC uses a smaller key size. In cryptography, the trapdoor function plays a significant role in security data, making the whole process foolproof. In essence, a trapdoor function entails a function that is easily computed in one direction but becomes difficult when trying to compute using the opposite direction (Singh & Singh, 2015). For instance, the function a + b = c can be computed in both directions if the values of two variables are known. As such, the function would not be classified as a trapdoor function.

In recent times, ECC has grown in popularity based on its smaller key size. While uses prime numbers to generate public and private keys, ECC employs an algebraic structure of a curved ellipse. The algorithm uses the function y 2 = x 3 + ax + b to determine the shape of the curve given values of a and b (Singh & Singh, 2015). The key size is crucial in determining how secure the encryption is as it also determines the size of the curve. A person accessing an ECC encrypted information would find it difficult without a private key. This is because recreating the function or guessing the number of times the curve was intersected is near impossible (Singh & Singh, 2015). Even with today's high computing power, solving an elliptic algorithm is more challenging than the factoring method used by RSA and other encryption mechanisms. ECC promises to provide better security and encryption features compared to the current algorithms at a smaller footprint.

Reference 

Singh, L. D., & Singh, K. M. (2015). Implementation of text encryption using elliptic curve cryptography.  Procedia Computer Science ,  54 , 73-82.  https://doi.org/10.1016/j.procs.2015.06.009