Elliptic Curve (EC) is the most recent and advanced technique of Elliptic Curve Cryptography (ECC). EC is often used to improve the security of open communication networks and to let specific persons with confirmed identities into the Modern Digital Era (MDE). Users of MDE make use of many technologies, such as social media, the cloud, and the IoT industry, among others. No matter what tool the users are using, the whole environment has to be able to keep their security and privacy preserved. The study of cryptography is required because unsecure networks make data transmission and the transfer of information susceptible to data theft and attack via an open channel. This makes it necessary to learn cryptography. The art of encrypting documents and communications using keys in such a way that only the individuals who are intended to receive them are able to decode and process them is referred to as cryptography. A digital signature, cryptographic data integrity, and authentication method all rely on the address of the receiver and the sender in addition to mathematical operations to find the signature. During the process of signature and verification, the solution that was presented is compared with the technique that is currently being used by ECDSA in order to illustrate the differences that exist between the two processes. This comprehensive survey of EC seeks to thoroughly investigate many scientific concepts, state-of-the-art, and innovative methodologies and implementations. This work will be useful for academics, who are interested in further analysis. Use and development of EC based schemes for cloud computing, e-health, and e-voting, is more secure as compared to RSA, and Diffie–Hellman schemes. In this comprehensive study, we claim that the adoption of EC methods in distributed computing and asynchronous networking provides significant benefits in distributed computing and interdependent networking.