The Overview of Elliptic Curve Cryptography (ECC)

Abstract Elliptic Curve Cryptography (ECC) is one of the strongest and most efficient cryptographic techniques in modern cryptography. This paper gives the following introduction: The introduction of cryptography’s development; the introduction of the elliptic curve; the principle of ECC; the horizontal comparison between ECC and other types of cryptography; the modern breakthrough of ECC; the applications of ECC; by using a method of literature review. The study’s findings indicate that this factor is responsible for the rapid historical development of cryptography, from the classical password to the leap to modern cryptography. Elliptic Curve Cryptography (ECC), as one of the most important modern cryptographies, is stronger than most other cryptographies both in terms of security and strength, because it uses an elliptic curve to construct and, at the same time, uses mathematical operations to encrypt and generate keys. At the same time, elliptic curve cryptography can continue to improve the speed and intensity with the improvement of accelerators, scalar multiplication, and the speed of order operation. The applications of the elliptic curve in ECDSA and SM2 are very efficient, which further illustrates the importance of elliptic curve cryptography.