Elliptic Curve Cryptography (ECC) has grown to be very popular in public-key cryptographic systems, most popularly used in Bitcoin. ECC is based on the algebraic structures of elliptic curves over finite fields and the complexity of the elliptic curves discrete logarithm problem.
ECC incorporates all important asymmetric cryptographic systems features, including encryption, signatures, and key exchange. Because ECC employs fewer keys and signatures for the same degree of security as RSA and enables very quick key generation, key agreement, and signatures, it is considered a natural contemporary successor to the RSA cryptographic systems.
This article aims to explain elliptic curve cryptography and digital signatures used in Bitcoin in detail as simply as possible.