Public-key cryptography algorithms, especially elliptic curve cryptography (ECC) and elliptic curve digital signature algorithm (ECDSA) have been attracting attention from many researchers in different institutions because these algorithms provide security and high performance when being used in many areas such as electronic-healthcare, electronic-banking, electronic-commerce, electronic-vehicular, and electronic-governance. These algorithms heighten security against various attacks and at the same time improve performance to obtain efficiencies (time, memory, reduced computation complexity, and energy saving) in an environment of the constrained source and large systems. This paper presents detailed and a comprehensive survey of an update of the ECDSA algorithm in terms of performance, security, and applications.