Analysis Of Attack Methods Based on Elliptic Curve Discrete Logarithm Problem

With growing public concern about information security issues, cryptography is becoming increasingly essential not only in the military sector, but also in daily life. Numerous cryptographic techniques have been invented during past hundreds of years. Elliptic Curve Cryptography (ECC) is one of the most modern and efficient cryptography methods. Therefore, research on exploring advantages and disadvantages is necessary in order to make the best use of ECC. This paper aims to briefly introduce Elliptic Curve (EC) and how it can be applied to ECC. Moreover, this paper indicates the mathematical principle Elliptic Curve Discrete Logarithm Problem (ECDLP) behind Elliptic Curve cryptography: how it is different from traditional Discrete Logarithm Problem (DLP) and the difficulty to solve ECDLP which protects ECDLP from various attacks. Most importantly, several potential attacks against ECC such as Exhaustive Search and Pollard’s Rho algorithm are listed and discussed, which lead to reflections on the security issues of ECC and prospects for possible developments in the future.