Elliptic Curves in Modern Cryptographic Systems
Sahun Andrii · International Journal of Advanced Trends in Computer Science and Engineering · 2020
Modern cryptographic algorithms used in cryptocurrencies applications, EDS systems, and blockchain technologies use a mathematical apparatus based on elliptic curves (EC).It is known that not every EC, described by elliptic functions can be used in practice.This is due to the requirements for cryptographic stability.For EC-based cryptosystem algorithms, it is necessary to use subgroups of high-order points.It is theoretically clear that the parameters a, b, k of random ECs can be chosen by the attacker arbitrarily.These curves, used to generate public and private keys, exist in the public domain.These ECs are described in public libraries.It is important to know whether it is possible to predict in practice the values of the secret parameter k , which depend on a particular EC, for all signatures or random number generators used in asymmetric cryptographic algorithms and systems.