Elliptic Curve Cryptography in Magma and its Computational Complexities
Jonathan Donahue, Jang Yong Hee · ScholarWorks (Boise State University) · 2010
Cryptology is a vibrant field of mathematics concerned with securing information in a hostile environment. Here, we are going to present Elliptic Curve Cryptography based on Magma, a Computer Algebra system designed to solve computationally sophisticated problems in algebra, number theory, geometry and combinatorics. Magma doesn't provide Elliptic Curve functions on its interface. We shall program these functions based on our knowledge of structures of Magma. Furthermore, we will implement several cryptosystems based on Elliptic Curves in Magma and explain the computational complexities that support the security of these cryptosystems.