Page 192 - Cyber Defense eMagazine Annual RSA Edition for 2024
P. 192
Fundamentals of Elliptic Curve Cryptography Operations
Somewhat…Unlocking the Mysteries of Secure Communication
By Joe Guerra, Cybersecurity Professor, Hallmark University
What is Elliptic Curve Cryptography?
Elliptic curve cryptography (ECC) is based on the algebraic structure
of elliptic curves over finite fields. The elliptic curves used in
cryptography are defined by an equation that looks like:
3
2
Y = x + ax + b
3
2
Where 4a + 27b != 0 (which ensures that the curve doesn’t have any
singularities.
The security of ECC comes from the difficulty of the Elliptic Curve Discrete Logarithm Problem (ECDLP).
For cryptographic purposes, we focus on the points on the curve that form a finite group under the addition
operation defined geometrically.
192
