EC Cryptography Tutorials - Herong's Tutorial Examples - v1.02, by Dr. Herong Yang
What Is Discrete Logarithm Problem (DLP)
This section describes what is Discrete Logarithm Problem (DLP), which is the reverse operation of an exponentiation (or scalar multiplication) operation in an Abelian group.
What Is Discrete Logarithm Problem (DLP)? DLP in an Abelian Group can be described as the following:
For a given element, P, in an Abelian Group, the resulting point of an exponentiation operation, Q = Pn, in multiplicative notation is provided. The problem of finding the smallest exponent, n, such that Pn = Q, is called Discrete Logarithm Problem (DLP).
In other words, the reverse operation of an exponentiation is called DLP, which can be expressed as the following using the "Logarithm" function, log(). This is where the "Discrete Logarithm Problem (DLP)" name comes from:
Given P and (Q = Pn), find the smallest n: n = logP(Q)
In additive notation, Discrete Logarithm Problem (DLP) can be expressed as the following using the "division" operation:
Given P and (Q = nP), find the smallest n: n = Q/P
Table of Contents
Geometric Introduction to Elliptic Curves
Algebraic Introduction to Elliptic Curves
Abelian Group and Elliptic Curves
►Discrete Logarithm Problem (DLP)
Doubling or Squaring in Abelian Group
Scalar Multiplication or Exponentiation
►What Is Discrete Logarithm Problem (DLP)
Examples of Discrete Logarithm Problem (DLP)
Scalar Multiplication on Elliptic Curve as Trapdoor Function
Generators and Cyclic Subgroups
tinyec - Python Library for ECC
ECDH (Elliptic Curve Diffie-Hellman) Key Exchange
ECDSA (Elliptic Curve Digital Signature Algorithm)