Solving the Discrete Logarithm Problem: Core Algorithms

The discrete logarithm problem forms the mathematical backbone of modern public-key cryptography and secure key exchange protocols. This text-based course guides you through the fundamental mathematical concepts and computational techniques used to approach and solve discrete logarithms step by step. You will build a solid understanding of algebraic structures, cyclic groups, and computational complexity before exploring square-root algorithms and subexponential methods through clear written explanations and algorithmic walkthroughs. What you'll learn: - Understand the mathematical definition and security implications of the discrete logarithm problem in cryptographic systems - Apply square-root time algorithms including the Baby-Step Giant-Step method - Analyze Pollard's rho algorithm and cycle detection techniques such as Floyd's and Brent's algorithms - Implement Pollard's kangaroo (lambda) method for targeted interval search - Master the two-phase Index Calculus algorithm for solving discrete logarithms over finite fields - Explore modern computational considerations and implications for elliptic curve cryptography The course begins with foundational terminology, modular arithmetic, and group theory basics before advancing sequentially through collision-based algorithms and index calculus methods. Designed for beginners in cryptographic mathematics, it requires no prior background in advanced number theory. Start reading today to deepen your understanding of foundational cryptographic algorithms.