Integer Factorization: Quadratic Sieve

This lecture delves into the analysis of integer factorization using the quadratic sieve method, discussing the factor base, polynomial degree manipulation, and the challenges of working with algebraic number fields. The instructor explains the importance of finding generators in groups and presents various algorithms, including the index calculus method and its limitations in elliptic curves. The lecture concludes with a focus on the discrete logarithm problem in cryptography, highlighting its relevance in key exchange protocols and signature schemes. The instructor also touches upon the birthday paradox and its application in finding collisions in cryptographic functions.