Lectures related to Commutative Groups: Foundations for Cryptography

Covers cohomology in real projective spaces, focusing on associative properties and algebraic structures.

Explores finitely generated abelian groups, focusing on their structure and isomorphism theorems.

Explores cyclic groups, generators, isomorphisms, and the discrete logarithm problem in depth, highlighting their importance and applications.

Explores quotients of groups by equivalence relations and the conditions for well-defined sets.

Explores the Chinese Remainders Theorem, RSA public-key cryptosystem, bijective properties, and key generation for encryption and decryption.

Explores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.

Explores associative operations on tuples and sets, demonstrating their properties through various examples and proofs.

Explores cryptography, perfect secrecy, group theory, and modern cryptographic milestones, emphasizing the trade-off between security and cost.