Lectures related to Algorithms for Big Numbers: Z_n and Orders

Covers the classification theorem for finite abelian groups and introduces rings, including zero divisors and domains.

Covers the RSA cryptosystem, encryption, decryption, group theory, Lagrange's theorem, and practical applications in secure communication.

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

Explores Diffie-Hellman key exchange, ElGamal cryptosystem, and their security applications in cryptography.

Covers the ring of polynomials, focusing on coefficients and multiplication.

Covers polynomials, their operations, division theorem, and provides illustrative examples.

Introduces number theory and its essential applications in cryptography.

Explores the properties of commutative rings and integral domains in algebra.

Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.

Covers commutative groups and their significance in cryptography.

Covers the operations in rings, ideals, classes, and quotient rings.

Explores algebraic geometry, focusing on rings, bodies, quotient rings, and irreducible polynomials.

Introduces the definition and examples of A-modules, including sub-modules and ideals.

Covers the Euclidean algorithm for GCD calculation and algorithmic complexity analysis.

Introduces sub-rings and morphisms in ring theory, emphasizing stability by multiplication.

Introduces Z/mZ for writing equations with congruence classes in modular arithmetic.

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

Discusses Fermat's equation and Gaussian integers' properties.

Explores the Euclidean algorithm, Bézout's identity, extended Euclid algorithm, and commutative groups in mathematics.

Covers the design of datapath subsystems, focusing on various types of adders and multiplication algorithms.