Commutative Groups: Foundations for Cryptography

Related lectures (28)

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Introduces modular arithmetic, its properties, and applications in cryptography and coding theory.

Explores isomorphism and the order of group elements, emphasizing matching identities and inverses.

Explores the arithmetic of direct sum of abelian groups and the process of turning a monoid into a commutative group.

Covers prime numbers, RSA cryptography, and primality testing, including the Chinese Remainder Theorem and the Miller-Rabin test.

Explores product groups and isomorphism between sets with different operations but the same structure.

Explores commutative groups, Euler's Totient Function, and Cartesian products in group theory.

Explores the group structure and isomorphism of elliptic curves, including inverses, associativity, and compactification to the torus.

Covers the Diffie-Hellman key exchange protocol and the ElGamal public-key cryptosystem.

Covers the basics of group theory, including elements, associativity, identity, inverses, and closure.