Lecture

Cyclic Groups: Structure and Applications

Related lectures (28)

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

Covers commutative groups and their significance in cryptography.

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

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Explores discrete exponentiation complexity, cyclic groups, and practical cryptography, including popular algorithms like Diffie-Hellman and RSA.

Explores chirality, group completeness, Abelian groups, conjugate classes, and isomorphic groups in symmetry and group theory.

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

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

Explores Diffie-Hellman key exchange, group orders, Z_p field, and cryptographic challenges.

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

Delves into advanced group theory concepts such as isomorphisms and homomorphisms.

Covers the theory of groups and homotopical algebra, emphasizing natural transformations, identities, and isomorphism of categories.

Explores RSA cryptography computational problems, finite fields construction, and computational challenges in RSA cryptography.

Covers the classification of finite abelian groups and the unique sequence of positive integers for isomorphism.

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

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Explores the properties of relations in computer science, including equivalence relations and the partition of a set.

Explores the local structure of totally disconnected locally compact groups and their isomorphisms through conjugation.