Sumários
RSA Cryptography
18 outubro 2021, 16:30 • John Huerta
Examples of using Sun-Tzu's remainder theorem. An introduction to RSA. The main theorem of RSA on the existence of the decryption exponent. Beginning group actions. Every finite group is isomorphic to a subgroup of the symmetric group S
n, for some natural number n.
Number theory from group theory
15 outubro 2021, 17:00 • John Huerta
More examples of the Euclidean algorithm, the extended Euclidean algorithm, and multiplicative inverses mod n. Recap of Euler's phi function. Euler's theorem. Sun-Tzu's remainder theorem, commonly called the Chinese remainder theorem.
More on the isomorphism theorem. Rings and fields.
11 outubro 2021, 16:30 • John Huerta
A
3 is a normal subgroup of S
3. The quotient group is Z
2. Cyclic groups. Order of an element. The Euclidean algorithm. Rings and fields. The group of units mod n.
The isomorphism theorem
8 outubro 2021, 17:00 • John Huerta
Review of normal subgroups. Checking a definition is well-defined. Homomorphisms and isomorphisms. Isomorphism theorem.