------------- TIME STAMP --------------

MODULAR ARITHMETIC
0:00:00 Numbers
0:06:18 Divisibility
0:13:09 Remainders
0:22:52 Problems
0:29:09 Divisibility Tests
0:34:44 Division by 2
0:47:05 Binary System
0:58:17 Modular Arithmetic
1:10:23 Applications
1:17:59 Modular Subtraction and Division

EULID'S ALGORITHM
1:29:44 Greatest Common Divisor
1:40:41 Eulid's Algorithm
1:55:48 Extended Eulid's Algorithm
2:05:57 Least Common Multiple
2:14:14 Diophantine Equations Examples
2:19:35 Diophantine Equations Theorem
2:35:13 Modular Division

BUILDING BLOCKS FOR CRYPTOGRAPHY
2:47:26 Introduction
2:55:16 Prime Numbers
2:58:28 Intergers as Products of Primes
3:01:31 Existence of Prime Factorization
3:04:06 Eulid's Lemma
3:09:01 Unique Factorization
3:19:01 Implications of Unique FActorization
3:29:50 Remainders
3:37:21 Chines Remainder Theorem
3:44:54 Many Modules
3:50:19 Fast Modular Exponentiation
4:00:20 Fermat's Little Theorem
4:07:36 Euler's Totient Function
4:14:25 Euler's Theorem

CRYPTOGRAPHY
4:19:01 Cryptography
4:26:16 One-time Pad
4:30:49 Many Messages
4:38:30 RSA Cryptosystem
4:53:08 Simple Attacks
4:58:25 Small Difference
5:04:18 Insufficient Randomness
5:12:01 Hastad's Broadcast Attack
5:20:18 More Attacks and Conclusion

About this Course
We all learn numbers from the childhood. Some of us like to count, others hate it, but any person uses numbers everyday to buy things, pay for services, estimated time and necessary resources. People have been wondering about numbers’ properties for thousands of years. And for thousands of years it was more or less just a game that was only interesting for pure mathematicians. Famous 20th century mathematician G.H. Hardy once said “The Theory of Numbers has always been regarded as one of the most obviously useless branches of Pure Mathematics”. Just 30 years after his death, an algorithm for encryption of secret messages was developed using achievements of number theory. It was called RSA after the names of its authors, and its implementation is probably the most frequently used computer program in the word nowadays. Without it, nobody would be able to make secure payments over the internet, or even log in securely to e-mail and other personal services. In this short course, we will make the whole journey from the foundation to RSA in 4 weeks. By the end, you will be able to apply the basics of the number theory to encrypt and decrypt messages, and to break the code if one applies RSA carelessly. You will even pass a cryptographic quest!

As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students.

⭐ Important Notes ⭐
⌨️ This course is created in collaboration with University of California SAN DIEGO

number theory lecture,
#numbertheoryandcryptography,
number theory course,
number theory computer science,
#numbertheorydiscretemath,
number theory discrete mathematics,
number theory examples,
number theory explained,
#numbertheoryfullcourse,
number theory in mathematics,
number theory introduction,
number theory in discrete mathematics,
number theory in cryptography,
number theory lecture series
number theory,
cryptography,
computer science,
math,
mathematics,
mathematics for computer science,
math that computer scientists learn,
how much math do computer scientists use,
what math is needed for computer science,
does computer science require math,
integers,