Lectures related to Number Theory: History and Concepts

Covers number theory, division, remainder, congruence, prime numbers, integer representation, and the Euclidean algorithm.

Introduces number theory and its essential applications in cryptography.

Introduces modulo arithmetic, Euclid's algorithm, and congruence in number theory.

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

Explores prime numbers, coprime integers, and their properties in number theory.

Explores Fermat's Little Theorem, its extensions, primality testing algorithms, and the significance of prime numbers in cryptography.

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

Covers the definition of a function to determine if a given number is prime.

Covers binary addition, prime numbers, and the sieve of Eratosthenes in number theory.

Explores Gaussian integers, prime factorization, and number theory concepts related to prime numbers.

Explores prime numbers, modular arithmetic, Wilson's theorem, and complexity analysis.

Covers examples of modular exponentiation, complexities, Lame's Theorem, Collatz Conjecture, and prime numbers.

Explores checking a generator of a group, the Diffie-Hellman key exchange, and cryptographic algorithms.

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

Explains congruence modulo m and its applications in arithmetic operations.

Introduces deterministic approaches to identify prime numbers and covers algorithms and modular arithmetic for prime number testing.

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

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

Introduces sets, maps, divisors, prime numbers, and arithmetic principles related to integers.

Covers the Bombieri-Vinogradov theorem and its implications for prime gaps and multiplicative sieve inequalities.