Lecture

Prime Numbers and Algorithms

Related lectures (27)

Explores optimizing exponentiation in modular arithmetic for efficient calculations and prime number determination.

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

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

Covers the fast exponentiation algorithm and its time complexity, prime number properties, and the El-Gamal encryption scheme.

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

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

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

Explores RSA cryptography, covering primality testing, quadratic residues, and cryptographic applications.

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

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

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

Covers classical and quantum computational complexity concepts and implications.

Explores practical aspects of solving parity games, including winning strategies, algorithms, complexity, determinism, and heuristic approaches.

Delves into the complexity of factoring polynomials and the implications for security.

Covers worst-case complexity, algorithms, and proofs including mathematical induction and recursion.

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

Explores methods and algorithms for integer factorization, including testing for B smoothness and computing small primes.

Explores algorithmic complexity, comparing growth rates using Theta notation and characterizing different complexity classes.

Explores prime number generation, Diffie-Hellman key exchange, and one-way operations in cryptography with practical examples.