Lecture

Prime Numbers and Primality Testing

Related lectures (23)

RSA Cryptography: Primality Testing and Quadratic Residues

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

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

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

Diffie-Hellman Cryptography: Key Exchange and ElGamal Encryption

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

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Explores Legendre and Jacobi symbols, quadratic residuosity, element orders, and RSA Cryptography complexities.

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

Integers: Sets, Maps, and Principles

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

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Commutative Groups: Foundations for Cryptography

Covers commutative groups and their significance in cryptography.

Prime Numbers and Algorithms

Covers prime numbers, primality testing algorithms, modular arithmetic, and efficient exponentiation methods.

Diffie-Hellman and ElGamal Cryptosystems

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

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

Fermat's Little Theorem: Applications and Probabilities

Explores Fermat's Little Theorem applications and probabilities in primality testing.

Generator of a Group

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

RSA Cryptography: Computational Problems

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

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Explores cyclic groups, generators, isomorphisms, and the discrete logarithm problem in depth, highlighting their importance and applications.

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Explores probability convergence, discussing conditions for random variable sequences to converge and the uniqueness of convergence.

Course Overview: Teaser on Course Contents

Offers an overview of propositional and predicate logic, sets, functions, relations, algorithms, Swiss cities, sorting tables, Covid infections, poker hands, and prime numbers.

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

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Explores the history and concepts of Number Theory, including divisibility and congruence relations.