Goal: The aim of the course is to familiarize students with the mathematical background required for cryptographic primitives and the algorithms related to them. The lectures will present encryption procedures that guarantee the security of cryptographic algorithms. From a practical perspective, students will learn about their implementation.
Course description: Historical overview, brief introduction to mono- and polyalphabetic systems, DES AES, divisibility, primes, number theory basics, relative prime, remainder division, linear congruence, remainder classes, first degree congruence equations, Euler’s φ function, Euler’s theorem, little Fermat’s theorem, Wilson’s prime test, Fermat’s prime test, AKS prime test, algebraic structure of fields, finite fields, field extension, RSA, SSL/TLS, PGP, elliptic curves, operation with elliptic curves, elliptic curves over finite fields, Diffie-Helmann key exchange, electronic signature properties, signature logic, signature content, signature with RSA, signature with elliptic curves, algorithms of quantum cryptography, Post quantum cryptography, standardizations.
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