Computational number theory in 2021/22's spring term

    Next exam: June 14 (Thuesday) 8:15-, D-0-827.
    Consultation: June 13 (Monday) 14:00-, D-817.

    Printed University Note (under preparation)

    1st Lecture     message
    2nd Lecture
    3rd Lecture
    4th Lecture
    5th Lecture
    6th Lecture
    7th Lecture
    8th Lecture
    9th Lecture
    10th Lecture
    11th Lecture
    12th Lecture (handwritten)
    12th Lecture (latex with sans-serif fonts)
    13th Lecture (latex with handwritten fonts)
    13th Lecture (latex with sans-serif fonts)
    14th Lecture

    The following two books serve as the foundation for the majority of the course:
    Neal Koeblitz, A Course in Number Theory and Cryptography, Springer, 1994.
    Abhijit Das, Computational Number Theory, CRC Press, 2013.
    The section about cryptography in history is mostly relied on Wikipedia articles.
    Besides from the abovementioned, the note is based on a variety of other literature. The complete bibliography can be found at the end of each chapter in the printed edition of the course (currently being translated from Hungarian).

    Additional materials:


    Caesar Cipher
    Substitution Cipher
    Vernam Cipher
    Vigenere Cipher
    Calculating square roots easily in 3 ways
    Everything you need to know about operations in modular arithmetic
    Modular exponentiation
    Multiplicative inverses mod n
    Fermat primality test
    Miller-Rabin Primality Test
    RSA Algorithm
    Elliptic Curve Diffie-Hellman
    Elliptic Curve Method of Factorization
    Random Numbers with LFSR (Linear Feedback Shift Register)

    Useful links:

    Chinese remainder theorem
    Primitive root modulo n
    Quadratic residue
    Legendre symbol
    Jacobi symbol

    Jegyzet magyarul (Hungarian version of the note)

    The first appearance of the substitution cipher in the literature:
    Edgar A. Poe, The gold-bug
    magyar fordítás