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

Subjects

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:

Videos:

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