Fundamentals of Cryptography

MSc course · AzTU Cybersecurity Department · Fall 2026 · Teaching Assistant: Ali Huseynli

Interactive algorithm explainers

Step-by-step visual walkthroughs of the algorithms covered in lectures. They run in the browser, no installation needed.

Classical ciphers

Classical · shift cipher

Shift every letter by k on a cipher wheel, and break it by trying all 26 keys.

Classical · multiply and shift

c = (a·p + b) mod 26: why a must have no common factor with 26, and how a⁻¹ decrypts.

Classical · polyalphabetic

Vigenère cipher

A key word gives a new shift for every letter: the Vigenère table, and why the repeating key is its weakness.

Classical · one-time pad

XOR every bit with a random key: perfect secrecy, and what goes wrong when a key is used twice.

Cryptanalysis · Kasiski 1863

Breaking Vigenère

Repeated pieces give the key length; then every column is a Caesar cipher, broken by letter frequencies.

Stream ciphers

LFSR · building block

LFSR, step by step

Taps, feedback and period; the LFSR as a stream cipher; and how Berlekamp–Massey breaks one LFSR from 2n bits.

A5/1 interactive demo

How GSM turns a 64-bit key and a frame number into keystream.

Block ciphers

Lecture 04 · DES

Feistel rounds, the inside of f, S-boxes and the key schedule.

AES · FIPS-197

AES, step by step

SubBytes, ShiftRows, MixColumns, AddRoundKey, the key expansion and diffusion.

PRESENT · lightweight

PRESENT, step by step

The 4-bit S-box, the bit permutation, the 80/128-bit key schedule and diffusion.

Dipper · lightweight SPN–ARX

Dipper, step by step

GIFT S-boxes, word rotations, modular additions with carries, the bit permutation and the key schedule.

Modes · ECB to GCM

Modes of operation, step by step

How a block cipher encrypts a whole message: ECB, CBC, CTR, CFB, OFB and GCM, why an IV is needed, bit errors and four real attacks.

Public-key cryptography

RSA · public key

RSA, step by step

Why public keys exist, the maths behind RSA, real 2048-bit keys, factoring, and the attacks that make padding necessary.

Discrete log · Diffie–Hellman

Discrete log, step by step

Diffie–Hellman, groups and generators, the man in the middle, three ways to attack the log, Pohlig–Hellman and ElGamal.

Coming soon

Digital signatures

RSA and (EC)DSA signatures, signing and verification.