Complete Cryptography and Ethical Hacking Masterclass 2025

Delve into cryptography’s maths foundations—sets, natural numbers, integers, modular arithmetic, gcd, and primes—tying these concepts to AES, RSA, and ElGamal basics.

This lecture explains inverse modulo and Euler's phi function, showing how to compute phi for primes and composites using gcd, with examples such as phi(6), phi(8), and phi(200).

Explore how cryptography protects data between authorized parties, covering encryption, signatures, hash functions, the CIA triad, and the Diffie-Hellman public key exchange in secure networks.

Develop skills in sets of integers, prime identification in z21, modular arithmetic, and gcd, while analyzing a function triplet with domain and codomain sizes.

Explore the extended gcd algorithm and how gcd(a, n) = 1 yields x*a + y*n = 1, giving the inverse of a mod n in practice.

Apply Euler's and Fermat's theorems, and learn the phi function and extended gcd to find modular inverses. Then explore groups, rings, polynomial rings, and finite fields such as GF(p^k).

Explore symmetric key cryptography and classical ciphers, including substitution and transposition methods, Caesar and affine ciphers, monoalphabetic and polyalphabetic systems, and core terms like plain text, cipher text, and key.

Master modular arithmetic techniques, including positive equivalents, binary, Fermat and Euler theorems, plus the Chinese remainder theorem. Understand confidentiality, integrity, availability, and threat versus attack.

Explore modern symmetric key cryptography, including Feistel ciphers, diffusion and confusion, and block and stream cipher modes such as ECB, CBC, CFB, OFB, and CTR.

Explore AES, the 1997 block cipher using 128-bit blocks in a 4x4 state, with key sizes 128/192/256 and rounds driven by subbytes, shift rows, mix columns, and add round key.

Explore stream and block ciphers, one-time pad limitations, symmetric versus asymmetric schemes, caesar cipher techniques, monoalphabetic versus polyalphabetic encoding, and the public key crypto system.

Explore the Chinese remainder theorem through practical congruences, with a quick review of functions, injective and surjective mappings, bijections, and pairwise relatively prime moduli.

Learn the proofs of RSA, from choosing p and q and computing n and phi(n) to selecting e and d, then encrypting and decrypting messages with public and private keys.

Learn public key cryptography with diffie-hellman and rsa, using public/private keys for encryption and signatures, addressing key distribution, man-in-the-middle risks, and attacks like cpa and cca.

Explain ciphertext-only, known-plaintext, chosen-plaintext, and chosen-ciphertext attacks, and RSA's vulnerability to chosen-ciphertext attacks. Describe Vernam one-time pad with modulo 26 and a 26-letter key in block cipher modes.

Explore RSA digital signatures: sign with a private key and verify with a public key, and see how hash functions support authentication and non-repudiation, with forgery and blinding issues.

Examine hash functions for data integrity and authentication, including unkeyed and keyed hashes, MDCs and CRCs, Merkle-Damgård construction, birthday attacks, and digital signatures using private keys.

Solve congruences using the chinese remainder theorem and derive rsa parameters by computing phi(n), selecting e, and finding d, with practical step-by-step calculations.

Examine a chosen ciphertext attack on a decryption oracle in RSA, including OAEP encoding with randomness, RSA-based digital signatures, and blinding concepts.

Explore hash functions, their preimage, second preimage, and collision resistance, Merkle compression, and key management concepts including KDC and Needham-Schroeder.

Explore rsa encryption with hash-based signatures, including verification by hashing messages, advantages of hash functions for arbitrary inputs, and properties like preimage and collision resistance, hash length, and crc caveats.

Master mac, hash mac, and public key certificates, including chain of trust and key management. Explore forward secrecy, Diffie-Hellman, ElGamal, and Merkle-tree proofs for secure communications.