🔐 Introduction to Cryptography

This repository centralizes the coding exercises and laboratory sessions for the Introduction to Cryptography course taught by Dr. Sandra Díaz Santiago at the Escuela Superior de Cómputo (ESCOM). The project covers classical cryptosystems, modular arithmetic algorithms, and modern symmetric/asymmetric implementations.

---

🚀 Course Projects

The coursework is divided into sequential laboratories, exploring fundamental and advanced concepts of cryptography:

1️⃣ Classical Ciphers & Modular Arithmetic

• Lab 01: Modular Arithmetic & Shift Cipher

  • Implementation of multiplication tables for $\mathbb{Z}_{n}-{0}$.
  • Analysis of multiplicative inverses in finite fields.
  • Shift Cipher: Full implementation of encryption/decryption using modular addition/subtraction in $\mathbb{Z}_{n}$.

• Lab 02: Affine Cipher

  • Generation of valid keys $K=(a,b)$ for the Affine Cipher checking $gcd(a,n)=1$.
  • Cryptanalysis: Algorithms to recover plaintext given a ciphertext and key.
  • Implementation of modular arithmetic over ASCII printable characters.

• Lab 03: Extended Euclidean Algorithm (EEA)

  • Implementation of the EEA to compute the greatest common divisor (GCD).
  • Calculation of Multiplicative Inverses for Affine keys ($a^{-1} \pmod n$).

• Lab 04: Permutation Cipher

  • Algorithm Design: Pseudocode for random permutation generation and inverse permutations ($\pi^{-1}$).
  • File Processing: Enciphering and deciphering text files (>10kb) using permutation blocks.

2️⃣ Block Ciphers & Modern Cryptography

• Lab 05: Bitwise Ops & SPN Construction (Parts I-V)

  • Bitwise Primitives: Low-level manipulation (getting/setting $n$-th bit, shifts, masks) and XOR encryption.
  • SPN Components: Design and implementation of random Substitution Boxes (S-Boxes) and Permutation Boxes (P-Boxes).
  • Toy Block Cipher: Full implementation of a custom SPN cipher including Key Mixing, Substitution, and Permutation layers.
  • Finite Fields: Implementation of polynomial multiplication in $GF(2^8)$ modulo $x^8+x^5+x^3+x+1$.
  • Modes of Operation: Implementation of CTR (Counter Mode) for the Toy Cipher and usage of 3DES-CBC via libraries.

• Lab 06: AES - Counter Mode (CTR)

  • Key Generation: Random generation of 128, 192, and 256-bit AES keys.
  • AES-CTR: Implementation of encryption and decryption using a unique nonce/IV.
  • Integration with Base64 encoding for ciphertext storage.

• Lab 07: RSA Implementation

  • Large Primes: Generation of primes (up to 2048 bits).
  • Key Generation: Computation of public $(e, n)$ and private $(d)$ keys verifying $gcd(e, \phi(n))=1$.
  • Core Logic: Implementation of $c = m^e \pmod n$ and $m = c^d \pmod n$ for secure integer exchange.

---

🗂️ Repository Structure

Each directory contains the source code and specific documentation for the lab session.

/
├── Practica1/       # Modular Arith. & Shift Cipher
├── Practica2/       # Affine Cipher & Modular Inverse
├── Practica3/       # Extended Euclidean Algorithm
├── Practica4/       # Permutation Cipher (Files)
├── Practica5/       # Bitwise Ops & SPN Construction
├── Practica6/       # AES-CTR & Base64
└── Practica7/       # RSA KeyGen & Crypto

🛠️ Technologies & Concepts

• Languages: C++ (Core), Python (Prototyping).
• Libraries: Standard I/O, Math libraries for modular arithmetic.
• Key Concepts:
  • Finite Fields ($\mathbb{Z}_n$).
  • Symmetric Key Cryptography (AES, Affine, Shift).
  • Public Key Cryptography (RSA).
  • Block Ciphers & Modes of Operation (CTR).

---

⚠️ Academic Integrity Note

This repository was created for educational purposes and personal reference.

Goal: To serve as a study archive and portfolio of the implemented cryptographic algorithms.

Disclaimer: It is strongly recommended not to copy or plagiarize the code presented here for academic submissions. Real learning comes from the self-implementation of these mathematical models.

---

👤 Author

• RobertLopez893

---

Introduction to Cryptography - Semester 26/1 - ESCOM IPN