Hello there!

In this repository I collect my adventures in the Cryptography world. What to expect?

• Medium-Highly detailed explanations of algorithms / concepts
• Implementations in Python / Sage (Every notebook is self contained up to prerequisites which you'll still find here)
• Common libraries for solving the problems
• Everything is full of resources (from Youtube videos with intuitive explanations to detailed papers on the subject)

IMPORTANT NOTE

I HIGHLY recommend using nbviewer if you're reading these online: https://nbviewer.jupyter.org/github/zademn/EverythingCrypto/tree/master/

• Github doesn't render the all mathematics inside the notebooks
• Github doesn't render images properly inside the notebooks

If nbviewer is down for some reason download them locally and run them on your machine and everything will render normally.

Disclaimer

• This whole repository is for educational purposes
• DO NOT USE ANY OF THE ALGORITHMS IN REAL WORLD APPLICATIONS

Structure?

Notebooks

• For educational and "ease to follow" purposes I decided to work in notebooks. Notebook are structured as follows:
  • Prerequisites = list of subjects/notebooks that you need to cover before attempting the subject
  • Theory = Mathematical explanation + intuitions
  • Code = Python,Sage or other library
  • Resources = List of resources for further reading

PDF's

• Some basic theory in the form of pdf's here and there

Directories

Directories are organized by categories (S = Symmetric, P = Public, E = Extra)

Extra

• Books
  • A collection of books I went through and found helpful
• Security theory
  • Basic definitions and what to expect (Start with this)
• Mathematics = Here you will find the basic structures(groups, curves, etc) and algorithms that I studied
  • Number theory - Start with this
  • Abstract algebra - Groups, Rings, Fields, Polynomials
  • Elliptic Curves - Theory
  • Discrete Logarithm Problem
  • Elliptic Curve Discrete Logarithm Problem
  • Factorizations
  • Lattices
  • Primes and primality tests
• Secret sharing schemes
  • General Idea and SSSS

Public

• Public Key = Each cryptosystem will have an introduction and a folder with vulnerabilities (NOTE: mathematical vulnerabilities (Ex: factorizations, dlp) will not be covered to avoid monotony. I assume you can connect the dots)
  • RSA + vulnerabilities
  • Diffie Hellman + vulnerabilities
  • Elgamal
• Digital signatures
  • ECDSA + vulnerabilities
  • RSADSA + vulnerabilities

Symmetric

• PRNG's
  • Pseudorandom generators, pseudorandom functions,
  • Implementations: chacha20, LFSRs, Geffe (Correlation attack)
• Block Ciphers
  • AES, DES
  • Block ciphers modes of operation - pdf
  • Cryptanalysis methods
• Message Integrity
  • MACs and hashes theory - pdf
  • Constructions - Merkle damgard and sponge
  • Length Extension attack
  • HMAC
• Authenticated Encryption
  • AE and AEAD - pdf
  • GCM and the the forbidden attack

Each directory will have a README.md that will contain the MY difficulty ranking of different subjects, attacks etc.

How to tackle this repository?

Whatever fits your needs (Start with the security theory folder though to know what to expect)

1. Follow along with a book (There is a book directory)
2. Depth-first fashion (for people that have good foundations):
   • Pick a bigger subject
   • Study it thoroughly (from the lowest difficulty to the highest)
3. Breadth-first fashion (for starters):
   • Go through every topic at the lowest difficulty
   • Raise the difficulty and start again
4. My Take

• Security theory dir -> Symmetric / Public
• Symmetric encryption
  • PRGNG -> Block ciphers -> Message Integrity -> Authenticated Encryption
• Public Encryption
  • Maths/Number Theory -> Public Key Encryption -> Digital Signatures
  • Maths when needed

TODO

Not necessarily in this order
(As of 26 jan 21)

• Hashes - 26 Dec 20
• Authenticated Encryption - 1 Jan 21
• RC4 and FMS
• Code for DES and Feistel ciphers
• Block cipher design + Linear cryptanalysis - 27 jun 21
• Differential cryptanalysis - 29 jun 21
• Lattice theory - 26 Jan 21
• SIS, LWE - 4 Feb 21
• Lattice Cryptosystems
• Homomorphic encryption
• Public key theory - 6 Jan 21
• Zero knowledge proofs
• Protocols (might make another repo)
• Reductions
• Add test vectors for algorithms