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)
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.
- This whole repository is for educational purposes
- DO NOT USE ANY OF THE ALGORITHMS IN REAL WORLD APPLICATIONS
- 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
- Some basic theory in the form of pdf's here and there
Directories are organized by categories (S = Symmetric, P = Public, E = 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 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
- 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.
Whatever fits your needs (Start with the security theory folder though to know what to expect)
- Follow along with a book (There is a book directory)
- Depth-first fashion (for people that have good foundations):
- Pick a bigger subject
- Study it thoroughly (from the lowest difficulty to the highest)
- Breadth-first fashion (for starters):
- Go through every topic at the lowest difficulty
- Raise the difficulty and start again
- 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
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
