Cryptography Notebook

What is that ?

It's a repository with some of the cryptographic implementations I have done for learning purposes.

Until then by solving cryptography challenges on CryptoHack and Root-Me.

Currently, I'm reading "An Introduction to Mathematical Cryptography" (Second edition), and in order to apply the mathematical knowledge and get a better understanding, I decided to create this repository.

Learn, understand, and create project is a long process, which is why the repository will contain more implementation month after month.

Content of the repository

Symmetric Ciphers

Note Work in progress

• AES (ECB / CBC / CFB / OFB / CTR)

Asymmetric Ciphers

Note Work in progress

Implementations

• Diffie-Hellman Key Exchange

• ElGamal PKC

• RSA

• Goldwasser–Micali Probabilistic PKC

• Elliptic Diffie-Hellman Key Exchange

• Elliptic Elgamal Public Key Cryptosystem

• Menezes-Vanstone variant of the Elliptic Elgamal PKC

• Tripartite Diffie-Hellman Key Exchange

• The Merkle–Hellman subset-sum cryptosystem

• GGH cryptosystem

• NTRUEncrypt cryptosystem

• X3DH

Attacks

Diffie-Hellman

• Small Subgroup Confinement Attack (Diffie-Hellman)

ElGamal

• ElGamal with a Diffie-Hellman Oracle

RSA

• Blinding Attack on RSA Digital Signature
• Bleinchenbacher's attack (PKCS 1 v1.5)

Man-in-the-Middle Attack (MITM)

• Diffie-Hellman MITM

ID-Based Public Key Cryptosystem

• The Boneh Franklin Id Based PKC

Commitment Schemes

• The Pedersen commitment scheme

Identification Schemes

• Feige–Fiat–Shamir identification scheme

• Schnorr's sigma protocol

Digital Signatures

Note Work in progress

• RSA Digital Signatures

• Elgamal Digital Signatures

• Digital Signature Algorithm (DSA)

• Elliptic Curve Digital Signature Algorithm (ECDSA)

• GGH Digital Signature Scheme

• NTRU Modular Lattice Signature Scheme (NTRUMLS)

Hash Functions

Note Basic knowledge -> Need to learn more

Message Authentification

• HMAC

Key Derivation Function

• HKDF

Secret Sharing Schemes

• Shamir's secret sharing

• Blakley's scheme

PRNG

Note Need to learn

• ANSI X9.17 PRNG

• DSA PRNG

• RSAREF PRNG

• fsrRand

One-Time pad

Note One-Time pad can be really simple to code, so I did it in assembly

• XOR based one-time pad

End-to-end encryption

• Double Ratchet Algorithm

• Double Ratchet with header encryption

Zero-Knowledge Proofs

Note Need to learn

Homomorphic Encryption

Note Ongoing learning of lattices to understand homomorphic encryption

Post-Quantum

Note Ongoing learning of lattices and learning with errors to understand Post-Quantum cryptography

Mathematics

Algorithm and Theorem

Note Work in progress

• Euclidean algorithm

• Shanks’s Babystep–Giantstep Algorithm

• Chinese Remainder Theorem

• Pohlig-Hellman Algorithm

• Miller–Rabin test for composite numbers

• Pollard’s p − 1 factorization algorithm

• Gaussian elimination

• Fermat's Factorization

• Kraitchik’s Factorization

• A three step factorization procedure (Relation Building / Elimination / GCD Computation)

• Quadratic sieve

• Index calculus

• Pollard's $\rho$ Method

Elliptic Curves

• Addition
• Double-and-Add Algorithm
• Lenstra's Elliptic Curve Factorization Algorithm
• Miller algorithm
• Weil Pairing
• MOV algorithm

Lattices

• Create a Lattice class

• Create a Knapsack class

• Gram-Schmidt Algorithm

• Hadamard ratio

• Babai's closest vertex algorithm

• Babai's closest plane algorithm

• Gaussian Lattice reduction

• LLL algorithm

Learning with errors (LWE)

Note Need to learn

Cryptography projects

• mini-signal

Resources

• An Introduction to Mathematical Cryptography (Second Edition)

• CryptoHack

• Cryptography Academy

• Signal

• Serious Cryptography A Practical Introduction to Modern Encryption