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https://github.com/kiooku/cryptography-notebook

Cryptography Notebook is a repository containing some of the cryptographic implementations I have done for learning purposes.
https://github.com/kiooku/cryptography-notebook

assymetric-encryption commitment-schemes cryptography digital-signature double-ratchet-algorithm e2ee ggh hkdf hmac identification-scheme one-time-pad post-quantum-cryptography public-key-cryptography rsa signal x3dh zero-knowledge-proof

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Cryptography Notebook is a repository containing some of the cryptographic implementations I have done for learning purposes.

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README 

        
# 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](https://cryptohack.org/user/Kioku/) 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



- [X] [Diffie-Hellman Key Exchange](./AsymmetricCiphers/Diffie_Hellman/)



- [X] [ElGamal PKC](./AsymmetricCiphers/ElGamal/)



- [X] [RSA](./AsymmetricCiphers/RSA/)



- [X] [Goldwasser–Micali Probabilistic PKC](./AsymmetricCiphers/GoldwasserMicaliProbabilisticPKC/)



- [X] [Elliptic Diffie-Hellman Key Exchange](./AsymmetricCiphers/Elliptic_Diffie_Hellman/)



- [X] [Elliptic Elgamal Public Key Cryptosystem](./AsymmetricCiphers/EllipticElgamalPKC/)



- [ ] Menezes-Vanstone variant of the Elliptic Elgamal PKC



- [X] [Tripartite Diffie-Hellman Key Exchange](./AsymmetricCiphers/Tripartite_Diffie_Hellman_Key_Exchange/)



- [X] [The Merkle–Hellman subset-sum cryptosystem](./Mathematics/Lattice/SubsetSum/)



- [X] [GGH cryptosystem](./AsymmetricCiphers/GGH_cryptosystem/)



- [X] [NTRUEncrypt cryptosystem](./AsymmetricCiphers/NTRUEncrypt/)



- [X] [X3DH](./AsymmetricCiphers/x3dh/)



#### Attacks



##### Diffie-Hellman



- [X] [Small Subgroup Confinement Attack *(Diffie-Hellman)*](./Attacks/README.md#small-subgroup-confinement-attack-diffie-hellman)



##### ElGamal



- [X] [ElGamal with a Diffie-Hellman Oracle](./AsymmetricCiphers/ElGamal/README.md#attacks-using-oracle)



##### RSA



- [X] [Blinding Attack on RSA Digital Signature](./Attacks/RSA/BlindingAttackonRSADigitalSignature.md)

- [X] [Bleinchenbacher's attack (PKCS 1 v1.5)](./Attacks/RSA/BleinchenbacherAttack(PKCS%201v1.5).md)



#### Man-in-the-Middle Attack *(MITM)*



- [ ] Diffie-Hellman MITM



### ID-Based Public Key Cryptosystem



- [ ] The Boneh Franklin Id Based PKC



### Commitment Schemes



- [X] [The Pedersen commitment scheme](./CommitmentScheme/pedersen-commitment-scheme/)



### Identification Schemes



- [X] [Feige–Fiat–Shamir identification scheme](./IdentificationSchemes/feige-fiat-shamir-identification-scheme/)



- [X] [Schnorr's sigma protocol](./IdentificationSchemes/schnorr_sigma_protocol/)



### Digital Signatures



> [!NOTE] 

> Work in progress



- [X] [RSA Digital Signatures](./DigitalSignatures/RSA_Digital_Signatures/)



- [X] Elgamal Digital Signatures



- [X] Digital Signature Algorithm (DSA)



- [X] Elliptic Curve Digital Signature Algorithm (ECDSA)



- [X] [GGH Digital Signature Scheme](./DigitalSignatures/GGH_Digital_Signature/)



- [ ] NTRU Modular Lattice Signature Scheme (NTRUMLS)



### Hash Functions



> [!NOTE]

> Basic knowledge -> Need to learn more



### Message Authentification



- [X] [HMAC](./MessageAuthentification/)



### Key Derivation Function



- [X] [HKDF](./KeyDerivationFunction/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



- [X] [XOR based one-time pad](./OneTimePad/)



### End-to-end encryption



- [X] [Double Ratchet Algorithm](./E2EE/double-ratchet-algorithm/)



- [X] [Double Ratchet with header encryption](./E2EE/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



- [X] Euclidean algorithm



- [X] Shanks’s Babystep–Giantstep Algorithm



- [X] Chinese Remainder Theorem



- [X] Pohlig-Hellman Algorithm



- [X] Miller–Rabin test for composite numbers



- [X] Pollard’s p − 1 factorization algorithm



- [ ] Gaussian elimination



- [X] Fermat's Factorization



- [X] Kraitchik’s Factorization



- [ ] A three step factorization procedure (Relation Building / Elimination / GCD Computation)



- [X] Quadratic sieve



- [ ] Index calculus



- [ ] Pollard's $\rho$ Method



#### Elliptic Curves



- [X] Addition

- [X] Double-and-Add Algorithm

- [X] Lenstra's Elliptic Curve Factorization Algorithm

- [X] Miller algorithm

- [X] Weil Pairing

- [X] MOV algorithm



#### Lattices



- [X] Create a Lattice class



- [X] Create a Knapsack class



- [X] Gram-Schmidt Algorithm



- [X] Hadamard ratio



- [X] Babai's closest vertex algorithm



- [X] Babai's closest plane algorithm



- [X] Gaussian Lattice reduction



- [X] LLL algorithm



### Learning with errors (LWE)



> [!NOTE] 

> Need to learn



### Cryptography projects



- [X] [mini-signal](https://github.com/Kiooku/mini-signal)



## Resources



- [An Introduction to Mathematical Cryptography (Second Edition)](https://link.springer.com/book/10.1007/978-1-4939-1711-2)



- [CryptoHack](https://cryptohack.org/)



- [Cryptography Academy](https://cryptographyacademy.com/identification-schemes/)



- [Signal](https://signal.org/docs/)



- [Serious Cryptography A Practical Introduction to Modern Encryption](https://nostarch.com/seriouscrypto)