My crypto library contents

Based

• Bacon cipher

Block Ciphers

• AES

  • CBC Mode

    • Padding Oracle attack implementation

  • GCM

    • Ghash implementation in python
    • oracle_access.py - GHASH without knowledge of key

  • linear_analysis

    • Example of Linear sbox usage in aes

  • other_implementations

    • open source implementations of aes

  • Ordinary AES implementation in python

  • Sbox gen implementation in c

• DES
  • des.py python implementation.
  • weak and semi-weak keys for des
  • cool property with bitwise flip

DLP

• Collision Algos
  • Baby-Step-Giant-Step implementation in python
  • Birthday Paradox based collision algorithm implementation in python
• Pollard Rho
  • Pollard Rho algorithm implementation in python(Including Field extensions)
• Auxialry Inputs
  • attack todo
• prime_power
  • Discrete log in the rings $\frac{ZZ}{p^sZZ}$ up to the power $p^{s-1}, s \ge 2$
• Pohlig-Hellman
  • based

Elliptic Curve Cryptography

• hash_to_curve.py - map the arbitrary message to the point on Weierstrass curve

• lift_p2.py - lift the points from E(F_p) to E(Zp^2) and find the amount of solutions "fast". Read comments inside.

• curves

  • elliptic_curves.py - python implementation of an arbitrary elliptic curve
    • including constant time multiplication
  • edwards_curve.py - python implmentation of Edwards curves
  • montgomery_curve.py - python implementation of Montgomery curves
  • equivalence.py - translation between curves
  • kind.sage - script that kinda automates curve analysis
  • kinds.md - Writeup on Elliptic Curve kinds
  • get_curves_of_specific_order.py - just elliptic curves order properties
  • multiplication - implmentations of several techniques to boost multiplication

• montgomery_curves

  • montgomery.py
    • Montgomery curves Affine implementation
    • Montgomery diffrential scalar implementation
    • Various optimizations for scalarmul

• order

  • curve_order.py - computation of elliptic curve order over finite field using bsgs

  • division_polynomial.py - computation of division_polynomials and rational functions for elliptic curves

    • including computation with unknown y

  • schoofs_algorithm.py - Schoof's algorithm to compute elliptic curve order over finite field

• Supersingular Curves

  • Supersingularity tests
  • Fast multiplication using supersingular curves

• Singular Curves

  • DLP on singular curves

• Anomalous Curves

  • Smart attack
  • Smart attack but mod p^2
  • Augmented addition attack
  • Fast multiplication using anomalous curves

• Isogenies

  • isogeny_evaluation.py
    • get_velu_isogeny - get an isogeny based on kernel, using Velu' isogeny
    • get_isogeny_of_smooth_order and evaluate_isogeny_of_smooth_order - fast isogeny computation
  • isogenies.py
    • get_all_isogenous_curves of degree l function
    • get_all_isognies of degree l function
  • isogeny_graph.py
    • brute_graph - Get a complete isogny graph. DFS
    • successive_graph - Compute an isogeny graph up to some depth and draw them

• MOV

  • weil_pairing.py - weil pairing python implementation
  • MOV algorithm implementation in python using weil pairing

• ecdsa

  • ecdsa.py - Elliptic Curve DSA implementation in python
  • attacks.py:
    • Linear Congruece attack
    • Polynomial Congruence attack
    • Repeated Nonce attack
    • Lattice Based attack(lower bits) ecdh:
  • tripartite Diffie-Hellman
  • SIDH - supersingular isogeny Diffie-Hellman

• encryption schemes

  • Massey-Omura cs
  • Elgamal cs
  • ECIES
  • KMOV - RSA like encryption
  • ID based encryption
  • malware one-sided DH

• common curves

HASH Functions

• sha1

  • sha1 implentation in python(stolen)
  • length_extension.py - le attack on sha1

• murmurhash3

  • murmurhash3_128.py

  • murmurhash3_128_x64.cpp

  • reverse_murmurhash.py - zero finder/collision finder

• md5

  • md5.py + tests
  • length_extension attack
  • collision - fast collision for md5(single block + two blocks)
    • diff.py + tests - diffrential analysis
    • verify_paper - tried to verify not very trustworthy facts from paper
    • fastcoll.py - attack implementation

• blake2b

  • blake2b.py + tests

• crc32

  • crc32.py CRC32 implementation
  • crc32_attack.py - mitm+algebraic+linear

Lattice Cryptography

• LLL

  • python
    • LLL algorithm implementation in python
    • Improved spped LLL algorithm
    • LLL sage? why
  • cpp
    • lattice_attacks.cpp
      • LLL
      • HadamardRatio
      • Gram-Schmidt
      • LLL_check reduced basis
      • Babai Closest Plain
      • Babai Closest Vertex
      • Gaussian Expected Length

• cryptosystems

  • Congruential Public Key CS
  • GGH Public Key CS
    • ggh implementation in python
    • gghdsa implementation in python
  • KnapSack like CS
    • subset sum
    • superincreasing knapsack
  • NTRU Public Key CS
    • NTRU implemntation in python
    • NTRUMLS implementation in python

• Integer Relation

  • Algebraic Roots recovery using LLL(square and cubic)
  • Coppersmith attacks
  • Finding an Algebraic relation using sage

• LWE

  • not so much yet

Linear Cryptoanalisys

• TODO

Permutation Ciphers

• Rail Fence cipher
• Symmetric_Group
  • Sqrt in S(n)

Post Quantum

• UoV - signature scheme

PRNG

• xorshift128p - truncated xorshift128p analysis

  • TODO

• xoshiro128++, 256++

RSA

• Full/Partial(brutable) knowledge of d

  • python + cpp implementation

• PKCS1 padding oracle attack

  • python + cpp implementation

• Notes on RSA key creation using python/openssl - todo

• wiener - Wiener attack on RSA with small private exponent

  • wiener.py

• Known bits of p

Simple substitution

• Shift cipher + analysis
• Vigenere Cipher + analysis
• frequencies
  • bigrams
  • singles

Stream Ciphers

• RC4

  • oracle implemenation in python
  • RC4 cipher implementation in python
  • 1st Round Attack on RC4
    • 1st round attack on rc4 IV||main_key
    • 1st round attack on rc4 main_key||IV
    • Chosen IV attack on rc4
  • 2nd Round Attack on RC4
    • 2nd round attack on rc4 IV||main_key
  • FMS attack on RC4
  • Special IV generation

• LFSR

  • lfsr decomposition

• ChaCha20

  • ChaCha20 implementation in python

ZKP

• KZG
  • KZG implementation from RealWorldCTF2023
• coolstuff
  • emulated_field.py - prove a * b = c(mod q)
  • discrete_log.py - prove bunch of facts about dl)
  • range_constraint.py - prove that a is less than 2^n
• PLONK
  • plonk todo
• sumcheck
  • sumcheck protocol implementation TODO improve....
• protostar/
• zcash_bug
  • zcash_protocol implementation
  • bug implmentation

ALGEBRAIC TOOLS

Polynomials

• polynomial_ring_analysis.py - Ring structure of polynomial quotient ring
  • Order of a multplicative subgroup
  • All the possible orders in this group
  • Ring factorization
  • TODO: find the number of elements in the group s.t. their order is K | minimal_power
• Groebner basis implentation
• symmetric_polynomials
  • symmetric_polynomial_decomposition.py - decompose any multivariate symmetric polynomial using symmetric_polynomial basis.
• hensels_lifting
  • univariate_lifting.py - Lift the root mod $p^e$ to $p^{e + 1}$
  • find_roots_mod_prime_power.py - Find all the polynomial roots mod $p^e$

Matrices

- Get Jordan General Decomposition of a matrix over a finite field
- Find the matrix order with help of previous thing
- LFSR analysis with help of matrix order

Boolean

• annihilators.py - Find annihilators of a boolean function

Varieties

Probablity Theory Tools

Distributions

Collection of some interesting probability distributions

• any_distribution.py - Produce an arbitrary distribution out of a uniform one

Statistics

UNDER CONSTRUCTION

TOOLS

• Factorization methods

  • 4p1factorization

    • Cheng's method - TODO
    • Simplified Cheng's method

  • EC(Lenstra) factorization

  • Fermatt Factorization

  • Naive Factorization

  • Pollard P Factorization

  • Pollard Rho Factorization

  • Stackoverflow

• Tonelli
  • tonelli algorithm to find square roots
• Inverse modulo
• Primeness check + gen
  • is_prime
  • Atkin
  • Simple Prime in range finder
  • Euler's pattern to find primes
  • Brute
  • Sundaram
• Carmichael Numbers
  • Generating Carmichael Numbers
  • Testing for Charmichaelness
• Strong PseudoPrimes
  • Generating Strong Pseudoprimes using Arnault algorithm!!!
• cvc5
  • cvc5 ff use case
  • ecc solver(lol)
• encoders
  • base64
  • circom witness
  • circom r1cs
  • openssh private key
  • pkcs1.5
• pade_approximation.py - Pade' M/N approximation of a function
• binary_search.py - Binary Search
• create_smooth_prime.py - Smooth Primes Creation
• Interval Union -
• Legendre symbol -
• rebase.py - Base n function
• use of gmp example
• use of z3 example
• use of cado-nfs example
• use of pari library
• x509cert_help.py - cert generation in python
• Other - some thoughts, theories and algorithms of my own implementation
  • Combinatorics
  • Math