# sha256.py

I coded the sha256 algorithm in python without using any modules.

The purpose of the code was to better understand the algorithm and learn how to implement hashing algorithms since there isn’t always modules available to use in c++.

This code was written in: nov 14, 2021. I am/was 15 when I wrote this code. By: Taha Canturk (Kibnakamoto in github)

The operations used:

XOR(): ^ (⊕)

rightrotate: (r_rotate function)

rightshift: (r_shift function)

bitwise and = &

bitwise complement = ~

all binary numbers are used with base 2.

X, Y, Z = w[index]

Equations: Ch(X, Y, Z) = (X & Y ) ⊕ (~X & Z)

Maj(X, Y, Z) = (X & Y ) ⊕ (X & Z) ⊕ (Y & Z)

capital sigma 0 = Σ0: r_rotate(X, 2) ⊕ r_rotate(X, 13) ⊕ r_rotate(X, 22)

capital sigma 1 = Σ1: r_rotate(e, 6) ⊕ r_rotate(e, 11) ⊕ r_rotate(e, 25)

small sigma 0 = σ0: r_rotate(X, 7) ⊕ r_rotate(X, 18) ⊕ r_shift(X, 3)

small sigma 1 = σ1: r_rotate(X, 17) ⊕ r_rotate(X, 19) ⊕ r_shift(X, 10)

T1 = h + Σ1(e) + Ch(e, f, g) + K[i] + W[i]

T2 = Σ0(a) + Maj(a, b, c)

constants: # 2**32 times the cube root of the first 64 primes

``````    K = [
0x428a2f98, 0x71374491, 0xb5c0fbcf, 0xe9b5dba5, 0x3956c25b, 0x59f111f1,
0x923f82a4, 0xab1c5ed5, 0xd807aa98, 0x12835b01, 0x243185be, 0x550c7dc3,
0x72be5d74, 0x80deb1fe, 0x9bdc06a7, 0xc19bf174, 0xe49b69c1, 0xefbe4786,
0x0fc19dc6, 0x240ca1cc, 0x2de92c6f, 0x4a7484aa, 0x5cb0a9dc, 0x76f988da,
0x983e5152, 0xa831c66d, 0xb00327c8, 0xbf597fc7, 0xc6e00bf3, 0xd5a79147,
0x06ca6351, 0x14292967, 0x27b70a85, 0x2e1b2138, 0x4d2c6dfc, 0x53380d13,
0x650a7354, 0x766a0abb, 0x81c2c92e, 0x92722c85, 0xa2bfe8a1, 0xa81a664b,
0xc24b8b70, 0xc76c51a3, 0xd192e819, 0xd6990624, 0xf40e3585, 0x106aa070,
0x19a4c116, 0x1e376c08, 0x2748774c, 0x34b0bcb5, 0x391c0cb3, 0x4ed8aa4a,
0x5b9cca4f, 0x682e6ff3, 0x748f82ee, 0x78a5636f, 0x84c87814, 0x8cc70208,
0x90befffa, 0xa4506ceb, 0xbef9a3f7, 0xc67178f2
]

# 2**32 times the square root of the first 8 primes
# hash values
h0 = 0x6a09e667
h1 = 0xbb67ae85
h2 = 0x3c6ef372
h3 = 0xa54ff53a
h4 = 0x510e527f
h5 = 0x9b05688c
h6 = 0x1f83d9ab
h7 = 0x5be0cd19
``````

NOTICE: for now the code is still being debugged and only works if message length is below 56.