Understanding SHA-256: A Deep Dive

SHA-256 (Secure Hash Algorithm 256-bit) is a cryptographic hash function that converts an input (message) into a fixed-length 256-bit (32-byte) hash value. It is part of the SHA-2 family and is widely used in security applications like password hashing, digital signatures, and blockchain.

How SHA-256 Works

SHA-256 follows the Merkle–Damgård construction and consists of several key steps:

1. Preprocessing

a) Message Padding

• The input message is padded so that its length becomes a multiple of 512 bits (64 bytes).
• Padding starts with a single “1” bit, followed by enough “0” bits.
• The last 64 bits store the original message length in bits.

b) Message Chunking

• The padded message is divided into 512-bit blocks.
• Each block is processed independently.

2. Hash Computation

SHA-256 uses a compression function that processes each 512-bit block using 64 rounds of transformations.

a) Initialization

SHA-256 starts with eight 32-bit hash values (H0 to H7), known as initial hash values:

H0 = 6a09e667
H1 = bb67ae85
H2 = 3c6ef372
H3 = a54ff53a
H4 = 510e527f
H5 = 9b05688c
H6 = 1f83d9ab
H7 = 5be0cd19

These are fractional parts of the square roots of the first 8 prime numbers.

b) Message Expansion (Schedule)

• Each 512-bit block is expanded into 64 words (W0 to W63), where each word is 32 bits.
• The first 16 words come from the original block.
• The remaining words are generated using bitwise operations.

c) Round Processing

For each of the 64 rounds, the algorithm:

1. Uses 8 working variables (A, B, C, D, E, F, G, H).
2. Computes two key functions:
   • Ch (Choose): Selects bits based on the value of E.
   • Maj (Majority): Chooses bits based on a majority vote of A, B, C.
3. Uses two bitwise rotation functions (Σ0 and Σ1).
4. Updates hash values using:

T1 = H + Σ1(E) + Ch(E,F,G) + K[i] + W[i]
T2 = Σ0(A) + Maj(A,B,C)

• K[i] is a predefined 64-element constant table derived from cube roots of the first 64 prime numbers.

5. The working variables are updated:

H = G
G = F
F = E
E = D + T1
D = C
C = B
B = A
A = T1 + T2

d) Hash Update

• After processing all 64 rounds, the final values of A, B, C, D, E, F, G, and H are added to the initial hash values.

3. Final Hash Output

• After processing all 512-bit chunks, the final hash is concatenated from H0 to H7.
• The final 256-bit output is represented as 64 hexadecimal characters.

Example: Hashing “hello”

SHA-256("hello") = 2cf24dba5fb0a30e26e83b2ac5b9e29e1b161e5c1fa7425e73043362938b9824

Properties of SHA-256

1. Deterministic: Same input always produces the same output.
2. Fixed Length: Always 256 bits, regardless of input size.
3. Avalanche Effect: Small changes in input cause large changes in output.
4. One-Way Function: Nearly impossible to reverse.
5. Collision Resistant: No two different inputs should produce the same hash.