How Hash Functions Work Internally

Modern cryptographic hash functions use complex internal structures combining confusion and diffusion principles from classical cryptography. The Merkle-Damgård construction, used by MD5 and SHA families, processes input in fixed-size blocks through a compression function. Each block's processing depends on the previous block's output, creating a chain that ensures the entire input influences the final hash.

# Simplified conceptual hash function structure (NOT for actual use)
def simple_hash_concept(message, block_size=64):
    # Initialize hash state
    state = [0x67452301, 0xEFCDAB89, 0x98BADCFE, 0x10325476]
    
    # Pad message to multiple of block_size
    padded = pad_message(message, block_size)
    
    # Process each block
    for i in range(0, len(padded), block_size):
        block = padded[i:i + block_size]
        state = compression_function(state, block)
    
    # Produce final hash
    return format_output(state)

def compression_function(state, block):
    # Complex operations mixing state and block
    # Includes bitwise operations, modular arithmetic, and non-linear functions
    # This is where the "magic" happens
    pass

The compression function performs multiple rounds of operations, each designed to increase diffusion and confusion. Operations typically include bitwise rotations, XOR operations, modular additions, and non-linear functions. SHA-256, for example, uses 64 rounds of operations involving logical functions, addition modulo 2³², and predefined constants derived from prime numbers. These intricate operations ensure the one-way property and avalanche effect.

Padding schemes ensure messages fit block boundaries while preventing length extension attacks. Most hash functions append a '1' bit, followed by zeros, and finally the original message length. This padding ensures different messages don't accidentally produce identical padded forms and prevents attackers from appending data to hashes without knowing the original message.