SHA-1 Hash Function

SHA-1 Hash Function | Generated by AI

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Let’s dive into how the given code snippet works, specifically the lines:

hash_obj = hashlib.sha1(piece)
hashes.append(hash_obj.hexdigest())
return hashes

The user has asked us to explain this without using a library, so I’ll first explain what the code does with the hashlib library, then explore how the same functionality could be achieved without it.

Understanding the Code with `hashlib`

This snippet computes a hash for a piece of data and stores it in a list. Here’s a step-by-step breakdown of what’s happening:

hash_obj = hashlib.sha1(piece)
- What it does: This line uses Python’s hashlib module to create a SHA-1 hash object. SHA-1 (Secure Hash Algorithm 1) is a cryptographic hash function that takes an input (here, piece) and produces a 160-bit (20-byte) hash value.
- Input: piece is a chunk of data, likely bytes, read from a file or another source.
- Process: The hashlib.sha1() function initializes a hash object and immediately updates it with the data in piece. Think of it as feeding the data into a hashing machine that starts crunching numbers.
hashes.append(hash_obj.hexdigest())
- What it does: The hexdigest() method retrieves the hash value computed by the hash object and converts it into a hexadecimal string (a human-readable format using digits 0-9 and letters a-f).
- Output: For SHA-1, this string is 40 characters long because each of the 20 bytes is represented by two hexadecimal digits (e.g., a byte value of 255 becomes “ff”).
- Storage: The resulting string is appended to a list called hashes, which presumably collects hashes for multiple pieces of data.
return hashes
- What it does: After processing all pieces (assuming this code is in a loop or function), the list hashes containing all the hexadecimal hash strings is returned.

In summary: For each piece of data, the code computes its SHA-1 hash using hashlib.sha1(), converts the hash to a hexadecimal string with hexdigest(), and stores it in the hashes list, which is then returned.

Without Using a Library: Computing SHA-1 from Scratch

The user’s instruction “do not use lib” suggests they want to understand how this could work without relying on hashlib. Implementing SHA-1 from scratch is complex, but I’ll explain the process clearly and provide a simplified version you could build upon.

What is SHA-1?

SHA-1 is a hash function that:

Takes any input data (e.g., piece).
Produces a fixed 160-bit (20-byte) output.
Uses a series of bitwise operations, rotations, and additions to transform the input.

Without hashlib, we’d need to replicate this algorithm ourselves. Here’s how it could work for the given code:

Step-by-Step SHA-1 Process

Prepare the Input (Padding)
- SHA-1 processes data in 512-bit (64-byte) blocks. If piece isn’t exactly 64 bytes, we pad it:
  - Append a 1 bit (e.g., 0x80 in bytes).
  - Add enough 0 bits to make the length 448 bits (56 bytes) modulo 512.
  - Append the original length of piece (in bits) as a 64-bit integer.
- For simplicity, if piece is smaller than 64 bytes, we can pad it to one block.
Initialize Hash Values
- SHA-1 uses five 32-bit variables (160 bits total), initialized to specific constants:
  - h0 = 0x67452301
  - h1 = 0xEFCDAB89
  - h2 = 0x98BADCFE
  - h3 = 0x10325476
  - h4 = 0xC3D2E1F0
Process the Data Block
- Split the 64-byte block into 16 32-bit words (4 bytes each).
- Expand these into 80 words using the formula:
```
w[i] = left_rotate(w[i-3] ^ w[i-8] ^ w[i-14] ^ w[i-16], 1)  # for i = 16 to 79
```
  where left_rotate shifts bits left and wraps them around.
- For 80 rounds, update temporary variables a, b, c, d, e (starting as copies of h0 to h4):
  - Use different functions and constants based on the round number (0-19, 20-39, etc.).
  - Example for rounds 0-19:
    f = (b & c) | (~b & d) k = 0x5A827999 temp = (left_rotate(a, 5) + f + e + k + w[i]) & 0xFFFFFFFF
  - Shift variables: e = d, d = c, c = left_rotate(b, 30), b = a, a = temp.

Update Hash Values

After 80 rounds, add the results to the initial hash values:

h0 = (h0 + a) & 0xFFFFFFFF
h1 = (h1 + b) & 0xFFFFFFFF
# ...and so on for h2, h3, h4

Produce the Hexadecimal Output
- Concatenate h0 to h4 as a 160-bit value and convert to a 40-character hexadecimal string.

Simplified Python Implementation

Here’s a basic version of how you might rewrite the code without hashlib:

def left_rotate(value, shift):
    """Rotate a 32-bit integer left by 'shift' bits."""
    return ((value << shift) | (value >> (32 - shift))) & 0xFFFFFFFF

def custom_sha1(piece):
    """Compute SHA-1 hash of 'piece' and return it as a hex string."""
    # For simplicity, assume piece is less than 56 bytes and pad to one block
    message = piece + b'\x80' + (b'\x00' * (55 - len(piece))) + (len(piece) * 8).to_bytes(8, 'big')
    
    # Initialize hash values
    h0, h1, h2, h3, h4 = (
        0x67452301, 0xEFCDAB89, 0x98BADCFE, 0x10325476, 0xC3D2E1F0
    )
    
    # Split into 16 32-bit words
    w = [int.from_bytes(message[i:i+4], 'big') for i in range(0, 64, 4)]
    
    # Expand to 80 words
    for i in range(16, 80):
        w.append(left_rotate(w[i-3] ^ w[i-8] ^ w[i-14] ^ w[i-16], 1))
    
    # Initialize working variables
    a, b, c, d, e = h0, h1, h2, h3, h4
    
    # 80 rounds of processing
    for i in range(80):
        if 0 <= i < 20:
            f = (b & c) | (~b & d)
            k = 0x5A827999
        elif 20 <= i < 40:
            f = b ^ c ^ d
            k = 0x6ED9EBA1
        elif 40 <= i < 60:
            f = (b & c) | (b & d) | (c & d)
            k = 0x8F1BBCDC
        else:
            f = b ^ c ^ d
            k = 0xCA62C1D6
        
        temp = (left_rotate(a, 5) + f + e + k + w[i]) & 0xFFFFFFFF
        e = d
        d = c
        c = left_rotate(b, 30)
        b = a
        a = temp
    
    # Update hash values
    h0 = (h0 + a) & 0xFFFFFFFF
    h1 = (h1 + b) & 0xFFFFFFFF
    h2 = (h2 + c) & 0xFFFFFFFF
    h3 = (h3 + d) & 0xFFFFFFFF
    h4 = (h4 + e) & 0xFFFFFFFF
    
    # Return as 40-character hex string
    return f"{h0:08x}{h1:08x}{h2:08x}{h3:08x}{h4:08x}"

# Rewritten code without hashlib
def compute_hashes(pieces):
    hashes = []
    for piece in pieces:  # Assuming pieces is a list of byte chunks
        hash_value = custom_sha1(piece)
        hashes.append(hash_value)
    return hashes

# Example usage
pieces = [b"hello", b"world"]
hashes = compute_hashes(pieces)
print(hashes)

How It Matches the Original

hash_obj = hashlib.sha1(piece): Replaced by custom_sha1(piece), which computes the SHA-1 hash manually.
hashes.append(hash_obj.hexdigest()): The custom_sha1 function returns the hex string directly, so we append it to hashes.
return hashes: Remains the same, returning the list of hash strings.

Key Differences and Caveats

Simplification: This implementation assumes each piece fits in one 512-bit block (less than 56 bytes due to padding). A full SHA-1 implementation would handle multiple blocks.
Performance: A manual implementation is slower and less optimized than hashlib.
Reliability: Libraries like hashlib are tested and secure; a custom version might have bugs unless thoroughly validated.

In essence, the original code uses hashlib as a shortcut to compute SHA-1 hashes efficiently, while doing it without a library requires manually coding the entire SHA-1 algorithm, handling padding, and converting the result to hexadecimal format. The logic remains the same: process each piece, compute its hash, store it, and return the collection.

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