Hashing File

Hashing File (Cryptographic Integrity Verification)

Authors:

• Amey Thakur (ORCID: 0000-0001-5644-1575)
• Mega Satish (ORCID: 0000-0002-1844-9557)

Release Date: January 9, 2022
License: MIT License

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Quick Start

To execute this implementation, ensure you have Python 3.x installed and follow these steps:

python HashingFile.py

1. Definition

File Hashing is the process of generating a fixed-size numerical representation (a digest) from an arbitrary-sized file. It is a fundamental technique for verifying Data Integrity, ensuring that a file has not been altered or corrupted during transmission or storage.

2. Mathematical Explanation

A cryptographic hash function $H$ satisfies three primary properties:

1. Pre-image Resistance: Given a hash $h$, it is computationally infeasible to find $x$ such that $H(x) = h$.
2. Second Pre-image Resistance: Given $x$, it is infeasible to find $y \neq x$ such that $H(x) = H(y)$.
3. Collision Resistance: It is infeasible to find any two distinct inputs $x, y$ such that $H(x) = H(y)$.

Merkle–Damgård Construction

This implementation processes files in discrete blocks $B_i$. The final hash is computed iteratively:

$$ h_i = f(h_{i-1}, B_i) $$

Where $f$ is a compression function and $h_0$ is an initial vector.

3. Computer Science Theory

• Streaming Buffer Logic: By reading the file in chunks (e.g., 64KB), the algorithm can hash files significantly larger than the available RAM, maintaining $O(1)$ memory complexity.
• Determinism: The same file will always produce the identical hash sum under the same algorithm, making it a reliable "Digital Fingerprint".
• Complexity:
  • Time Complexity: $O(N)$ where $N$ is the file size in bytes.
  • Space Complexity: $O(B)$ where $B$ is the block size (auxiliary space).

4. Python Implementation Logic

• Hashlib Abstraction: Leverages Python's hashlib library, which provides a thread-safe interface to highly optimized C implementations of SHA-2 and MD5.
• Binary I/O: Files are accessed in rb mode to ensure cross-platform consistency of byte streams, regardless of text encoding or newline conventions.

5. Visual Representation

Cryptographic Workflow & Digest Verification

flowchart TD
    A["Start: hashing process"] --> B["Open File in Binary Mode"]
    B --> C["Read chunk (block_size)"]
    C --> D{"Data read?"}
    D -- "Yes" --> E["Update Hasher object"]
    E --> C
    D -- "No" --> F["Finalize Digest (hexdigest)"]
    F --> G["Return hexadecimal string"]
    G --> H["Close File"]

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flowchart TD
    Title["<b>Merkle-Damgård Iterative Construction</b>"]
    Title --- IV
    
    subgraph Process ["Hashing Execution"]
        direction TB
        IV["Initial Vector"] --- F1["Compression f"]
        B1["Block 1"] --- F1
        F1 --- F2["Compression f"]
        B2["Block 2"] --- F2
        F2 --- F3["..."]
        F3 --- FN["Compression f"]
        BN["Block n"] --- FN
        FN --- Digest["Final Hash Digest"]
    end

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