🧮 Basis-Vector-Encoding

This project demonstrates encoding and decoding messages using basis vectors.

🔍 Portfolio Project Showcase

This is a conceptual demonstration, not production-ready code.

✨ Key Concepts Demonstrated

Concept	Implementation Example
Basis Vectors	Custom basis matrices define new coordinate systems for message projection
Coordinate System Conversion	Messages transformed between standard basis ↔ arbitrary basis spaces
Linear Transformation	Matrix operations applied to vectors during encoding/decoding
Basis Change	Messages re-encoded using transformation matrices between systems
Inverse Transformations	Message recovery through matrix inversion operations

Key Notes:
⚠️ Prioritizes mathematical clarity over practicality
⚠️ Intentional unoptimized implementation to showcase step-by-step logic and enhance code clarity
⚠️ Serves as skills exhibit for technical interviews

📖 Description

This project demonstrates encoding and decoding messages using basis vectors. In simple terms, it transforms a message into a different 'language' where each set of basis vectors represents a specific perspective or coordinate system. To decode the message, you need the appropriate 'translation' - the corresponding basis vectors from that same 'language.'

The project involves:

1. Mapping each symbol in a message to a vector using a predefined symbol mapping.
2. Encoding the message by transforming these vectors using a custom basis matrix.
3. Decoding the message by applying the inverse transformation to retrieve the original vectors and mapping them back to symbols.

📂 Project Structure

File	Purpose
main.py	Core encoding/decoding logic
tools.py	Vector class & transformation utilities
symbol_mapping.json	Maps 95+ symbols to ℝⁿ coordinates

🛠️ Usage

Disclaimer: This project is intentionally non-practical and serves as a showcase.

To use this project, follow these steps:

1. Prepare the Symbol Mapping: Ensure symbol_mapping.json contains the mappings for all symbols you want to encode.

2. Encrypt a Message: Use the encrypt function from main.py to encode a message. Provide the raw message, symbol mapping, and a basis matrix.

   from main import encrypt
   import numpy as np
   import json
   
   with open("symbol_mapping.json", "r") as f:
       symbol_mapping = json.load(f)
   
   raw_message = "Hello, World!"
   basis_matrix = np.array([[1, 1], [1, -1]])
   encrypted_message = encrypt(raw_message, symbol_mapping, basis_matrix)

3. Decrypt a Message: Use the decrypt function from main.py to decode the message. Provide the encrypted message, the same basis matrix, and the symbol mapping.

   from main import decrypt
   
   decrypted_message = decrypt(encrypted_message, symbol_mapping, basis_matrix)
   print("Decrypted message:", decrypted_message)

🔧 Workflow

So, how the code works? Here is a step by step explanation.

1. The goal of a file is to encode a string message in specific coordinate system (described by specific basis matrix). Then we decode the same encoded message, using basis representation of that coordinate system in another coordinate system (Jenifer's basis vectors represented using Mike's basis vectors)

2. To do all of the described operations, first we need to map each symbol to a vector in space. For this, we read symbol_mapping.json which is file that mapps each symbol/token to an integer. It also contains UNK (Unkown Token) and PAD (Padding Token). Mapping symbols in vectors in such way implicitly makes them in std basis.

{
    "UNK": -1,
    "PAD": 70,
    "a": 1,
    "b": 2,
    "c": 3,
    "d": 4,
    "e": 5,
    ...
    "\\": 65,
    "|": 66,
    "`": 67,
    "~": 68,
    " ": 69

}

3. We use encrypt() functions to map each symbol. Then we pad it based on the dimensions of the basis matrix provided (2, 3, ...). Then we vectorize them using Vector class and transform using new basis matrix.

4. In decrypt() function, we pass the encrypted message along with the same basis represenation of the basis we used to encode the message. Note: We must pass to decrypt() function the same basis change representaion matrix as to encrypt() function. That transformation matrix says "Jenifer's basis vectors in Mike's perspective/ described by vectors in the Mike's coordinate system".

Additional Notes:

• In this implementation, each symbol in the string corresponds to a single vector.
• Vector() class is a simple overlay of np.ndarray with just a simple shape manipulation and clarity in names