1. The problem is to design, analyze, and implement a complete encryption–decryption scheme using mathematical principles of cryptography. 2. The general formula for encryption can be stated as $$C = E_K(P)$$ where $P$ is the plaintext, $C$ is the ciphertext, and $E_K$ is the encryption function using key $K$. 3. The decryption formula is $$P = D_K(C)$$ where $D_K$ is the decryption function using the same or related key $K$. 4. Important rules include: - The encryption and decryption functions must be inverses: $$D_K(E_K(P)) = P$$. - Keys and parameters must be defined clearly. - The scheme must be mathematically valid and reversible. 5. Intermediate work involves defining the encryption and decryption functions explicitly, for example, using modular arithmetic, substitution, or matrix transformations. 6. Manual encryption and decryption must be shown step-by-step with all intermediate calculations. 7. Implementation can be done in Python or MATLAB following the mathematical model. 8. Results should demonstrate correctness by showing that decrypting the ciphertext returns the original plaintext. 9. Security analysis should discuss the scheme's strengths and weaknesses. 10. Conclusion summarizes the design and learning outcomes. This outlines the full approach to the assignment as requested.