🛡️ PrimeNode RSA: A Pure Logic Implementation

PrimeNode RSA is a custom implementation of the RSA (Rivest–Shamir–Adleman) asymmetric algorithm. This project was developed as an academic assignment to demonstrate the step-by-step process of converting plaintext into ciphertext using pure mathematical logic without relying on high-level cryptographic libraries.

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🎯 Project Objectives

Based on the assignment requirements, this project aims to:

• Analyze the theoretical concepts of asymmetric encryption.
• Implement the RSA algorithm from scratch (Key Generation, Encryption, and Decryption).
• Visualize the mathematical flow of data security.

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🛠️ Core Components

1. Introduction (History & Usage)

The RSA algorithm, named after Ron Rivest, Adi Shamir, and Leonard Adleman, was first published in 1977. It is the backbone of modern internet security, widely used for:

• Digital Signatures: Verifying the authenticity of documents.
• Key Exchange: Securely sharing symmetric keys over insecure channels (SSL/TLS).

2. Key Generation Process

This implementation uses the Extended Euclidean Algorithm to ensure mathematical accuracy in finding the private key.

• Select Primes: Choose two distinct prime numbers, $p$ and $q$.
• Compute Modulus ($n$): $n = p \times q$.
• Compute Totient ($\phi$): $\phi(n) = (p-1) \times (q-1)$.
• Public Key ($e$): An integer such that $1 < e < \phi(n)$ and $gcd(e, \phi(n)) = 1$.
• Private Key ($d$): Calculated as the modular multiplicative inverse of $e$ modulo $\phi(n)$.

3. Encryption Mechanism

The encryption process converts plaintext characters into numerical values (ASCII) and applies the formula: $$C = M^e \pmod{n}$$

• $M$: Plaintext message (numeric)
• $e$: Public exponent
• $n$: Modulus
• $C$: Resulting ciphertext

4. Decryption Mechanism

The decryption process restores the original message using the private key ($d$) with the formula: $$M = C^d \pmod{n}$$ The resulting numeric values are then converted back into human-readable characters.

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📊 Security Analysis

Aspect	Description
Strengths	Extremely difficult to break due to the "Integer Factorization Problem." High reliability for secure key distribution.
Weaknesses	Computationally expensive and slower than symmetric algorithms (like DES/RC4). Requires very large prime numbers (e.g., 2048-bit) to remain secure against modern hardware.

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🚀 How to Run

1. Ensure you have Python 3.x installed.
2. Clone this repository:

   git clone [https://github.com/KirshX07/PrimeNode_RSA.git](https://github.com/KirshX07/PrimeNode_RSA.git)

3. Run the main script:

   python primenode_rsa.py

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👤 Author Information

• Name: Kirana Shofa Dzakiyyah
• NIM: 25051204358
• Course: Cryptography (Individual Assignment)