A progressive, educational implementation of the Rivest-Shamir-Adleman (RSA) algorithm in C#. This project breaks down the intimidating mathematics of public-key cryptography into four digestible levels of complexity.

RSA is built on the computational difficulty of factoring large prime numbers. This implementation demonstrates the core relationship between the Public Key (for encryption/distribution) and the Private Key (for decryption/retention), utilizing the System.Numerics.BigInteger library for high-precision arithmetic.

The project is structured into four distinct unit tests, each increasing in sophistication:

1. Level 1 (Manual Math): Uses a custom MulMod() function to handle powers and modulo operations on individual characters.
2. Level 2 (Modular Power): Introduces a dedicated ModularPow() function for more efficient character-by-character processing.
3. Level 3 (BigInteger Integration): Leverages BigInteger.ModPow() for optimized, large-scale modular exponentiation.
4. Level 4 (Data Packing): Demonstrates bit-packing by compressing four characters into a 32-bit integer before encryption—the first step toward real-world data throughput.

This is an Educational Proof of Concept. It is not hardened for production environments:

• Key Length: The exponents used here are for demonstration. Modern security requires at least 2,000 to 3,000-bit keys to resist factorization.
• Storage: In a production setting, keys must be held in cryptographically secure containers (HSMs) and distributed via secure protocols like Diffie-Hellman.
• Optimizations: Advanced features like the Rabin-Miller primality test and massive prime generation are left as advanced exercises.

• Language: C# / .NET
• Compiler: Visual Studio 2022+
• Dependencies: System.Numerics

• Wikipedia: RSA Cryptosystem
• Menezes et al.: Handbook of Applied Cryptography, CRC Press.
• Rivest, Shamir, & Adleman (1978): A Method for Obtaining Digital Signatures and Public-Key Cryptosystems.