🚀 Features

Converts numbers from different bases (binary, hex, etc.) to decimal Uses basic interpolation to find polynomial coefficients Automatically processes JSON test case files Simple, student-friendly code structure No external libraries required

📁 Files

main.cpp - Main program source code testcase1.json - First test case with 4 shares testcase2.json - Second test case with 10 shares

🛠️ Compilation & Usage Prerequisites

C++ compiler (g++, clang++, etc.) JSON test case files in the same directory

Compile bashg++ -o solver main.cpp Run bash./solver The program automatically processes both testcase1.json and testcase2.json files and outputs the secret for each test case. 📊 Expected Output 3 39932017850922179524 📖 How It Works

Base Conversion: Converts share values from various number bases to decimal Point Collection: Extracts (x, y) coordinate pairs from JSON data Polynomial Reconstruction: Uses basic mathematical interpolation Secret Extraction: Evaluates the polynomial at x=0 to find the constant term

🧮 Mathematical Approach The program uses elementary mathematics to solve the system:

For each point (xi, yi), calculate its contribution to f(0) Use the formula: weight = Π(0 - xj)/(xi - xj) for j ≠ i Sum up: secret = Σ(yi × weight)

📝 JSON Input Format json{ "keys": { "n": 4, "k": 3 }, "1": { "base": "10", "value": "4" }, "2": { "base": "2", "value": "111" } } Where:

n: Total number of shares k: Minimum shares needed to reconstruct secret Numbered entries: Individual shares with base and encoded value

🤝 Contributing Feel free to fork this repository and submit pull requests for improvements. 📄 License This project is open source and available under the MIT License. 🎯 Use Cases

Cryptography assignments Understanding secret sharing schemes Learning polynomial interpolation Educational demonstrations