tree-ecdh

🌳 Tree ECDH 🔐

🚀 Introduction

Tree ECDH (Tree Diffie-Hellman on Elliptic Curves) is an efficient key exchange protocol designed for secure group communication. It extends the classical Diffie-Hellman algorithm by introducing a hierarchical key structure, significantly reducing computational complexity from O(N²) to O(N log N). This implementation leverages elliptic curve cryptography (ECC) for enhanced security and efficiency.

🎯 Features

• ✅ Efficient group key exchange. Uses a tree-based structure to reduce computational complexity.
• 🔐 Elliptic curve cryptography. Implements ECDH on the P-521 curve for enhanced security.
• 🌲 Hierarchical key management. Supports scalable and efficient key computation for large groups.
• 🛠️ Unit-tested implementation. Ensures correctness and reliability.

🌳 Tree Diffie-Hellman algorithm

1. 🌲 Arrange nodes in a binary tree structure.
2. 🔄 Recursively compute shared secrets between pairs of nodes.
3. 🔑 Generate an intermediate public key for each pair.
4. 🎯 Continue the process until a single root key is obtained.

📝 Usage

To generate a key pair:

privateKey, publicKey, err := tree_ecdh.GenerateKeypair()

To compute a shared secret between two nodes:

sharedSecret := tree_ecdh.GenerateSharedSecret(privateKeyA, publicKeyB)

To compute a group key for multiple nodes:

groupSecret, err := tree_ecdh.GenerateTreeKeypair(nodes)

📜 License

This project is licensed under the MIT License. See LICENSE for details.