Chatgpt:
Using Elliptic Curve Cryptography (ECC) is a great way to align with NOSTR's encryption and signing schemes. Here’s how you can create a secure WebSocket communication using ECC for encryption and signing, similar to how NOSTR handles notes.

### Step-by-Step Guide

#### 1. Key Generation

Generate ECC key pairs for the server and client using `cryptography` library in Python.

#### 2. Implement the Relay Server

The relay server will use its private key to decrypt the initial connection request and then use symmetric encryption (AES) for the WebSocket communication.

#### 3. Implement the Client

The client will use the server's public key to encrypt the initial connection request.

### Example Code

#### 1. Key Generation

Use the `cryptography` library to generate ECC key pairs.

```python
from cryptography.hazmat.primitives.asymmetric import ec
from cryptography.hazmat.primitives import serialization

# Generate server private key
server_private_key = ec.generate_private_key(ec.SECP256R1())
server_public_key = server_private_key.public_key()

# Save server private key
with open("server_private_key.pem", "wb") as f:
    f.write(server_private_key.private_bytes(
        encoding=serialization.Encoding.PEM,
        format=serialization.PrivateFormat.PKCS8,
        encryption_algorithm=serialization.NoEncryption()
    ))

# Save server public key
with open("server_public_key.pem", "wb") as f:
    f.write(server_public_key.public_bytes(
        encoding=serialization.Encoding.PEM,
        format=serialization.PublicFormat.SubjectPublicKeyInfo
    ))
```

#### 2. Relay Server Implementation

Using the `websockets` library and `cryptography` for the relay server.

```python
import asyncio
import websockets
from cryptography.hazmat.primitives.asymmetric import ec
from cryptography.hazmat.primitives import hashes
from cryptography.hazmat.primitives.kdf.hkdf import HKDF
from cryptography.hazmat.primitives import serialization
from cryptography.hazmat.primitives.kdf.concatkdf import ConcatKDFHash
from cryptography.hazmat.primitives.kdf.concatkdf import ConcatKDFHash
from cryptography.hazmat.primitives.ciphers import Cipher, algorithms, modes
from cryptography.hazmat.primitives.ciphers.aead import AESGCM
from base64 import b64encode, b64decode
import os

# Load server private key
with open("server_private_key.pem", "rb") as f:
    server_private_key = serialization.load_pem_private_key(
        f.read(),
        password=None
    )

# Function to handle WebSocket connections
async def echo(websocket, path):
    try:
        # Receive the client's public key
        client_public_key_pem = await websocket.recv()
        client_public_key = serialization.load_pem_public_key(client_public_key_pem.encode('utf-8'))

        # Perform ECDH key exchange
        shared_key = server_private_key.exchange(ec.ECDH(), client_public_key)

        # Derive AES key from the shared key
        aes_key = HKDF(
            algorithm=hashes.SHA256(),
            length=32,
            salt=None,
            info=b'handshake data'
        ).derive(shared_key)

        while True:
            encrypted_message = await websocket.recv()
            nonce, ciphertext, tag = [b64decode(x) for x in encrypted_message.split(":")]

            # Decrypt the message
            aesgcm = AESGCM(aes_key)
            message = aesgcm.decrypt(nonce, ciphertext + tag, None).decode('utf-8')

            print(f"Received: {message}")
            response = f"Echo: {message}"

            # Encrypt response
            nonce = os.urandom(12)
            aesgcm = AESGCM(aes_key)
            ciphertext = aesgcm.encrypt(nonce, response.encode('utf-8'), None)
            encrypted_response = b64encode(nonce).decode('utf-8') + ":" + b64encode(ciphertext[:-16]).decode('utf-8') + ":" + b64encode(ciphertext[-16:]).decode('utf-8')

            await websocket.send(encrypted_response)
    except websockets.exceptions.ConnectionClosed as e:
        print(f"Connection closed: {e}")

# Start the WebSocket server
start_server = websockets.serve(echo, "localhost", 8765)

asyncio.get_event_loop().run_until_complete(start_server)
asyncio.get_event_loop().run_forever()
```

#### 3. Client Implementation

The client will use the server's public key to perform ECDH key exchange and then use the derived AES key for encryption.

```python
import asyncio
import websockets
from cryptography.hazmat.primitives.asymmetric import ec
from cryptography.hazmat.primitives import hashes
from cryptography.hazmat.primitives.kdf.hkdf import HKDF
from cryptography.hazmat.primitives import serialization
from cryptography.hazmat.primitives.kdf.concatkdf import ConcatKDFHash
from cryptography.hazmat.primitives.ciphers.aead import AESGCM
from base64 import b64encode, b64decode
import os

# Load server public key
with open("server_public_key.pem", "rb") as f:
    server_public_key = serialization.load_pem_public_key(f.read())

async def hello():
    uri = "ws://localhost:8765"

    # Generate client private key
    client_private_key = ec.generate_private_key(ec.SECP256R1())
    client_public_key = client_private_key.public_key()

    # Perform ECDH key exchange
    shared_key = client_private_key.exchange(ec.ECDH(), server_public_key)

    # Derive AES key from the shared key
    aes_key = HKDF(
        algorithm=hashes.SHA256(),
        length=32,
        salt=None,
        info=b'handshake data'
    ).derive(shared_key)

    async with websockets.connect(uri) as websocket:
        # Send client's public key to the server
        client_public_key_pem = client_public_key.public_bytes(
            encoding=serialization.Encoding.PEM,
            format=serialization.PublicFormat.SubjectPublicKeyInfo
        ).decode('utf-8')
        await websocket.send(client_public_key_pem)

        message = "Hello, Server!"
        print(f"Sending: {message}")

        # Encrypt the message
        nonce = os.urandom(12)
        aesgcm = AESGCM(aes_key)
        ciphertext = aesgcm.encrypt(nonce, message.encode('utf-8'), None)
        encrypted_message = b64encode(nonce).decode('utf-8') + ":" + b64encode(ciphertext[:-16]).decode('utf-8') + ":" + b64encode(ciphertext[-16:]).decode('utf-8')

        await websocket.send(encrypted_message)

        encrypted_response = await websocket.recv()
        nonce, ciphertext, tag = [b64decode(x) for x in encrypted_response.split(":")]

        # Decrypt the response
        aesgcm = AESGCM(aes_key)
        response = aesgcm.decrypt(nonce, ciphertext + tag, None).decode('utf-8')
        print(f"Received: {response}")

asyncio.get_event_loop().run_until_complete(hello())
```

### Summary

1. **Key Generation**: Generate ECC key pairs for the server and client.
2. **Relay Server**: Implement the server to handle WebSocket connections, perform ECDH key exchange, and use AES-GCM for symmetric encryption.
3. **Client**: Implement the client to perform ECDH key exchange and use AES-GCM for encryption.

This setup ensures that WebSocket communication is encrypted using keys derived from the public-private key pairs, aligning with NOSTR's encryption scheme and avoiding centralized CAs.