diff --git a/nostr_relay_discovery.py b/nostr_relay_discovery.py
index f8348db..94c6fad 100644
--- a/nostr_relay_discovery.py
+++ b/nostr_relay_discovery.py
@@ -22,7 +22,6 @@ from typing import Set, List, Dict, Optional, Tuple
 from urllib.parse import urlparse
 import websockets
 import websockets.exceptions
-from coincurve import PrivateKey
 
 
 # Configure logging
@@ -35,6 +34,134 @@ logger = logging.getLogger(__name__)
 # Save progress every N relays processed
 SAVE_POINT = 10
 
+# secp256k1 parameters used by Nostr's BIP-340 Schnorr signatures.
+SECP256K1_FIELD = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F
+SECP256K1_ORDER = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141
+SECP256K1_GENERATOR = (
+    0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798,
+    0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8,
+)
+
+
+def _tagged_hash(tag: str, message: bytes) -> bytes:
+    tag_hash = hashlib.sha256(tag.encode()).digest()
+    return hashlib.sha256(tag_hash + tag_hash + message).digest()
+
+
+def _point_add(left, right):
+    if left is None:
+        return right
+    if right is None:
+        return left
+
+    x1, y1 = left
+    x2, y2 = right
+    if x1 == x2 and y1 != y2:
+        return None
+    if left == right:
+        slope = (3 * x1 * x1) * pow(2 * y1, -1, SECP256K1_FIELD)
+    else:
+        slope = (y2 - y1) * pow(x2 - x1, -1, SECP256K1_FIELD)
+    slope %= SECP256K1_FIELD
+    x3 = (slope * slope - x1 - x2) % SECP256K1_FIELD
+    y3 = (slope * (x1 - x3) - y1) % SECP256K1_FIELD
+    return x3, y3
+
+
+def _point_multiply(scalar: int, point=SECP256K1_GENERATOR):
+    result = None
+    addend = point
+    while scalar:
+        if scalar & 1:
+            result = _point_add(result, addend)
+        addend = _point_add(addend, addend)
+        scalar >>= 1
+    return result
+
+
+def _schnorr_sign(message: bytes, secret: int) -> bytes:
+    """Create a BIP-340 Schnorr signature for a 32-byte message."""
+    if len(message) != 32 or not 1 <= secret < SECP256K1_ORDER:
+        raise ValueError("invalid BIP-340 signing input")
+
+    public_point = _point_multiply(secret)
+    public_x, public_y = public_point
+    normalized_secret = secret if public_y % 2 == 0 else SECP256K1_ORDER - secret
+    secret_bytes = normalized_secret.to_bytes(32, "big")
+    auxiliary = secrets.token_bytes(32)
+    masked_secret = bytes(
+        left ^ right
+        for left, right in zip(
+            secret_bytes, _tagged_hash("BIP0340/aux", auxiliary)
+        )
+    )
+    nonce_hash = _tagged_hash(
+        "BIP0340/nonce",
+        masked_secret + public_x.to_bytes(32, "big") + message,
+    )
+    nonce = int.from_bytes(nonce_hash, "big") % SECP256K1_ORDER
+    if nonce == 0:
+        raise RuntimeError("BIP-340 nonce generation failed")
+
+    nonce_point = _point_multiply(nonce)
+    nonce_x, nonce_y = nonce_point
+    normalized_nonce = nonce if nonce_y % 2 == 0 else SECP256K1_ORDER - nonce
+    challenge = int.from_bytes(
+        _tagged_hash(
+            "BIP0340/challenge",
+            nonce_x.to_bytes(32, "big")
+            + public_x.to_bytes(32, "big")
+            + message,
+        ),
+        "big",
+    ) % SECP256K1_ORDER
+    response = (
+        normalized_nonce + challenge * normalized_secret
+    ) % SECP256K1_ORDER
+    return nonce_x.to_bytes(32, "big") + response.to_bytes(32, "big")
+
+
+def _schnorr_verify(message: bytes, public_x_bytes: bytes, signature: bytes) -> bool:
+    """Verify a BIP-340 signature. Kept small for tests and signer self-checks."""
+    if len(message) != 32 or len(public_x_bytes) != 32 or len(signature) != 64:
+        return False
+
+    public_x = int.from_bytes(public_x_bytes, "big")
+    nonce_x = int.from_bytes(signature[:32], "big")
+    response = int.from_bytes(signature[32:], "big")
+    if (
+        public_x >= SECP256K1_FIELD
+        or nonce_x >= SECP256K1_FIELD
+        or response >= SECP256K1_ORDER
+    ):
+        return False
+
+    public_y_squared = (pow(public_x, 3, SECP256K1_FIELD) + 7) % SECP256K1_FIELD
+    public_y = pow(
+        public_y_squared, (SECP256K1_FIELD + 1) // 4, SECP256K1_FIELD
+    )
+    if pow(public_y, 2, SECP256K1_FIELD) != public_y_squared:
+        return False
+    if public_y % 2:
+        public_y = SECP256K1_FIELD - public_y
+    public_point = (public_x, public_y)
+
+    challenge = int.from_bytes(
+        _tagged_hash(
+            "BIP0340/challenge", signature[:32] + public_x_bytes + message
+        ),
+        "big",
+    ) % SECP256K1_ORDER
+    nonce_point = _point_add(
+        _point_multiply(response),
+        _point_multiply(SECP256K1_ORDER - challenge, public_point),
+    )
+    return (
+        nonce_point is not None
+        and nonce_point[1] % 2 == 0
+        and nonce_point[0] == nonce_x
+    )
+
 
 @dataclass
 class RelayDiscoveryStats:
@@ -127,10 +254,10 @@ class NostrRelayDiscovery:
         return base64.b64encode(random_bytes).decode()
 
     @staticmethod
-    def _load_private_key(private_key_hex: Optional[str]) -> PrivateKey:
+    def _load_private_key(private_key_hex: Optional[str]) -> int:
         """Load a configured Nostr secret or generate an ephemeral discovery key."""
         if private_key_hex is None:
-            return PrivateKey()
+            return secrets.randbelow(SECP256K1_ORDER - 1) + 1
 
         try:
             secret = bytes.fromhex(private_key_hex)
@@ -140,14 +267,15 @@ class NostrRelayDiscovery:
         if len(secret) != 32:
             raise ValueError("--private-key must be 64 hexadecimal characters")
 
-        try:
-            return PrivateKey(secret)
-        except ValueError as exc:
-            raise ValueError("--private-key is not a valid secp256k1 secret") from exc
+        secret_scalar = int.from_bytes(secret, "big")
+        if not 1 <= secret_scalar < SECP256K1_ORDER:
+            raise ValueError("--private-key is not a valid secp256k1 secret")
+        return secret_scalar
 
     def build_auth_event(self, relay_url: str, challenge: str) -> Dict:
         """Build and sign a NIP-42 kind 22242 authentication event."""
-        pubkey = self.private_key.public_key.format(compressed=True)[1:].hex()
+        public_point = _point_multiply(self.private_key)
+        pubkey = public_point[0].to_bytes(32, "big").hex()
         event = {
             "pubkey": pubkey,
             "created_at": int(time.time()),
@@ -172,7 +300,10 @@ class NostrRelayDiscovery:
         ).encode()
         event_id = hashlib.sha256(serialized).digest()
         event["id"] = event_id.hex()
-        event["sig"] = self.private_key.sign_schnorr(event_id).hex()
+        signature = _schnorr_sign(event_id, self.private_key)
+        if not _schnorr_verify(event_id, bytes.fromhex(pubkey), signature):
+            raise RuntimeError("generated an invalid BIP-340 signature")
+        event["sig"] = signature.hex()
         return event
 
     async def receive_with_auth(
diff --git a/requirements.txt b/requirements.txt
index 175a289..8f79324 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,5 +1,4 @@
 websockets>=12.0
-coincurve>=20.0.0
 matplotlib>=3.5.0
 pandas>=1.4.0
 numpy>=1.20.0
diff --git a/tests/test_nostr_relay_discovery.py b/tests/test_nostr_relay_discovery.py
index 5525d50..356f174 100644
--- a/tests/test_nostr_relay_discovery.py
+++ b/tests/test_nostr_relay_discovery.py
@@ -4,9 +4,7 @@ import json
 import unittest
 from unittest.mock import patch
 
-from coincurve import PublicKeyXOnly
-
-from nostr_relay_discovery import NostrRelayDiscovery
+from nostr_relay_discovery import NostrRelayDiscovery, _schnorr_verify
 
 
 class FakeWebSocket:
@@ -50,8 +48,10 @@ class Nip42Tests(unittest.TestCase):
 
         self.assertEqual(event["id"], event_id.hex())
         self.assertTrue(
-            PublicKeyXOnly(bytes.fromhex(event["pubkey"])).verify(
-                bytes.fromhex(event["sig"]), event_id
+            _schnorr_verify(
+                event_id,
+                bytes.fromhex(event["pubkey"]),
+                bytes.fromhex(event["sig"]),
             )
         )