diff --git a/tests/executor/test_integration.py b/tests/executor/test_integration.py
index 2f39ada..2071767 100644
--- a/tests/executor/test_integration.py
+++ b/tests/executor/test_integration.py
@@ -1,9 +1,10 @@
 import datetime as dt
 from hashlib import sha256
-from typing import Dict, Any, Union
+from typing import Dict, Any, Union, Tuple
 
 import aiohttp
 import pytest
+import pytest_asyncio
 from aleph.sdk import AlephClient
 from aleph_message.models import (
     ItemType,
@@ -74,6 +75,21 @@ def mock_vrf_request() -> VRFRequest:
     return vrf_request
 
 
+@pytest_asyncio.fixture
+async def published_vrf_request(
+    mock_ccn_client: aiohttp.ClientSession, mock_vrf_request: VRFRequest
+) -> Tuple[MessageDict, VRFRequest]:
+    sender = "aleph_vrf_coordinator"
+    message_dict = make_post_message(mock_vrf_request, sender=sender)
+
+    resp = await mock_ccn_client.post(
+        "/api/v0/messages",
+        json={"message": message_dict, "sync": True},
+    )
+    assert resp.status == 200, await resp.text()
+    return message_dict, mock_vrf_request
+
+
 def assert_vrf_hash_matches_request(
     response_hash: VRFResponseHash, vrf_request: VRFRequest, request_item_hash: ItemHash
 ):
@@ -163,7 +179,7 @@ async def assert_aleph_message_matches_random_bytes(
 async def test_normal_request_flow(
     mock_ccn_client: aiohttp.ClientSession,
     executor_client: aiohttp.ClientSession,
-    mock_vrf_request: VRFRequest,
+    published_vrf_request: Tuple[MessageDict, VRFRequest],
 ):
     """
     Test that the executor works under normal circumstances:
@@ -172,15 +188,8 @@ async def test_normal_request_flow(
     3. The coordinator calls /publish.
     """
 
-    sender = "aleph_vrf_coordinator"
-    message_dict = make_post_message(mock_vrf_request, sender=sender)
-    item_hash = ItemHash(message_dict["item_hash"])
-
-    resp = await mock_ccn_client.post(
-        "/api/v0/messages",
-        json={"message": message_dict, "sync": True},
-    )
-    assert resp.status == 200, await resp.text()
+    message_dict, vrf_request = published_vrf_request
+    item_hash = message_dict["item_hash"]
 
     resp = await executor_client.post(f"/generate/{item_hash}")
     assert resp.status == 200, await resp.text()
@@ -188,7 +197,7 @@ async def test_normal_request_flow(
 
     response_hash = VRFResponseHash.parse_obj(response_json["data"])
 
-    assert_vrf_hash_matches_request(response_hash, mock_vrf_request, item_hash)
+    assert_vrf_hash_matches_request(response_hash, vrf_request, item_hash)
     random_hash_message = await assert_aleph_message_matches_response_hash(
         mock_ccn_client._base_url, response_hash
     )
@@ -201,7 +210,7 @@ async def test_normal_request_flow(
     assert_random_number_matches_request(
         random_bytes=random_bytes,
         response_hash=response_hash,
-        vrf_request=mock_vrf_request,
+        vrf_request=vrf_request,
     )
     random_number_message = await assert_aleph_message_matches_random_bytes(
         mock_ccn_client._base_url, random_bytes
@@ -210,3 +219,74 @@ async def test_normal_request_flow(
     # Sanity checks on the message
     assert random_number_message.sender == random_hash_message.sender
     assert random_number_message.chain == random_hash_message.chain
+
+
+@pytest.mark.asyncio
+async def test_call_publish_before_generate(
+    executor_client: aiohttp.ClientSession,
+    published_vrf_request: Tuple[MessageDict, VRFRequest],
+):
+    """
+    Test that calling /publish before /generate does not leak any data.
+    """
+
+    # Create the coordinator request
+    message_dict, vrf_request = published_vrf_request
+    item_hash = message_dict["item_hash"]
+
+    # Use the item_hash of an existing POST message, just for fun
+    resp = await executor_client.post(f"/publish/{item_hash}")
+    assert resp.status == 404
+
+
+@pytest.mark.asyncio
+async def test_call_publish_twice(
+    mock_ccn_client: aiohttp.ClientSession,
+    executor_client: aiohttp.ClientSession,
+    published_vrf_request: Tuple[MessageDict, VRFRequest],
+):
+    """
+    Test that the executor will only return data the first time POST /publish is called.
+    This feature makes it possible for the coordinator to detect that someone else already received
+    the generated random number.
+    """
+    message_dict, vrf_request = published_vrf_request
+    item_hash = message_dict["item_hash"]
+
+    resp = await executor_client.post(f"/generate/{item_hash}")
+    assert resp.status == 200, await resp.text()
+    response_json = await resp.json()
+
+    response_hash = VRFResponseHash.parse_obj(response_json["data"])
+
+    # Call POST /publish a first time
+    resp = await executor_client.post(f"/publish/{response_hash.message_hash}")
+    assert resp.status == 200, await resp.text()
+
+    # Call it a second time
+    resp = await executor_client.post(f"/publish/{response_hash.message_hash}")
+    assert resp.status == 404, await resp.text()
+
+
+@pytest.mark.asyncio
+async def test_call_generate_twice(
+    mock_ccn_client: aiohttp.ClientSession,
+    executor_client: aiohttp.ClientSession,
+    published_vrf_request: Tuple[MessageDict, VRFRequest],
+):
+    """
+    Test that calling POST /generate twice with the same request does not generate a new random number.
+    """
+    ...
+
+
+@pytest.mark.asyncio
+async def test_call_generate_without_aleph_message(
+    mock_ccn_client: aiohttp.ClientSession,
+    executor_client: aiohttp.ClientSession,
+    mock_vrf_request: VRFRequest,
+):
+    """
+    Test that calling POST /generate without an aleph message fails.
+    """
+    ...