diff --git a/moto/iot/exceptions.py b/moto/iot/exceptions.py
index 7a578c22..e3acf969 100644
--- a/moto/iot/exceptions.py
+++ b/moto/iot/exceptions.py
@@ -52,3 +52,11 @@ class DeleteConflictException(IoTClientError):
     def __init__(self, msg):
         self.code = 409
         super(DeleteConflictException, self).__init__("DeleteConflictException", msg)
+
+
+class ResourceAlreadyExistsException(IoTClientError):
+    def __init__(self, msg):
+        self.code = 409
+        super(ResourceAlreadyExistsException, self).__init__(
+            "ResourceAlreadyExistsException", msg or "The resource already exists."
+        )
diff --git a/moto/iot/models.py b/moto/iot/models.py
index ebd15d10..258a387f 100644
--- a/moto/iot/models.py
+++ b/moto/iot/models.py
@@ -19,6 +19,7 @@ from .exceptions import (
     InvalidRequestException,
     InvalidStateTransitionException,
     VersionConflictException,
+    ResourceAlreadyExistsException,
 )
 from moto.utilities.utils import random_string
 
@@ -130,7 +131,7 @@ class FakeThingGroup(BaseModel):
 class FakeCertificate(BaseModel):
     def __init__(self, certificate_pem, status, region_name, ca_certificate_pem=None):
         m = hashlib.sha256()
-        m.update(str(uuid.uuid4()).encode("utf-8"))
+        m.update(certificate_pem.encode("utf-8"))
         self.certificate_id = m.hexdigest()
         self.arn = "arn:aws:iot:%s:1:cert/%s" % (region_name, self.certificate_id)
         self.certificate_pem = certificate_pem
@@ -145,7 +146,7 @@ class FakeCertificate(BaseModel):
         self.ca_certificate_id = None
         self.ca_certificate_pem = ca_certificate_pem
         if ca_certificate_pem:
-            m.update(str(uuid.uuid4()).encode("utf-8"))
+            m.update(ca_certificate_pem.encode("utf-8"))
             self.ca_certificate_id = m.hexdigest()
 
     def to_dict(self):
@@ -668,6 +669,12 @@ class IoTBackend(BaseBackend):
     def list_certificates(self):
         return self.certificates.values()
 
+    def __raise_if_certificate_already_exists(self, certificate_id):
+        if certificate_id in self.certificates:
+            raise ResourceAlreadyExistsException(
+                "The certificate is already provisioned or registered"
+            )
+
     def register_certificate(
         self, certificate_pem, ca_certificate_pem, set_as_active, status
     ):
@@ -677,11 +684,15 @@ class IoTBackend(BaseBackend):
             self.region_name,
             ca_certificate_pem,
         )
+        self.__raise_if_certificate_already_exists(certificate.certificate_id)
+
         self.certificates[certificate.certificate_id] = certificate
         return certificate
 
     def register_certificate_without_ca(self, certificate_pem, status):
         certificate = FakeCertificate(certificate_pem, status, self.region_name)
+        self.__raise_if_certificate_already_exists(certificate.certificate_id)
+
         self.certificates[certificate.certificate_id] = certificate
         return certificate
 
diff --git a/tests/test_iot/test_iot.py b/tests/test_iot/test_iot.py
index 12e1ff7b..7a04cdc1 100644
--- a/tests/test_iot/test_iot.py
+++ b/tests/test_iot/test_iot.py
@@ -503,6 +503,20 @@ def test_endpoints():
         raise Exception("Should have raised error")
 
 
+@mock_iot
+def test_certificate_id_generation_deterministic():
+    # Creating the same certificate twice should result in the same certificate ID
+    client = boto3.client("iot", region_name="us-east-1")
+    cert1 = client.create_keys_and_certificate(setAsActive=False)
+    client.delete_certificate(certificateId=cert1["certificateId"])
+
+    cert2 = client.register_certificate(
+        certificatePem=cert1["certificatePem"], setAsActive=False
+    )
+    cert2.should.have.key("certificateId").which.should.equal(cert1["certificateId"])
+    client.delete_certificate(certificateId=cert2["certificateId"])
+
+
 @mock_iot
 def test_certs():
     client = boto3.client("iot", region_name="us-east-1")
@@ -584,6 +598,29 @@ def test_certs():
     res.should.have.key("certificates")
 
 
+@mock_iot
+def test_create_certificate_validation():
+    # Test we can't create a cert that already exists
+    client = boto3.client("iot", region_name="us-east-1")
+    cert = client.create_keys_and_certificate(setAsActive=False)
+
+    with assert_raises(ClientError) as e:
+        client.register_certificate(
+            certificatePem=cert["certificatePem"], setAsActive=False
+        )
+    e.exception.response["Error"]["Message"].should.contain(
+        "The certificate is already provisioned or registered"
+    )
+
+    with assert_raises(ClientError) as e:
+        client.register_certificate_without_ca(
+            certificatePem=cert["certificatePem"], status="ACTIVE"
+        )
+    e.exception.response["Error"]["Message"].should.contain(
+        "The certificate is already provisioned or registered"
+    )
+
+
 @mock_iot
 def test_delete_policy_validation():
     doc = """{