diff --git a/paramiko/dsskey.py b/paramiko/dsskey.py
index 4644e9a675..3b0f09d3f7 100644
--- a/paramiko/dsskey.py
+++ b/paramiko/dsskey.py
@@ -82,13 +82,7 @@ def __str__(self):
         return self.asbytes()
 
     def __hash__(self):
-        h = hash(self.get_name())
-        h = h * 37 + hash(self.p)
-        h = h * 37 + hash(self.q)
-        h = h * 37 + hash(self.g)
-        h = h * 37 + hash(self.y)
-        # h might be a long by now...
-        return hash(h)
+        return hash((self.get_name(), self.p, self.q, self.g, self.y))
 
     def get_name(self):
         return 'ssh-dss'
diff --git a/paramiko/ecdsakey.py b/paramiko/ecdsakey.py
index e4f74310f3..cb5d77b8c9 100644
--- a/paramiko/ecdsakey.py
+++ b/paramiko/ecdsakey.py
@@ -165,10 +165,8 @@ def __str__(self):
         return self.asbytes()
 
     def __hash__(self):
-        h = hash(self.get_name())
-        h = h * 37 + hash(self.verifying_key.public_numbers().x)
-        h = h * 37 + hash(self.verifying_key.public_numbers().y)
-        return hash(h)
+        return hash((self.get_name(), self.verifying_key.public_numbers().x,
+                     self.verifying_key.public_numbers().y))
 
     def get_name(self):
         return self.ecdsa_curve.key_format_identifier
diff --git a/paramiko/rsakey.py b/paramiko/rsakey.py
index fa2b4c4449..8ad6d6e44b 100644
--- a/paramiko/rsakey.py
+++ b/paramiko/rsakey.py
@@ -89,10 +89,8 @@ def __str__(self):
             return self.asbytes().decode('utf8', errors='ignore')
 
     def __hash__(self):
-        h = hash(self.get_name())
-        h = h * 37 + hash(self.public_numbers.e)
-        h = h * 37 + hash(self.public_numbers.n)
-        return hash(h)
+        return hash((self.get_name(), self.public_numbers.e,
+                     self.public_numbers.n))
 
     def get_name(self):
         return 'ssh-rsa'