diff --git a/lib/rack/session/cookie.rb b/lib/rack/session/cookie.rb
index 830a4e3..04b341e 100644
--- a/lib/rack/session/cookie.rb
+++ b/lib/rack/session/cookie.rb
@@ -161,7 +161,7 @@ def initialize(app, options = {})
         secrets = [*(options[:secrets] || options[:secret])]
 
         encryptor_opts = {
-          purpose: options[:key], serialize_json: options[:serialize_json]
+          purpose: options[:key] != RACK_SESSION ? options[:key] : nil, serialize_json: options[:serialize_json]
         }
 
         # For each secret, create an Encryptor. We have iterate this Array at
diff --git a/test/spec_session_cookie.rb b/test/spec_session_cookie.rb
index 0e4094b..951389f 100644
--- a/test/spec_session_cookie.rb
+++ b/test/spec_session_cookie.rb
@@ -366,8 +366,9 @@ def decode(str); @calls << :decode; JSON.parse(str); end
   end
 
   it 'rejects session cookie with different purpose' do
-    app = [incrementor, { secrets: @secrets }]
-    other_app = [incrementor, { secrets: @secrets, key: 'other' }]
+    app = [incrementor, { secrets: @secret }] # key defaults to 'rack.session'
+    other_app = [incrementor, { secrets: @secret, key: 'other' }]
+    explicit_default_app = [incrementor, { secrets: @secret, key: 'rack.session' }]
 
     response = response_for(app: app)
     response.body.must_equal ({"counter"=>1}.to_s)
@@ -375,6 +376,9 @@ def decode(str); @calls << :decode; JSON.parse(str); end
     response = response_for(app: app, cookie: response)
     response.body.must_equal ({"counter"=>2}.to_s)
 
+    response = response_for(app: explicit_default_app, cookie: response)
+    response.body.must_equal ({"counter"=>3}.to_s)
+
     response = response_for(app: other_app, cookie: response)
     response.body.must_equal ({"counter"=>1}.to_s)
   end