diff --git a/lib/jwt/jwk/rsa.rb b/lib/jwt/jwk/rsa.rb
index 61249692..ebb0f888 100644
--- a/lib/jwt/jwk/rsa.rb
+++ b/lib/jwt/jwk/rsa.rb
@@ -3,7 +3,6 @@
 module JWT
   module JWK
     class RSA < KeyAbstract
-      attr_reader :keypair
 
       BINARY           = 2
       KTY              = 'RSA'.freeze
@@ -11,9 +10,7 @@ class RSA < KeyAbstract
 
       def initialize(keypair, kid = nil)
         raise ArgumentError, 'keypair must be of type OpenSSL::PKey::RSA' unless keypair.is_a?(OpenSSL::PKey::RSA)
-
-        @keypair = keypair
-        @kid     = kid
+        super(keypair, kid || self.class.generate_kid(keypair.public_key))
       end
 
       def private?
@@ -24,10 +21,6 @@ def public_key
         keypair.public_key
       end
 
-      def kid
-        @kid ||= generate_kid
-      end
-
       def export(options = {})
         exported_hash = {
           kty: KTY,
@@ -54,12 +47,6 @@ def append_private_parts(the_hash)
         )
       end
 
-      def generate_kid
-        sequence = OpenSSL::ASN1::Sequence([OpenSSL::ASN1::Integer.new(public_key.n),
-                                            OpenSSL::ASN1::Integer.new(public_key.e)])
-        OpenSSL::Digest::SHA256.hexdigest(sequence.to_der)
-      end
-
       def encode_open_ssl_bn(key_part)
         ::Base64.urlsafe_encode64(key_part.to_s(BINARY), padding: false)
       end
@@ -73,6 +60,12 @@ def import(jwk_data)
           self.new(rsa_pkey(pkey_params), kid)
         end
 
+        def generate_kid(public_key)
+          sequence = OpenSSL::ASN1::Sequence([OpenSSL::ASN1::Integer.new(public_key.n),
+                                            OpenSSL::ASN1::Integer.new(public_key.e)])
+          OpenSSL::Digest::SHA256.hexdigest(sequence.to_der)
+        end
+
         private
 
         def jwk_attributes(jwk_data, *attributes)