diff --git a/lib/jwt/jwk/key_abstract.rb b/lib/jwt/jwk/key_abstract.rb
index b9271469..fd8a234c 100644
--- a/lib/jwt/jwk/key_abstract.rb
+++ b/lib/jwt/jwk/key_abstract.rb
@@ -3,7 +3,8 @@
 module JWT
   module JWK
     class KeyAbstract
-      attr_reader :keypair, :kid
+      attr_reader :keypair
+      attr_accessor :kid
 
       def initialize(keypair, kid = nil)
         @keypair = keypair
diff --git a/lib/jwt/jwk/rsa.rb b/lib/jwt/jwk/rsa.rb
index 431a809a..d177bf72 100644
--- a/lib/jwt/jwk/rsa.rb
+++ b/lib/jwt/jwk/rsa.rb
@@ -9,7 +9,8 @@ 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)
-        super(keypair, kid || self.class.generate_kid(keypair.public_key))
+        super
+        kid ||= generate_kid
       end
 
       def private?
@@ -35,6 +36,12 @@ def export(options = {})
 
       private
 
+      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 append_private_parts(the_hash)
         the_hash.merge(
           d: encode_open_ssl_bn(keypair.d),
@@ -59,12 +66,6 @@ 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)