diff --git a/lib/jwt/jwk/rsa.rb b/lib/jwt/jwk/rsa.rb
index aa8d4835..9c8cfc86 100644
--- a/lib/jwt/jwk/rsa.rb
+++ b/lib/jwt/jwk/rsa.rb
@@ -10,6 +10,9 @@ class RSA < KeyBase # rubocop:disable Metrics/ClassLength
       RSA_PRIVATE_KEY_ELEMENTS = %i[d p q dp dq qi].freeze
       RSA_KEY_ELEMENTS = (RSA_PRIVATE_KEY_ELEMENTS + RSA_PUBLIC_KEY_ELEMENTS).freeze
 
+      RSA_OPT_PARAMS    = %i[p q dp dq qi].freeze
+      RSA_ASN1_SEQUENCE = (%i[n e d] + RSA_OPT_PARAMS).freeze # https://www.rfc-editor.org/rfc/rfc3447#appendix-A.1.2
+
       def initialize(key, params = nil, options = {})
         params ||= {}
 
@@ -25,7 +28,7 @@ def initialize(key, params = nil, options = {})
       end
 
       def keypair
-        @keypair ||= create_rsa_key(jwk_attributes(*(RSA_KEY_ELEMENTS - [:kty])))
+        @keypair ||= self.class.create_rsa_key(jwk_attributes(*(RSA_KEY_ELEMENTS - [:kty])))
       end
 
       def private?
@@ -108,31 +111,52 @@ def encode_open_ssl_bn(key_part)
         ::JWT::Base64.url_encode(key_part.to_s(BINARY))
       end
 
-      if ::JWT.openssl_3?
-        ASN1_SEQUENCE = %i[n e d p q dp dq qi].freeze
-        def create_rsa_key(rsa_parameters)
-          sequence = ASN1_SEQUENCE.each_with_object([]) do |key, arr|
+      def decode_open_ssl_bn(jwk_data)
+        self.class.decode_open_ssl_bn(jwk_data)
+      end
+
+      class << self
+        def import(jwk_data)
+          new(jwk_data)
+        end
+
+        def decode_open_ssl_bn(jwk_data)
+          return nil unless jwk_data
+
+          OpenSSL::BN.new(::JWT::Base64.url_decode(jwk_data), BINARY)
+        end
+
+        def create_rsa_key_using_der(rsa_parameters)
+          validate_rsa_parameters!(rsa_parameters)
+
+          sequence = RSA_ASN1_SEQUENCE.each_with_object([]) do |key, arr|
             next if rsa_parameters[key].nil?
 
             arr << OpenSSL::ASN1::Integer.new(rsa_parameters[key])
           end
 
-          if sequence.size > 2 # For a private key
+          if sequence.size > 2 # Append "two-prime" version for private key
             sequence.unshift(OpenSSL::ASN1::Integer.new(0))
+
+            raise JWT::JWKError, 'Creating a RSA key with a private key requires the CRT parameters to be defined' if sequence.size < RSA_ASN1_SEQUENCE.size
           end
 
           OpenSSL::PKey::RSA.new(OpenSSL::ASN1::Sequence(sequence).to_der)
         end
-      elsif OpenSSL::PKey::RSA.new.respond_to?(:set_key)
-        def create_rsa_key(rsa_parameters)
+
+        def create_rsa_key_using_sets(rsa_parameters)
+          validate_rsa_parameters!(rsa_parameters)
+
           OpenSSL::PKey::RSA.new.tap do |rsa_key|
             rsa_key.set_key(rsa_parameters[:n], rsa_parameters[:e], rsa_parameters[:d])
             rsa_key.set_factors(rsa_parameters[:p], rsa_parameters[:q]) if rsa_parameters[:p] && rsa_parameters[:q]
             rsa_key.set_crt_params(rsa_parameters[:dp], rsa_parameters[:dq], rsa_parameters[:qi]) if rsa_parameters[:dp] && rsa_parameters[:dq] && rsa_parameters[:qi]
           end
         end
-      else
-        def create_rsa_key(rsa_parameters) # rubocop:disable Metrics/AbcSize
+
+        def create_rsa_key_using_accessors(rsa_parameters) # rubocop:disable Metrics/AbcSize
+          validate_rsa_parameters!(rsa_parameters)
+
           OpenSSL::PKey::RSA.new.tap do |rsa_key|
             rsa_key.n = rsa_parameters[:n]
             rsa_key.e = rsa_parameters[:e]
@@ -144,17 +168,22 @@ def create_rsa_key(rsa_parameters) # rubocop:disable Metrics/AbcSize
             rsa_key.iqmp = rsa_parameters[:qi] if rsa_parameters[:qi]
           end
         end
-      end
 
-      def decode_open_ssl_bn(jwk_data)
-        return nil unless jwk_data
+        def validate_rsa_parameters!(rsa_parameters)
+          return unless rsa_parameters.key?(:d)
 
-        OpenSSL::BN.new(::JWT::Base64.url_decode(jwk_data), BINARY)
-      end
+          parameters = RSA_OPT_PARAMS - rsa_parameters.keys
+          return if parameters.empty? || parameters.size == RSA_OPT_PARAMS.size
 
-      class << self
-        def import(jwk_data)
-          new(jwk_data)
+          raise JWT::JWKError, 'When one of p, q, dp, dq or qi is given all the other optimization parameters also needs to be defined' # https://www.rfc-editor.org/rfc/rfc7518.html#section-6.3.2
+        end
+
+        if ::JWT.openssl_3?
+          alias create_rsa_key create_rsa_key_using_der
+        elsif OpenSSL::PKey::RSA.new.respond_to?(:set_key)
+          alias create_rsa_key create_rsa_key_using_sets
+        else
+          alias create_rsa_key create_rsa_key_using_accessors
         end
       end
     end
diff --git a/lib/jwt/version.rb b/lib/jwt/version.rb
index 7ad81897..12e1773a 100644
--- a/lib/jwt/version.rb
+++ b/lib/jwt/version.rb
@@ -27,6 +27,10 @@ def self.openssl_3?
   end
 
   def self.openssl_3_hmac_empty_key_regression?
-    openssl_3? && ::Gem::Version.new(OpenSSL::VERSION) <= ::Gem::Version.new('3.0.0')
+    openssl_3? && openssl_version <= ::Gem::Version.new('3.0.0')
+  end
+
+  def self.openssl_version
+    @openssl_version ||= ::Gem::Version.new(OpenSSL::VERSION)
   end
 end
diff --git a/spec/jwk/rsa_spec.rb b/spec/jwk/rsa_spec.rb
index d677f54a..b888e6b0 100644
--- a/spec/jwk/rsa_spec.rb
+++ b/spec/jwk/rsa_spec.rb
@@ -135,4 +135,97 @@
       end
     end
   end
+
+  shared_examples 'creating an RSA object from complete JWK parameters' do
+    let(:rsa_parameters) { jwk_parameters.transform_values { |value| described_class.decode_open_ssl_bn(value) } }
+    let(:all_jwk_parameters) { described_class.new(rsa_key).export(include_private: true) }
+
+    context 'when public parameters (e, n) are given' do
+      let(:jwk_parameters) { all_jwk_parameters.slice(:e, :n) }
+
+      it 'creates a valid RSA object representing a public key' do
+        expect(subject).to be_a(::OpenSSL::PKey::RSA)
+        expect(subject.private?).to eq(false)
+      end
+    end
+
+    context 'when only e, n, d, p and q are given' do
+      let(:jwk_parameters) { all_jwk_parameters.slice(:e, :n, :d, :p, :q) }
+
+      it 'raises an error telling all the exponents are required' do
+        expect { subject }.to raise_error(JWT::JWKError, 'When one of p, q, dp, dq or qi is given all the other optimization parameters also needs to be defined')
+      end
+    end
+
+    context 'when all key components n, e, d, p, q, dp, dq, qi are given' do
+      let(:jwk_parameters) { all_jwk_parameters.slice(:n, :e, :d, :p, :q, :dp, :dq, :qi) }
+
+      it 'creates a valid RSA object representing a public key' do
+        expect(subject).to be_a(::OpenSSL::PKey::RSA)
+        expect(subject.private?).to eq(true)
+      end
+    end
+  end
+
+  shared_examples 'creating an RSA object from partial JWK parameters' do
+    context 'when e, n, d is given' do
+      let(:jwk_parameters) { all_jwk_parameters.slice(:e, :n, :d) }
+
+      before do
+        skip 'OpenSSL prior to 2.2 does not seem to support partial parameters' if ::JWT.openssl_version < ::Gem::Version.new('2.2')
+      end
+
+      it 'creates a valid RSA object representing a private key' do
+        expect(subject).to be_a(::OpenSSL::PKey::RSA)
+        expect(subject.private?).to eq(true)
+      end
+
+      it 'can be used for encryption and decryption' do
+        expect(subject.private_decrypt(subject.public_encrypt('secret'))).to eq('secret')
+      end
+
+      it 'can be used for signing and verification' do
+        data = 'data_to_sign'
+        signature = subject.sign(OpenSSL::Digest.new('SHA512'), data)
+        expect(subject.verify(OpenSSL::Digest.new('SHA512'), signature, data)).to eq(true)
+      end
+    end
+  end
+
+  describe '.create_rsa_key_using_der' do
+    subject(:rsa) { described_class.create_rsa_key_using_der(rsa_parameters) }
+
+    include_examples 'creating an RSA object from complete JWK parameters'
+
+    context 'when e, n, d is given' do
+      let(:jwk_parameters) { all_jwk_parameters.slice(:e, :n, :d) }
+
+      it 'expects all CRT parameters given and raises error' do
+        expect { subject }.to raise_error(JWT::JWKError, 'Creating a RSA key with a private key requires the CRT parameters to be defined')
+      end
+    end
+  end
+
+  describe '.create_rsa_key_using_sets' do
+    before do
+      skip 'OpenSSL without the RSA#set_key method not supported' unless OpenSSL::PKey::RSA.new.respond_to?(:set_key)
+      skip 'OpenSSL 3.0 does not allow mutating objects anymore' if ::JWT.openssl_3?
+    end
+
+    subject(:rsa) { described_class.create_rsa_key_using_sets(rsa_parameters) }
+
+    include_examples 'creating an RSA object from complete JWK parameters'
+    include_examples 'creating an RSA object from partial JWK parameters'
+  end
+
+  describe '.create_rsa_key_using_accessors' do
+    before do
+      skip 'OpenSSL if RSA#set_key is available there is no accessors anymore' if OpenSSL::PKey::RSA.new.respond_to?(:set_key)
+    end
+
+    subject(:rsa) { described_class.create_rsa_key_using_accessors(rsa_parameters) }
+
+    include_examples 'creating an RSA object from complete JWK parameters'
+    include_examples 'creating an RSA object from partial JWK parameters'
+  end
 end