diff --git a/lib/jwt/jwk/rsa.rb b/lib/jwt/jwk/rsa.rb
index b4e763f1..5f6d2288 100644
--- a/lib/jwt/jwk/rsa.rb
+++ b/lib/jwt/jwk/rsa.rb
@@ -86,28 +86,44 @@ def jwk_attributes(jwk_data, *attributes)
         def rsa_pkey(rsa_parameters)
           raise JWT::JWKError, 'Key format is invalid for RSA' unless rsa_parameters[:n] && rsa_parameters[:e]
 
-          populate_key(OpenSSL::PKey::RSA.new, rsa_parameters)
+          create_rsa_key(rsa_parameters)
         end
 
-        if OpenSSL::PKey::RSA.new.respond_to?(:set_key)
-          def populate_key(rsa_key, rsa_parameters)
-            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]
-            rsa_key
+        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|
+              next if rsa_parameters[key].nil?
+
+              arr << OpenSSL::ASN1::Integer.new(rsa_parameters[key])
+            end
+
+            if sequence.size > 2 # For a private key
+              sequence.unshift(OpenSSL::ASN1::Integer.new(0))
+            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)
+            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 populate_key(rsa_key, rsa_parameters)
-            rsa_key.n = rsa_parameters[:n]
-            rsa_key.e = rsa_parameters[:e]
-            rsa_key.d = rsa_parameters[:d] if rsa_parameters[:d]
-            rsa_key.p = rsa_parameters[:p] if rsa_parameters[:p]
-            rsa_key.q = rsa_parameters[:q] if rsa_parameters[:q]
-            rsa_key.dmp1 = rsa_parameters[:dp] if rsa_parameters[:dp]
-            rsa_key.dmq1 = rsa_parameters[:dq] if rsa_parameters[:dq]
-            rsa_key.iqmp = rsa_parameters[:qi] if rsa_parameters[:qi]
-
-            rsa_key
+          def create_rsa_key(rsa_parameters) # rubocop:disable Metrics/AbcSize
+            OpenSSL::PKey::RSA.new.tap do |rsa_key|
+              rsa_key.n = rsa_parameters[:n]
+              rsa_key.e = rsa_parameters[:e]
+              rsa_key.d = rsa_parameters[:d] if rsa_parameters[:d]
+              rsa_key.p = rsa_parameters[:p] if rsa_parameters[:p]
+              rsa_key.q = rsa_parameters[:q] if rsa_parameters[:q]
+              rsa_key.dmp1 = rsa_parameters[:dp] if rsa_parameters[:dp]
+              rsa_key.dmq1 = rsa_parameters[:dq] if rsa_parameters[:dq]
+              rsa_key.iqmp = rsa_parameters[:qi] if rsa_parameters[:qi]
+            end
           end
         end
 
diff --git a/lib/jwt/version.rb b/lib/jwt/version.rb
index 360e8d56..222af076 100644
--- a/lib/jwt/version.rb
+++ b/lib/jwt/version.rb
@@ -20,4 +20,9 @@ module VERSION
     # Build version string
     STRING = [MAJOR, MINOR, TINY, PRE].compact.join('.')
   end
+
+  def self.openssl_3?
+    return false if OpenSSL::OPENSSL_VERSION.include?('LibreSSL')
+    return true if OpenSSL::OPENSSL_VERSION_NUMBER >= 3 * 0x10000000
+  end
 end
diff --git a/spec/jwk/decode_with_jwk_spec.rb b/spec/jwk/decode_with_jwk_spec.rb
index 0caf3028..fe90a092 100644
--- a/spec/jwk/decode_with_jwk_spec.rb
+++ b/spec/jwk/decode_with_jwk_spec.rb
@@ -82,8 +82,8 @@
     context 'mixing algorithms using kid header' do
       let(:hmac_jwk)           { JWT::JWK.new('secret') }
       let(:rsa_jwk)            { JWT::JWK.new(OpenSSL::PKey::RSA.new(2048)) }
-      let(:ec_jwk_secp384r1)   { JWT::JWK.new(OpenSSL::PKey::EC.new('secp384r1').generate_key) }
-      let(:ec_jwk_secp521r1)   { JWT::JWK.new(OpenSSL::PKey::EC.new('secp521r1').generate_key) }
+      let(:ec_jwk_secp384r1)   { JWT::JWK.new(OpenSSL::PKey::EC.generate('secp384r1')) }
+      let(:ec_jwk_secp521r1)   { JWT::JWK.new(OpenSSL::PKey::EC.generate('secp521r1')) }
       let(:jwks)               { { keys: [hmac_jwk.export(include_private: true), rsa_jwk.export, ec_jwk_secp384r1.export, ec_jwk_secp521r1.export] } }
 
       context 'when RSA key is pointed to as HMAC secret' do
diff --git a/spec/jwk_spec.rb b/spec/jwk_spec.rb
index 5b4fca79..3d3543f0 100644
--- a/spec/jwk_spec.rb
+++ b/spec/jwk_spec.rb
@@ -2,7 +2,7 @@
 
 RSpec.describe JWT::JWK do
   let(:rsa_key) { OpenSSL::PKey::RSA.new(2048) }
-  let(:ec_key) { OpenSSL::PKey::EC.new('secp384r1').generate_key }
+  let(:ec_key) { OpenSSL::PKey::EC.generate('secp384r1') }
 
   describe '.import' do
     let(:keypair) { rsa_key.public_key }