diff --git a/CHANGELOG.md b/CHANGELOG.md
index 87615ed6..bb8b0ead 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,5 +1,18 @@
 # Changelog
 
+## [v3.1.3](https://github.com/jwt/ruby-jwt/tree/v3.1.3) (NEXT)
+
+[Full Changelog](https://github.com/jwt/ruby-jwt/compare/v3.1.2...v3.1.3)
+
+**Features:**
+
+- Your contribution here
+
+**Fixes and enhancements:**
+
+- Fix compatibility with the openssl 4.0 gem [#706](https://github.com/jwt/ruby-jwt/pull/706)
+- Your contribution here
+
 ## [v3.1.2](https://github.com/jwt/ruby-jwt/tree/v3.1.2) (2025-06-28)
 
 [Full Changelog](https://github.com/jwt/ruby-jwt/compare/v3.1.1...v3.1.2)
diff --git a/lib/jwt/jwk/rsa.rb b/lib/jwt/jwk/rsa.rb
index c4918602..2a28e0f7 100644
--- a/lib/jwt/jwk/rsa.rb
+++ b/lib/jwt/jwk/rsa.rb
@@ -195,7 +195,7 @@ def validate_rsa_parameters!(rsa_parameters)
 
         if ::JWT.openssl_3?
           alias create_rsa_key create_rsa_key_using_der
-        elsif OpenSSL::PKey::RSA.new.respond_to?(:set_key)
+        elsif OpenSSL::PKey::RSA.method_defined?(:set_key)
           alias create_rsa_key create_rsa_key_using_sets
         else
           alias create_rsa_key create_rsa_key_using_accessors
diff --git a/lib/jwt/version.rb b/lib/jwt/version.rb
index 34436db0..4c1321c0 100644
--- a/lib/jwt/version.rb
+++ b/lib/jwt/version.rb
@@ -16,7 +16,7 @@ def self.gem_version
   module VERSION
     MAJOR = 3
     MINOR = 1
-    TINY  = 2
+    TINY  = 3
     PRE   = nil
 
     STRING = [MAJOR, MINOR, TINY, PRE].compact.join('.')
diff --git a/spec/jwt/jwk/rsa_spec.rb b/spec/jwt/jwk/rsa_spec.rb
index 1b283fb6..321dafee 100644
--- a/spec/jwt/jwk/rsa_spec.rb
+++ b/spec/jwt/jwk/rsa_spec.rb
@@ -262,7 +262,7 @@
 
   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 without the RSA#set_key method not supported' unless OpenSSL::PKey::RSA.method_defined?(:set_key)
       skip 'OpenSSL 3.0 does not allow mutating objects anymore' if JWT.openssl_3?
     end
 
@@ -274,7 +274,7 @@
 
   describe '.create_rsa_key_using_accessors' do
     before do
-      skip 'OpenSSL if RSA#d= is not available there is no accessors anymore' unless OpenSSL::PKey::RSA.new.respond_to?(:d=)
+      skip 'OpenSSL if RSA#d= is not available there is no accessors anymore' unless OpenSSL::PKey::RSA.method_defined?(:d=)
     end
 
     subject(:rsa) { described_class.create_rsa_key_using_accessors(rsa_parameters) }