diff --git a/ext/openssl/ossl_x509req.c b/ext/openssl/ossl_x509req.c
index 37ba03728..4a4d3f286 100644
--- a/ext/openssl/ossl_x509req.c
+++ b/ext/openssl/ossl_x509req.c
@@ -312,7 +312,11 @@ ossl_x509req_sign(VALUE self, VALUE key, VALUE digest)
 
     GetX509Req(self, req);
     pkey = GetPrivPKeyPtr(key); /* NO NEED TO DUP */
-    md = ossl_evp_get_digestbyname(digest);
+    if (NIL_P(digest)) {
+        md = NULL; /* needed for some key types, e.g. Ed25519 */
+    } else {
+        md = ossl_evp_get_digestbyname(digest);
+    }
     if (!X509_REQ_sign(req, pkey, md)) {
 	ossl_raise(eX509ReqError, NULL);
     }
diff --git a/test/openssl/test_x509req.rb b/test/openssl/test_x509req.rb
index b98754b8c..89f348907 100644
--- a/test/openssl/test_x509req.rb
+++ b/test/openssl/test_x509req.rb
@@ -17,7 +17,11 @@ def issue_csr(ver, dn, key, digest)
     req = OpenSSL::X509::Request.new
     req.version = ver
     req.subject = dn
-    req.public_key = key.public_key
+    if key.oid == "ED25519"
+      req.public_key = key
+    else
+      req.public_key = key.public_key
+    end
     req.sign(key, digest)
     req
   end
@@ -132,6 +136,29 @@ def test_sign_and_verify_dsa_md5
       issue_csr(0, @dn, @dsa512, OpenSSL::Digest.new('MD5')) }
   end
 
+  def test_sign_and_verify_ed25519
+    # See test_ed25519 in test_pkey.rb
+
+    # Ed25519 is not FIPS-approved.
+    omit_on_fips
+
+    begin
+      ed25519  = OpenSSL::PKey::generate_key("ED25519")
+    rescue OpenSSL::PKey::PKeyError => e
+      # OpenSSL < 1.1.1
+      #
+      pend "Ed25519 is not implemented" unless openssl?(1, 1, 1)
+
+      raise e
+    end
+
+    # See ASN1_item_sign_ctx in ChangeLog for 3.8.1: https://github.com/libressl/portable/blob/master/ChangeLog
+    pend 'ASN1 signing with Ed25519 not yet working' unless openssl? or libressl?(3, 8, 1)
+
+    req = issue_csr(0, @dn, ed25519, nil)
+    assert_equal(true, req.verify(ed25519))
+  end
+
   def test_dup
     req = issue_csr(0, @dn, @rsa1024, OpenSSL::Digest.new('SHA256'))
     assert_equal(req.to_der, req.dup.to_der)