diff --git a/CHANGELOG b/CHANGELOG
index af3fe850c..03f5ee993 100644
--- a/CHANGELOG
+++ b/CHANGELOG
@@ -25,6 +25,7 @@ CHANGELOG Roundcube Webmail
 - Managesieve: Fix so "Create filter" option does not show up when Filters menu is disabled (#6723)
 - Enigma: Fix bug where revoked users/keys were not greyed out in key info
 - Enigma: Fix error message when trying to encrypt with a revoked key (#6607)
+- Enigma: Fix "decryption oracle" bug [CVE-2019-10740] (#6638)
 - Fix so advanced search dialog is not automatically displayed on searchonly addressbooks (#6679)
 - Fix so an error is logged when more than one attachment plugin has been enabled, initialize the first one (#6735)
 - Fix bug where flag change could have been passed to a preview frame when not expected
diff --git a/plugins/enigma/lib/enigma_engine.php b/plugins/enigma/lib/enigma_engine.php
index de6afd678..521c614d3 100644
--- a/plugins/enigma/lib/enigma_engine.php
+++ b/plugins/enigma/lib/enigma_engine.php
@@ -368,20 +368,36 @@ class enigma_engine
      */
     function part_structure($p, $body = null)
     {
+        static $got_content = false;
+
+        // Prevent from "decryption oracle" [CVE-2019-10740] (#6638)
+        // On mail compose (edit/reply/forward) we support encrypted content only
+        // in the first "content part" of the message.
+        if ($got_content && $this->rc->task == 'mail' && $this->rc->action == 'compose') {
+            return;
+        }
+
         // Don't be tempted to support encryption in text/html parts
         // Because of EFAIL vulnerability we should never support this (#6289)
 
         if ($p['mimetype'] == 'text/plain' || $p['mimetype'] == 'application/pgp') {
             $this->parse_plain($p, $body);
+            $got_content = true;
         }
         else if ($p['mimetype'] == 'multipart/signed') {
             $this->parse_signed($p, $body);
+            $got_content = true;
         }
         else if ($p['mimetype'] == 'multipart/encrypted') {
             $this->parse_encrypted($p);
+            $got_content = true;
         }
         else if ($p['mimetype'] == 'application/pkcs7-mime') {
             $this->parse_encrypted($p);
+            $got_content = true;
+        }
+        else {
+            $got_content = $p['structure']->type === 'content';
         }
 
         return $p;