Update SECURITY.md

SECURITY.md

@@ -6,4 +6,20 @@ The latest released version of Trilinos is the only version supported with secur
 
 ## Reporting a Vulnerability
 
-For run-of-the mill memory errors, etc., please file a Github issue.  For specific, sensitive security issues, please click on "Report a vulnerability" at https://github.com/trilinos/Trilinos/security.
+For run-of-the mill memory errors, etc., please file a Github issue.  
+
+If you discover a security vulnerability within Trilinos, please follow these steps to report it:
+
+1. **Do Not Create a Public Issue**: Please do not disclose the vulnerability publicly until it has been addressed.
+2. **Contact Us**: Please click on "Report a vulnerability" at https://github.com/trilinos/Trilinos/security.
+3. **Provide Details**: Include as much information as possible about the vulnerability, including:
+   - A description of the vulnerability
+   - Steps to reproduce the issue
+   - Any relevant logs or screenshots
+   - Your contact information (optional, but helpful for follow-up)
+
+## Response Process
+
+We will acknowledge your report within 5 days and aim to provide a resolution or further information within 30 days. 
+
+We appreciate your help in keeping our project secure!