The Statement of Accomplishment issued by the class.stanford.edu Team is signed by a gpg key so that it can be validated independently by anyone who has the class.stanford.edu public key. For independent verification OpenEdX uses what is called a "detached signature" meaning that the signature for the Statement of Accomplishment is contained in a separate file with a ".sig" extension.
To complete the verification procedure you will need the following three files:
Ensure you have the pdf, the ".sig" signature file and the class.stanford.edu public key copied to a single directory before you begin.
Download and install gpgtools.
After installation, GPG Keychain Access will prompt for a new personal keypair.
Click the import icon to import the public key file, class_stanford_edu.pub.
CTRL-click the class.stanford.edu public key and select "sign" to validate it.
Confirm that the class.stanford.edu public key is listed in the GPG Keychain Access window and it has Short ID 3E862F0D.
Download and install the full version of gpg4win.
After the installation is complete, launch Kleapatra from the start menu.
Create a new personal certificate if don't have one listed under "My Certificates".
When prompted, select "Create personal OpenPGP key pair."
Import the class.stanford.edu public key file, class_stanford_edu.pub for class.stanford.edu by clicking on the "Import Certificate" icon.
Certify the class.stanford.edu public key by highlighting the class.stanford.edu public key/certificate and selecting "Certify Certificate" under the "Certificates" menu.
Make sure that the class.stanford.edu public key/certificate is listed under the "Trusted Certificates" tab and verify it has the Key-ID 3E862F0D.
gpg --verify Certificate.pdf.sig Certificate.pdf