I don't think there is native functionality to do what you are trying to do.  You might be able to have the workflow edit the permissions to the document or apply a tag that includes permission restrictions. 

But be aware that the workflow can't be triggered simply by editing the value of Field A.  The workflow triggers for editing a document are not occurring with each individual change you make to a document, but rather after you complete all changes.  Soo it wouldn't trigger until you had made the edits and closed the document.