Official comment
We currently aren't planning that type of granularity for permissions, but we'll leave this up to see if there's more interest in expanding the Permissions to include every single field. Our existing structure allows you to do this a slightly different way.
Move your sensitive fields into their own section, and then set permissions for that section. You can add as many custom sections as you want so you could have a section named "Finance - Admin only" or "Lead Info - Admin only". Then, move the fields into the new sections and set the permissions within the field editor. See this article for a complete explanation of how to do this.