Slap any number of digital signatures on an electronic invoice and still you cannot guarantee any integrity and authenticity. The legal harmonization debate in EU is unfortunately still wrongly focusing on this one document.
The answer is in the holistic business process - when the (any form of) invoice has arrived and VAT auditors understandably from time to time want to check that less and less fraud is taking place (which will happen with migration to the e-version) - the supporting elements like order, delivery and payment documents related to it need to be checked. As simple as that - as well documented in the Code of Practise adopted by the EC Expert Group on e-Invoicing.
Additional supplementary tools will be used by some enterprises to improve processes - but technology neutrality should be the base for the much needed pan-EU harmonization.