This petition was rejected

The Government e-Petitions Team gave the following reason:

We can't accept your petition because we aren't sure what action you would like the UK Government or Parliament to take.

We aren't sure what you mean by "at least as authenticated and secure, online, as that of Election Postal Votes" given that postal votes rely on hard copy signatures and the electoral roll for authentication. E-petitions can be signed by anyone who is a British citizen or UK resident, including people who aren't on the electoral roll.

You could start a new petition calling for only people who are on the electoral roll to be able to sign petitions and for signatories' details to be checked against it if that is something you would like to see happen.