In Sweden your SSN is public information. I posted the same comment on another Equifax thread and got some pretty interesting replies relevant to this discussion: https://news.ycombinator.com/item?id=15208223
The way it is done in Italy (it is called "Codice Fiscale") it is composed through a public algorithm from name, surname, place and date of birth with a final "control" character (derived by the preceding characters) so - with the exception of the very few cases of total homonimy - it can be recreated "on the spot".
Nowadays it is however printed on an electronic card, with both a magnetic stripe and a chip and it is the actual card (together with an ID document[1]) that "authenticates" your identity (in person) while on some government sites you can use the card (with a smart card reader) to authenticate.
[1] actually the main thing is the ID document, passport, ID card or - in some cases - driving license, with that you can declare your Codice Fiscale even if you don't have the actual card with you.