Remember the basics of security, please!
If you think back to those early lessons in security, and to a certain Kevin Mitnik's career as a criminal, then you will be well aware (as the governments of the world don't seem to be) that the weak link in security is usually the human element. Government IT is unusually vulnerable, mostly due to gibbering idiocy and computer illiteracy in their higher echelons of command. MPs, politicians and senior civil servants are almost universally IT-illiterate, and unusually susceptible to fast-talking IT outsourcing companies, to the extent that in Britain at least the civil service is woefully de-skilled in IT, outsourcing everything but common sense (which all parties seem to lack) to external suppliers.
So, the main problem here is that the outsourcing companies will give the civil servants a Noddy guide to cryptographic authentication, then hand over the system to underpaid, under-motivated, and woefully under-skilled civil servants for day to day running. Pretty soon, someone will approach one of these muppets with the classic hold-all full of used twenties, in return for a copy of the signing key, and eventually this approach will succeed. Alternatively it is always possible to throw the forces of an international botnet against the problem, and try to crack the keys.
Government IT, as I said, is under-skilled to the extent that the senior people will actually believe the suppliers when they claim that the signing system is all the security they will ever need. Thus when (not if) this system gets broken into, the people running it will sincerely believe it to be invincible and the poor PFY who breaks the terrible news is going to get a dose of shoot-the-messenger syndrome.
So, like all big IT schemes, this one will fail.