> The problem is for the government to factor the huge composite number
> for each candidate afterwards. Can someone give me a rough
> estimate of
> how long it would take a good supercomputer to check an arbitrary
> 100,000,000 digit number for several factors that are each a known 150
> digit arbitrary prime?
Not long at all, and you don't need a supercomputer. It's perfectly
parallelizable. Use a room full of PCs and give them disjoint ranges of
primes to test.
A major problem, which no-one has yet commented on, is that the protocol as
stated doesn't allow a secret vote. Only if no-one other than the voter
knows who received which number, and the voter knows only his/her own, can
it be secret. Patching up this hole is relatively straightforward and is
left as an exercise for the reader ;-)
Paul
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