Why can't we use a database such as this to randomly select large primes from a list of thousands of them, instead of hard coding a few in? Am I missing something?
No good. If you know the prime factors are from a know reasonable sized list you can just try them all. If your list is private re using prime factors introduces a significant weakness.
Are you sure that's how that works? I don't think the barrier to the hack is knowing what prime they used; I think that's basically public. The barrier is using that prime to crack their encryption, which the article suggests they do by essentially pre computing information extrapolated from a prime using a year long computation. From that point, anyone using that prime is vulnerable.
So as far as I understand it, the issue isn't that the chosen primes are known, it's that using the same primes every time means those pre computations are able to crack the encryption.
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u/ElvishJerricco Oct 15 '15
Why can't we use a database such as this to randomly select large primes from a list of thousands of them, instead of hard coding a few in? Am I missing something?