[Cryptography] factoring small(ish) numbers
Viktor Dukhovni
cryptography at dukhovni.org
Wed Oct 15 15:24:25 EDT 2014
On Tue, Oct 14, 2014 at 11:53:48AM -0700, Tom Mitchell wrote:
> This may open door number two.
> Many key pairs depend on pairs of large primes.
> However discovering large pairs is problematic so
> large pseudo primes get used.
Modern pseudo-primality tests are very good.
> This does open an attack family because finding
> large primes that have not been found by others
> seems less likely and pseudo primes present a false
> view of the number of valuable underlying bits.
Primes are very common. Read about the prime-number theorem. For
512 bit numbers roughly one in every 384 is prime.
> For a laptop or desktop to generate sufficiently interesting
> prime number dependent key pairs seems difficult perhaps as difficult
> as factoring large pseudo primes.
This is wrong.
> Perhaps I misjudge difficulty
Grossly.
--
Viktor.
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