Thomas Schoene wrote:

"R. Steve Walz" wrote in message


Nothing CAN magically guess extraordinarily long primes. That will
never just magically become possible. This intrinsic truth resides
in the very mathematics itself, a fact outside of time and progress,
and not in any technology of any kind.

That's true now, but only to a point. That point is the advent of quantum
computing, which allows you to effectively solve for all the possible
factors in very little time (say 10^500 times faster than conventional
computing for this sort of problem). If QC happens, large prime number
encryption is crackable in a matter of seconds. And there is at least some
reason to beleive that QC is achievable within a couple of decades.
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Or DNA computing, sure.

Just an escalation, the power of operations easier one way than the
other persists and an increase in length results in the same safety.

For it to be otherwise you need to postulate that the govt will be
doing its own fundamental research, and it NEVER does, and that it
will develop QC to that level BEFORE the market sells it or the people
developing it steal it and spread it around to prevent a national
monopoly on power, and that's pretty unlikely.


OTOH, the real danger in the near- to mid-term is not crypto-system attack,
but physical compromise of the crypto-system (the adversary getting hold of
the both the mechanism and the keys themselves). If they have the actual
keys, the eavesdroppers can decode RSA just as easily as the intended
recipients.

--
Tom Schoene Replace "invalid" with "net" to e-mail
"If brave men and women never died, there would be nothing
special about bravery." -- Andy Rooney (attributed)
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Yes. Goes without saying.

-Steve
--
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