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I'm not too familiar with the math involved with the exchange of keys, I've read it over several times, but math isn't my strong point. My understanding is that smart people are hard at work to overcome the difficulty of factoring the shared secret.

So assuming that quantum processors overcome the current implementations and 'brute-factor' the keys involved, can the exchange be scaled up similarly to other forms of encryption?

Is there a way to scale up the effort of required to brute-factor the shared key so that not even a Quantum Computer could efficiently compute it, while still maintaining acceptable performance for the good-guys with consumer-grade non-quantum computers?

Sorry if this has already been asked, but like I said math isn't my strong point, I'm not even sure how to identify if its been asked.

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    $\begingroup$ From what I recollect, quantum computing doesn't solve certain classes of encryption any better than normal computing. $\endgroup$ Oct 14 '14 at 14:12
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    $\begingroup$ When you're worried about quantum computers, don't use RSA or Diffie-Hellman. With these algorithms increasing sizes enough to avoid QCs implies unacceptable performance for the defender. $\endgroup$ Oct 14 '14 at 14:16
  • $\begingroup$ @LateralFractal Yeah I know that quantum computing wont trivialize traditional encryption, but I've heard that the factoring of diffie-hellman shared secrets are one of the things that it will theoretically trivialize. $\endgroup$ Oct 14 '14 at 14:23
  • $\begingroup$ @CodesInChaos I thought that the key-exchange process was only needed to secure or 'wrap' a more traditional shared secret like a 512 bit key? Is that not the case? $\endgroup$ Oct 14 '14 at 14:29
  • $\begingroup$ @AndrewHoffman That's the case, but I don't get your point. If establishing a connection needs a terabyte RSA key and hours of computation, that's not acceptable performance for me. $\endgroup$ Oct 14 '14 at 14:32
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Short Answer: Yes

Long Answer: From what I understand about quantum computing, they are only more efficient as long as the bit-depth of the problem falls within the bit-processing capabilities of the quantum processor. Example: a 64-bit quantum processor could solve 64-bit traditional encryption keys in a near-zero real time. 128-bit keys would still take a very long time, as would 256-bit. 512-bit, 1024-bit and higher bit-depth encryption schemes. Even if quantum computers get much much much more powerful, it is fairly easy to scale the key size to an arbitrarily high number of bits to defeat quantum computing methods.

Diffie-Hellman keys can be generated for very-high bit lengths, as it is not difficult to generate the numbers required for it. It IS, however, difficult so solve, and that hasn't changed, and likely won't change for a very long while.

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