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Not all. Academics refer to it as "post-quantum cryptography", see http://pqcrypto.org/

From a talk by D. J. Bernstein http://cr.yp.to/talks/2008.10.18/slides.pdf :

    RSA: Dead.
    DSA: Dead.
    ECDSA: Dead.
    ECC in general: Dead.
    HECC in general: Dead.
    Buchmann–Williams: Dead.
    Class groups in general: Dead.

    Still alive:
    Hash-based cryptography.
    Example: 1979 Merkle hash-tree public-key signature system.
    Code-based cryptography.
    Example: 1978 McEliece hidden-Goppa-code public-key encryption system.
    Lattice-based cryptography.
    Example: 1998 “NTRU.”
    Multivariate-quadraticequations cryptography.
    Example: 1996 Patarin “HFE^V-” public-key signature system.
    Secret-key cryptography.
    Example: 1998 Daemen–Rijmen “Rijndael” cipher, aka “AES"

To be more specific: The only known things quantum computers are algorithmically superior for are factorization, computing discrete logarithms, and things that reduce to those. This happens to include all currently popular public-key cryptography. Fortunately, that is typically unrelated to symmetric-key cryptography.

At its core, to do public-key cryptography, you just need a difficult instance of an NP-but-non-P problem. Quantum computers put factorization and discrete logarithms into P, but there are still plenty of harder NP problems that have not been tapped. If quantum computing starts to become a significant threat, we'll probably see renewed interest in those.

"an NP-but-non-P problem"

Maybe I'm misunderstanding but if you had one of these you would have answered a fairly important question in CS theory. Perhaps you mean to say "NP-complete", but even then I'm not sure the proposition is correct.

You're right that my statement wasn't specific enough; I was going for brevity. The precise statement is: You need a problem with a known polynomial-time nondeterministic algorithm, but no known polynomial-time deterministic algorithm.

A very important point though: public-key cryptosystems rely on one-way functions, functions that are hard to invert in the average case, NOT just the worst case, which is not your typical complexity-theory mindset. So, I would be careful when talking about complexity classes in the context of crypto because it can be very, very easy to trip up and say something that's either not comprehensive or just downright incorrect.

It's closer to "NP-but-not-weaker". NP-complete also means you can convert other NP problems into them, which isn't necessary.

So, basically, we won't have any means of key exchange which isn't quantum crypto.

I don't realy like rocking a boat... but quantum cryptography can't realy be used in practice.

Or, better, any practical implementation of quantum cryptography is succeptible to attacks. And the entire thing still needs an authentication method, guess what we use for authentication nowadays.

It is being used in commercial systems (e.g. idquantique). Practical implementations are prone to vulnerabilities, but none have been found that cannot be remedied. Some techniques such as device independent or measurement device independent QKD offer to make it far more difficult to come up with attacks in the future too.

The #1 advantage of QKD is not that the methods being used today will be immune to all attacks found in the future. It's that quantum states are unclonable, so there's no way to archive cipher-text for future attacks, as can be done with classically encrypted messages. e.g. If you send encrypt a message and send it via email today, the encryption method has to stand up to advances in algorithms and computational hardware for as long as the information remains sensitive. If you send something via QKD, an eavesdropper must break the protocol at the moment you send the message or it will be safe for all time.

Authenticating strangers, as in credit card transactions, is something that quantum computing may disrupt. QKD can be used safely by people who have met at some point in the past, but we probably have a bit of time before CC transactions need to be encrypted by QKD. i.e. While you should probably not send medical records or state secrets via many classical encryption protocols now, your CC info will change in a couple years so it's not as big of an issue if your transactions are cracked a few years after that.

No. One of the most promising is NTRU, an asymmetric cryptosystem which isn't broken by quantum computers.

Many key exchange protocols treat the asymmetric operations as black boxes, so you can replace RSA with any other asymmetric cipher.

No, we would be using one of the numerous lattice/linear code cryptosystems for which quantum computers provide no known advantage.

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