A new global geek squad is harnessing cryptography to stay a step ahead of cybercriminals.

At the heart of almost everything we do on the web is a special kind of number, a prime number. ... But what makes them so special to codes is when you combine two of them. ... If ... you've got to figure out the two original primes, the only way is trial and error. ...I do not think that these explanations are very helpful. It is true that most SSL web servers use RSA, but Diffie-Hellman came first and is arguably superior for most purposes. That was the real breakthrough. And trial and error is not the only way to break RSA, as other methods are asymptotically much faster.

This system of public and private keys is known as the RSA algorithm. That beautiful piece of mathematics has fundamentally changed the world around us.

It has made the hunt for very very large prime numbers one of the most important quests in the field of mathematics. And here is the current largest, all 5000 pages of it.This is nonsense. These numbers have almost no importance to either mathematics or cryptography. They are just a silly curiosity.

The mathematics of the world of the very small means that things can be in many places at the same time. ... They may be a way to crack the world's most powerful codes.Not really. Saying that particles can be in more than one place at the same time is just an interpretation of the wave function, and has never been observed. So you can choose to believe in it or not, and no one can disprove you.

They go on to explain qubits as being 0 and 1 at the same time, so that a quantum computer can calculate both simultaneously. Scott Aaronson argues on his blog that this is a bad explanation, because it leads you to believe that quantum computers are more powerful than they really are.

It blows the doors off of RSA encryption. Right. All we need is more and more qubits, a larger quantum computer. Really all that's left to do is to scale up this particular architecture.This is just nonsense. They have not made a scalable qubit, and there is no known way to scale up what they have. They have never achieved that quantum speedup.

Seth LLoyd says:

Quantum computers are particular fine for ... or for simulating happens when a black hole collapses, or for that matter, a recent experiment that we did to actually implement a version of time travel.He is dreaming here.

But quantum mechanics also provides methods of communicating securely in a way that is guaranteed by the laws of physics.More nonsense from Lloyd.

Quantum cryptography is already used by folks who want extreme security. By banks and by agencies whose job is to protect information. And nowadays there are number of commercial companies who actually build quantum cryptographic systems. For a fee, you too can communicate in communicate in complete and utter privacy guaranteed by the laws of quantum mechanics.Before you pay that fee, you should realize: Every one of those systems has been broken. No bank or agency uses them for anything important. They cannot be used with routers or any other internet equipment. They cannot authenticate who you are communicating with. Even that supposed quantum mechanics guarantee is just a probabilistic statement that is much weaker than you can get with RSA or other methods.

Lloyd admits that these systems are susceptible to an impostor at the other end, but then implies that all crypto systems have this same problem. But that is not true. The main technical advance of RSA was actually not encryption, but authentication. When you log into Ebay or Amazon, it verifies that you are really connecting to Ebay or Amazon. In worst case, you could be connecting to someone who has hijacked the DNS servers and stolen Ebay's RSA secret key, or who built a quantum computer to factor the RSA public key. Neither has ever happened. Quantum crypto offers no such assurances, and you would be on your own to verify that a cable connects directly from your computer to the Ebay server. It can detect certain kinds of tampering, but it cannot detect some hijacking the whole line.

I don't know how respectable professors like Lloyd can shamelessly over-hype their field like this. They are charlatans. Even Aaronson is not this bad.

A better popular explanation can be found in this Wired article on the double slit experiment:

To summarize, we’ve arrived at a pattern of fringes that’s built up one particle at a time. But when you try to work out exactly how those particles got there, you find that they didn’t take the left route, they didn’t take the right route, they didn’t take both routes, and they didn’t take neither routes. As MIT professor Allan Adams puts it, that pretty much exhausts all the logical possibilities!Some people prefer to think of the electron as being two places at once, or being a wave, or even as being immune to the usual laws of logic. If one of those makes you feel better, then go ahead. But there is no perfect classical analogy of the sort sought by Einstein and Bell. Those who use these analogies to promote quantum crypto or computing are just charlatans.

An electron is not like a wave of water, because unlike a wave, it hits a screen at a single location. An electron is not like a baseball, because when you throw in a bunch of them through a double slit, they interfere and create patterns of fringes. There is no satisfying analogy that anyone can give you for what an electron is.