Solving Quantum Cryptography

**SPEAKER_1** (0:00)
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**Matt O'Dowd** (1:00)
Your extensive posting history on Ah, Birds with Arms and your old fan fiction heavy live journal are both one tiny math problem away from becoming public knowledge. That math problem is prime number factoring and the new era of quantum computers may lay bare your indiscretions, as well as collapse the entire digital economy. Unless we get some post quantum cryptography, post haste. So how close are we?
It's said that quantum computers will threaten the security of our digital civilization because they can easily overcome the encryption method that underpins almost all of it. Every email, every online purchase, every login is secured by the fact that it's a lot harder to factor out prime numbers than it is to multiply them together.
Large products of prime numbers become encryption locks, and the prime numbers that go into them become the keys to the secrets in your inbox.
Your secrets are safe-ish for now, because the most powerful classical computers will take thousands to billions of years to find those factors depending on the key size. But in 1994, a mathematician named Peter Shor developed an algorithm, Shor's algorithm, that could use a quantum computer to factor a prime number in, well, a human lifetime or a human lunch break. Quantum computers did not exist in 1994, but just last year, Google's quantum computer, Sycamore, outspread the best classical computers for a very specific task. According to the researchers, Sycamore performed calculations to simulate another quantum system exponentially faster than would have been possible with a pure classical computer. We'll talk about exactly what happened here in another episode, but what does this mean for internet cryptography? Is it game over? Not quite. Quantum computers need to become far more reliable, have better fault tolerance, and or support vastly more qubits to do the sort of prime factoring required for decryption. But those computers will eventually arrive, so what's to be done? One option is to match quantum decryption with new quantum encryption techniques to replace prime factoring. We talked about this in our episode on quantum key distribution, and we've also talked about the challenges. To distribute a quantum key, you also need a quantum internet to transport quantum states. This is a far more challenging problem. Quantum states are insanely fragile and difficult to transport, and the quantum internet may not arrive before better quantum computers can crack current encryption techniques and collapse the modern digital world.
Fortunately, there is another option, and one that will be a lot cheaper than building a quantum internet. It turns out that there are some ingenious non-quantum ways to thwart the hacking powers of quantum computers. Enter post-quantum cryptography or quantum resistant algorithms. I'm Arch Manning.

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**Matt O'Dowd** (4:42)
Which might replace our vulnerable prime factoring based cryptography. To understand why some algorithms are vulnerable to quantum computing attacks while others are thought to be quantum resistant, we need to review a bit about encryption.
Prime factoring is an example of what we call a one-way function. That's a mathematical operation that's very easy to figure out in one direction, but very difficult to reverse. Let's start with a more visual example. Let's say Alice has a secret shade of yellow. Bob has a secret shade of blue. And there's a shade of red that is publicly broadcast. That's the public key. Alice combines her yellow with the public shade of red, which gives her an orange. Bob combines his blue with the red to get a purple. Then Alice sends her orange to Bob, and Bob sends his purple to Alice. And then Alice combines Bob's purple with her yellow, and Bob combines Alice's orange with his blue. The resulting brown is a shared secret that can be used to encode text between them. Unless an eavesdropper, Eve, can unmix Alice and Bob's colors, she can't figure out what the shared secret key is. The current dominant encryption protocol uses prime factors instead of colors. And this is the RSA protocol named after Ron Rivest, Adi Shamir and Leonard Adelman, who came up with it in 1977