How quantum physics leads to deciphering common algorithms

The rise of quantum computing and its implications for current encryption standards are well known. But why exactly should quantum computers be particularly adept at cracking encryption? The answer is a clever mathematical juggling game called Shor’s Algorithm. The question that remains is: what does this algorithm do to make quantum computers so much better at cracking encryption? In this videoYouTuber minutephysics explains it in his traditional whiteboard cartoon style.

“Quantum computing has the potential to make access to encrypted data super, super easy – like having a lightsaber that you can use to cut through any lock or barrier, no matter how strong,” explains minutephysics. . “Shor’s algorithm is that lightsaber.”

According to the video, Shor’s algorithm assumes that for any pair of numbers, possibly multiplying one of them by itself, it will achieve a factor of the other number plus or minus 1. So you guess the first number and factor it out, adding and subtracting 1, until you get to the second number. This would unlock the encryption (specifically RSA here, but it works on other types) because then we would have both factors.

One of the reasons why this seemingly simple process relies on the development of powerful quantum computers is that finding the correct power to multiply the first number by to find a factor of the second number (N) ± 1 takes an awful lot of trial and error. . The encryption key is quite a long number, so the strength can range from 1 to millions. But brute force isn’t the reason quantum computers work so well here.

The Superpowers of Layering

In short, thanks to quantum superposition, a quantum computer can calculate multiple answers for a single input. However, the video says you only get one response output at a time, with probabilities attached. To solve this problem, the calculation is configured so that the wrong answers interfere with each other so that only the correct answer (or at least a correct guess) is likely to be output. This calculation, which focuses on finding the right power pis Shor’s algorithm.

Everything is extremely mathematical, involving a help of Euclid’s algorithm, as well as a quantum Fourier transform that transforms a series of superpositions of superpositions into sine waves that either interfere constructively (add to each other) or destructively – that is, they cancel each other out. The video says that basically you can rig it so that only 1/p is logged, with all other destructively interfered responses out of contention. Once there, it’s a walk in the park to find p, which makes it much easier to find the two encryption factors. Watch the whole video for more details and to maybe feel a little smarter.

By the way, Peter Shor is always prosperousand if you’re interested in a deep dive into how he broke the internet, here’s another video where the man himself explains how he understood his eponymous masterpiece.

Sharon D. Cole