Opinion: advances in quantum computing will mean secure transaction sites will have to up their game to stay clear of quantum hackers.

You've just purchased your groceries online or transferred €700 from your current account to pay an outstanding bill. You probably did this by credit card, using a "secure" site. At least, the site seemed secure - well, it's run by a bank, or a reputable company, so it must be OK, right?

The unsettling fact - and one probably unknown by the general public - is that there are tens of thousands of people who know how to "hack" in to your secure transaction, and basically do whatever they want (benign or malicious) once they have that info. These people are not some shady cybercriminals, merely any mathematician worth their salt in any university in the world.

But - and here's the big but - knowing how to do something, and being able to do it quickly or efficiently are two different things. If one was to know how to do something (i.e. have an algorithm or step by step procedure for it), but could only do it very slowly, you might say at some point that the procedure is useless in practice because it takes so long.

From RTÉ Radio 1's The Business, Liam Geraghty reports on the history of the credit card

This is exactly the case in point with online payments through secure transaction sites. They rely on a simple mathematical idea that mathematicians all believe, but none have proven to be correct: Factoring large numbers is hard!

Suppose I ask you to break 24 into its multiplicative parts. Well, the answer is (2)(2)(2)(3). How long did that take you? Now I ask you to break 3016 into its parts. The answer it turns out is (2)(2)(2)(13)(29). If you were able to do it, how long did that take you? There are lots of (clever) algorithms for factoring large numbers (a credit card number with 16 digits is large, right?), known by lots of clever mathematicians, but none of them are efficient. In fact, the best are so inefficient that it would take years for the result to come out even on a supercomputer. There's not much point hacking someone's secure transaction if it takes years to get in.

Enter quantum computers. In a quantum computer, we work with both the two classical bits, 0 and 1, and the infinite number of numbers that are in between these. These correspond to the states of the smalled objects in the Universe, or fundamental particles. Manipulating a particle, which can be in a superposition of two different states, and sets of interacting particles, that can be in a state which is called entangled - more than the sum of the parts, is what gives quantum computers their power.