Security in a digital world requires that our communications are safe from digital eavesdroppers. The way we do that is to encrypt our messages using mathematical tools. The most powerful of these use trapdoor functions – that is, ones that work easily in one direction (making encryption easy) but not in the other (making decryption difficult).
Trapdoor functions utilise a property of multiplication – its asymmetry. It’s simple to multiply two numbers together, for example, 971 and 1,249, to get 1,212,779, but it’s quite hard to start with 1,212,779 and work out which two prime numbers (its factors) have to be multiplied to produce it. And the task becomes exponentially harder the bigger the original numbers are. Which is why, up to now, computer scientists believe that it’s impossible in practice for a conventional computer, no matter how powerful, to factorise any number that’s longer than 2,048 bits. Why so? Because it would take it 300tn years, or about 22,000 times longer than the age of the universe (to use just one of the popular analogies), for the machine to crack the problem.
