Sending information over the internet is often encrypted — that means it is only readable to the sender and recipient. So when you send a message to a friend over WhatsApp, the only devices the message is visible in are your phone and your friend’s phone. Asymmetric cryptography is a common method for achieving this
But how does it actually work?
This explanation I found from Terrance Tao is the best I’ve seen, so thought I would share it here.
So what can Alice do? 🤷♀️
She has an amazing idea 💡
Obviously this is an over-simplified example — in reality, the box is a digitised code that only Alice and Bob can decipher.
All types of cryptography rely on prime numbers — they are an integral part of securely sending information over the internet. There are two reasons for this:
So the scientific version of Alice and Bob’s message transmission relies on primes. Here’s how can Alice can send a secret message (in the form of a number) g to Bob.
FYI: mod is like the remainder. For example, 3 mod 2 = 1 because 2 goes into 3 once remainder 1. Or, 25 mod 7 = 4. Or 25 mod 5 = 0.
And there we have it. This time Alice hasn’t sent a physical box, but some kind of digital message. And, just like the box, anyone intercepting this message in the middle will not be able to make sense of it — i.e. “unlock it”
So some of the basic principles of keeping information private and secure online rely on prime numbers; if anyone were to figure out a simple formula for prime numbers they’d be rich not only from the mathematical awards they’ll undoubtedly win, but also from the number of credit card details they’ll be able to intercept and decipher.