What’s the maths behind encryption? │ The History of Mathematics with Luc de Brabandère
Why are prime numbers so important to encryption technology?
Because they are indivisible and there’s an infinite number of them.
Luc de Brabandère explains the maths behind the art of safeguarding our data in this latest episode of his amazing series, The History of Maths.
Find out more:
Why are prime numbers so exciting? https://kids.frontiersin.org/article/...
Encryption methods https://en.wikipedia.org/wiki/Encryption
The time-honoured knowledge that prime numbers are indivisible is keeping us safe today.
Find out how. And while we're here, subscribe to our series ‘The History of Maths’ on the YouTube channel ‘What makes it tick?’
A prime number is a number, positive, integer, that can only be divided by 1 and itself.
For example, 97 is a prime number because you cannot divide 97 by anything but 1 and itself.
It's a very old concept, but suddenly they are fashionable again. Why? Because prime numbers are the key components of a discipline widely used today: cryptography.
On networks, you want to keep information secret, and probably one of the best ways is to use combinations of prime numbers. It's funny, because again very old theory suddenly becomes very useful.
But one of the conditions for using prime numbers in cryptography is an infinity of prime numbers. You have to prove there is an infinity of prime numbers. The Greeks proved it. How without a computer? They proved it in a very interesting way. It's called 'proof by the absurd'.
The starting point is exactly the opposite of the thing you want to prove. So here is how they did it. Let's imagine there is a largest prime number and we call it N. So, the starting point: there is no infinity, there is a largest prime number.
Now let's define P as the product of all those existing prime numbers. P is equal to 2 x 3 x 5 x 7 x 11, etc. And now just add 1 to P and take P + 1. It's a number that cannot be divided by 2, the remainder is 1; cannot be divided by 5, the remainder is 1; cannot be divided by 13, the remainder is 1. You cannot divide P + 1 by any existing prime number.
OK, so there are only two possibilities, either P + 1 is a prime number or P + 1 can be divided by a prime number larger than N. But in both cases, the statement, the beginning is proved wrong. There is a prime number larger than N.
So, this is the absurd and it shows, it proves that there is an infinity of prime numbers. And they can be used in cryptography.
In the final episode of our series ‘The History of Maths’ we will show how jumping to conclusions is the enemy of good maths.
Watch the full series on the YouTube channel ‘What makes it tick?’
