Catalyst: Prime number keys

RUBEN MEERMAN:
Billions of dollars crisscross the internet every day. But all this e-commerce wouldn't be safe without some very special numbers. They're called prime numbers - numbers divisible only by themselves and one. And they've long fascinated mathematicians, like my friend Simon Pampena.
SIMON PAMPENA:
Hey, Ruben.
RUBEN MEERMAN:
Hey, Simon. What's this?
SIMON PAMPENA:
This is a prime number.
RUBEN MEERMAN:
Hang on, this whole thing is one number?
SIMON PAMPENA:
Yep, it's 2 raised to the power of 43,112,609, take 1.
RUBEN MEERMAN:
Whoa! And we know that this is prime?
SIMON PAMPENA:
Correct. It's been verified by computer to be the largest one known to date.
RUBEN MEERMAN:
So hang on a minute, you're saying this one gigantic number is only divisible by itself and one?
SIMON PAMPENA:
You got it. It's indestructible.
RUBEN MEERMAN:
That's amazing. How many pages is it?
SIMON PAMPENA:
4,376.
RUBEN MEERMAN:
That's incredible! So why are prime numbers so useful for internet security?
SIMON PAMPENA:
OK, it works like this. Start with two really big primes, call them 'P1' and 'P2'. And then you multiply them together to get a composite number we'll call 'C'.
RUBEN MEERMAN:
OK, and C is not a prime number?
SIMON PAMPENA:
No, of course not. YYYRUBEN MEERMAN:YYY No.
SIMON PAMPENA:
But the point is that while computers are very good at multiplying numbers together, if you start with C and try working back to get P1 and P2, it turns out to be superhard.
RUBEN MEERMAN:
Ah, right. So then what?
SIMON PAMPENA:
So this number C is used to generate what's called a public key - a code that's available for anyone to use.
RUBEN MEERMAN:
Hence 'public' key? YYYSIMON PAMPENA:YYY Yeah. The bank sends you this public key which you use to encrypt your credit card or what have you. And then it returns back safe and sound.
RUBEN MEERMAN:
So then what?
SIMON PAMPENA:
But P1 and P2 are used to decrypt this code, so they have to be kept secret. They're what's called the private key.
RUBEN MEERMAN:
Right, so they're not beamed across the internet?
SIMON PAMPENA:
No. Only your bank, or whoever is receiving your information knows what P1 and P2 are.
RUBEN MEERMAN:
So THEY'RE the only ones that can access my credit card. OK, but what if a thief does intercept my message?
SIMON PAMPENA:
Not a problem. A hacker using a state-of-the-art computer system would need 1,000 years to find the original primes and crack the code. Your bank already knows P1 and P2, so can do it in a second.
RUBEN MEERMAN:
Ah. But isn't there some kind of catalogue of all the known primes that a hacker could use to crack my code?
SIMON PAMPENA:
Mm, well this is the crazy thing about primes - no-one has a complete list. This goliath is the largest prime found so far, but the number of primes yet to be discovered smaller than this one, is a number the same size, take off a couple of digits.
RUBEN MEERMAN:
Right, so then how big is the NEXT biggest prime number going to be?
SIMON PAMPENA:
Nobody knows. It's a mystery.
RUBEN MEERMAN:
Ah-ha. Well, there you go. It's just another one of those things we just don't know.