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# Banks and Prime Factorisation

Can you find the prime factors of 14? 7 x 2 right? EASY! What about 1159? a little more difficult 19 x 61. Okay so, do you think you could solve the prime factors of a number 100 characters long? No? As you've gathered, it is very difficult.

Doing a multiplication is easy though! You could multiply two primes together using a calculator for example 7 x 6 = 42, but if you were to give 42 to someone and asked them to find the prime factors, they would find it more difficult. If the primes are large enough, the problem would become exponentially more difficult and the person will certainly give up.

Believe it or not, this is how your bank secures every transaction you make, how NASA can control probes on distant planets, how power stations can protect against hackers switching off power, how governments secure classified documents from the public. It all relies on the complexity of large prime factorisation.

In Cryptography, this is known as a one way function, which means, without the key, it can take a while to crack the lock. Using two primes that are 50 characters long will take a computer about a week to crack. 100 characters would take about a year, and so banks rely on primes of around 1000 digits long being multiplied together to protect your money.

It could take a lifetime to crack a password using large enough primes using your desktop. Can you imagine if 80 years on, the user changed the password? Most banks however, change their password daily, or even hourly, so cracking them is close to impossible.

Note by Jack Barker
2 years ago

## Comments

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These notes are really nice! I really think that you should write a wiki on such stuff . · 2 years ago

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Lovely post! BTW, the prime factorisation of 6916 is 2 * 2 * 7 * 13 * 19 · 11 months, 2 weeks ago

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@Calvin Lin sir

Is it a thumbs up from you for writing a wiki on Hacking and Cryptography ? I'll post questions on it , if you want . But it's up to you sir .

Thanks :) · 2 years ago

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Yes, that would be great! We can add them into the CS maps (which are still quite empty) Staff · 2 years ago

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Thanks sir :) I'll start thinking up some nice questions and stuff for the wiki . · 2 years ago

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