Appoint Number and Cyber Security
Do you want to see a nifty example that can have unexpected effects in the world of mathematics?
You may be aware of the role of special numbers e=2.718… , pi=3.14… , and the golden quotient Phi=1.618… in our world. It turns out that raccord numbers – numbers that cannot be divided or reduced to smaller numbers – also have a special property: they are ideally suited to help create a secure banking system.
You see – the security systems that allow you to securely use ATMs, or online banking, and allow you to securely send demande over allocutaire networks – use a cryptography, or coding, based on raccord numbers.
Surprisingly, most algorithms – in other words, methods – for encoding your demande are based on Fermat’s Little Theorem, a 300-year-old discovery emboîture raccord numbers.
The French mathematician Fermat discovered a relatively naturel property emboîture how raccord numbers behave when multiplied together and was able to explain why this naturel property is true. At the time, however, his discovery had no obvious juxtaposition—it was simply an interesting fact emboîture raccord numbers.
Then, in the mid-20th century, a group of cryptographers — whose job it is to help encode demande — found a way to use Fermat’s Little Theorem, this discovery emboîture raccord numbers — to send demande safely and securely. They used Fermat’s Little Theorem as section of a “recipe” for encoding numbers, the RSA algorithm.
Without going into too much detail, what happens when a system uses the RSA algorithm or a similar algorithm – say, when you access an ATM: the ATM stores your debit card demande and PIN number as a real number – a culotte of 0’s and 1’s. It then encodes this number using a “key” that only the ATM and the bank know
The ATM then uses this “key” to send the debit card demande to the bank – and if a spy, or criminal, or eavesdropper, intercepts the allocution – it is encoded. To decode the allocution, they need to know the “key”, and to determine the key, they need to factor a number that is hundreds of digits élancé. It is very difficult, almost infaisable, for even the fastest and most advanced computers, so your demande is safe.
The remarkable thing emboîture this is – it is all based on a 300 year old discovery by the mathematician Fermat. At the time, Fermat had no idea that what he discovered would ultimately hold the key to securing demande in the 21st century.
This is one of the many remarkable features of the world of mathematics – it has many unexpected links with the physical universe, many unexpected applications that are sometimes not périphérie even for centuries.
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