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- Prime Numbers and Cyber Security
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## Prime Numbers and Cyber Security

Would you like to see an ingenious example of how the world of mathematics can have unexpected ramifications in the world?

You may be aware of the role that the special numbers e=2.718… , pi=3.14… , and the golden ratio Phi=1.618… , play in our world. It turns out that prime numbers (numbers that cannot be divided or reduced into smaller numbers) also have a special property: they are ideal for helping to create a secure banking system.

You see: the security systems that allow you to safely use an ATM or bank online, and allow you to securely send information over public networks, use a form of cryptography, or coding, that is based on numbers first

Amazingly, most algorithms, meaning methods, for encoding your information are based on a 300-year-old discovery about prime numbers, Fermat’s Little Theorem.

The French mathematician Fermat discovered a relatively simple property about how prime numbers behave when multiplied together, and he was able to explain why this property is true. At the time, however, his discovery had no obvious application: it was simply an interesting fact about prime numbers.

Then, in the middle of the 20th century, a team of cryptographers – people whose job it is to help encode information – found a way to use Fermat’s Little Theorem, this discovery about prime numbers, to send information from safe and secure way. They used Fermat’s Little Theorem as part of a “recipe” for number encryption, the RSA algorithm.

Without going into too much detail, what happens when a system uses the RSA algorithm or a similar algorithm, for example when you access the ATM – the ATM stores your debit card information and PIN number as a real number : a string of 0’s and 1’s. It then encodes that number using a “key” known only to the ATM and the bank.

The ATM then sends the debit card information to the bank using this “key” – and if a spy, or criminal or eavesdropper sees the message – it is encrypted. To decode the message, they would have to know the “key”, and to determine the key, they would have to factor a number of several hundred digits. This is very difficult, almost impossible, even for the fastest and most advanced computers, so your information is safe.

What is remarkable about this is that it is all based on the discovery of the mathematician Fermat, 300 years ago. At the time, Fermat had no idea that what he discovered would eventually be the key to keeping information secure in the 21st century.

This is one of the many remarkable properties of the world of mathematics: it has many unexpected links to the physical universe, many unexpected applications that are sometimes not apparent for centuries.

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