How does RSA Cryptography work?

Oxford Sedleian Professor of Natural Philosophy Jon Keating explains the RSA Cryptography Algorithm. Get 25% off Blinkist premium and enjoy 2 memberships for the price of 1! Start your 7-day free trial by clicking here https://www.blinkist.com/tomrocksmaths RSA encryption is used everyday to secure information online, but how does it work? And why is it referred to as a type of public key cryptography? Professor Jon Keating worked alongside the UK intelligence agency GCHQ for many years, and therefore knows a thing or two about encrypting secret messages. Here, he explains how the RSA algorithm works in general, and goes through 2 worked examples with small prime numbers. The algorithm relies on the idea that whilst it is very easy to multiply two prime numbers together, it is extremely difficult to break up a large number (with several hundred digits) back into its prime factors. Using some clever results from Number Theory - including Fermat's Little Theorem and the Euler Totient Function - the message can be decrypted only if you know the original prime factors. This means advertising the product of the primes, or 'public key', enables people to send you a message without compromising the security of the encryption system. Even if the message is intercepted, it can only be decoded with knowledge of the prime factors - and these are incredibly difficult to obtain. This video is sponsored by Blinkist. Additional images and footage are used under a creative commons licence – links below. Blockchain Travel: https://www.youtube.com/watch?v=_Ui3s-Vp8_k Produced by Dr Tom Crawford at the University of Oxford. Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: https://www.seh.ox.ac.uk/people/tom-crawford For more maths content check out Tom's website https://tomrocksmaths.com/ You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths. https://www.facebook.com/tomrocksmaths/ https://twitter.com/tomrocksmaths https://www.instagram.com/tomrocksmaths/ Get your Tom Rocks Maths merchandise here: https://beautifulequations.net/collections/tom-rocks-maths