This video is sponsored by blinkist when I I thought I'd explain is um public key cryptography and this is the kind of cryptography that's used ubiquitously in um in modern Communications and it relies on remarkably simple um mathematics relies on properties of prime numbers and are modular arithmetic so prime numbers as everyone will know are numbers divisible only by themselves and one and we know there are infinitely many of those but there's a huge amount we don't know about the primes and a lot of mathematics that involve primes is still extremely difficult to us so we can find prime numbers we've got good um methods for doing that with computers but we don't have a good method for breaking um numbers up in terms of their prime factors so that um asymmetry is critical to a public key cryptography so it's a bit like making a cake it's easy to find the constituent Parts but once you've mixed them together it's very hard to separate them back out again that's one component of public key cryptography the other is modular arithmetic the idea that you can take a number and subtract from it multiples of some other number and do arithmetic a bit like you would with a with a clock where the um you do arithmetic modulo 12 we tend to only record um the time in terms of up to 12 so 1500 hours is the same as three o'clock because you can subtract off 12 and you get to three so for example example 10 is is we would say congruent to three modulo seven because if you subtract off seven from ten you get three and um and 17 is congruent to 3 mod 7 because you can subtract off twice...
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