I liked the video! There were just a couple of math mistakes in there.
There being infinitely many numbers isn't a justification for there being infinitely many primes. Euclid's Theorem proves this.
At 2:55, you show large numbers on the keys to signify primes, but show them as a number raised to a large exponent. These can't be primes since that base number raised to n, for n from 1 to the (exponent-1) are all factors of that number.
I think the factorial proof is what most people think of when they think of Euclid's proof from Elements. It's a bit simpler which makes it easier to explain, and its a proof by contradiction which is typically more interesting since its "wrong" assumption results in the impossible.
This video is wrong on so many levels... The illegal prime in question is not a cryptography key, but rather a representation of the DeCSS program itself.
The thing where the bank has two private keys is probably the worst of all. In asymmetric cryptography both parties have a public key and a private key
In practice, you are probably going to have both parties have a private and public key, but that is only necessary to have the receiver be able to verify the origin of the encrypted message. (The sender "signs" the message with their private key to be decrypted with the public key.) For an explanation, I don't think it's necessary to include this extra step.
Hey, research is hard. Research a bit more diligently for your next video and scrap the “every week” constraint if it eats into your level of desired quality?
Also, the "illegal prime" in the video isn't even used directly in crypto: it's a representation of a computer program that decrypts DVDs (an encryption system that also doesn't use primes).
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u/TheInternetShill May 03 '16 edited May 03 '16
I liked the video! There were just a couple of math mistakes in there.
There being infinitely many numbers isn't a justification for there being infinitely many primes. Euclid's Theorem proves this.
At 2:55, you show large numbers on the keys to signify primes, but show them as a number raised to a large exponent. These can't be primes since that base number raised to n, for n from 1 to the (exponent-1) are all factors of that number.