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Errors:
*Typo on the «hard problem» at 14:11, it should be a/(b c) b/(a c) c/(a b) = 4
*Typo-turned-speako: The classification of quasithin groups is 1221 pages long, not 12,000. The full collection of papers proving the CFSG theorem do make up tens of thousands of pages, but no one paper was quite _that_ crazy.
Thanks to Richard Borcherds for helpful comments while putting this video together. He has a wonderful hidden gem of a channel: youtu.be/a9k_QmZbwX8
The Monster image comes from the Noun Project, via Nicky Knicky
— These animations are largely made using manim, a scrappy open-source python library: github.com/3b1b/manim
If you want to check it out, I feel compelled to warn you that its not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then «add subtitles/cc». I really appreciate those who do this, as it helps make the lessons accessible to more people.
— 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: 3b1b.co/subscribe
How do you secure messages over the internet? How do quantum computers break it? How do you fix it? Why dont you watch the video to find out? Why does this description have so many questions? Why are you still reading? What is the meaning of life?
0:00 Intro — Are we DOOOOMED??
0:52 How NOT to Send Secret Messages
2:09 RSA — Encryption Today
5:19 One-Way Functions and Post-Quantum Cryptography
7:28 Qubits and Measurement
9:03 BB84 — Quantum Cryptography
12:43 Alternatives and Problems
14:26 A Case for Quantum Computing
CLARIFICATIONS:
You dont actually need a quantum computer to do quantum-safe encryption. As briefly mentioned at 7.04, there are encryption schemes that can be run on regular computers that cant be broken by quantum computers.
CORRECTIONS:
«The public key can only be used to scramble information.» (2.18) Technically, you can use any key to encrypt or decrypt whatever you want. But theres a specific way to use them thats useful, which is whats shown in the video.
«Given a private key, its easy to create its corresponding public key.» (5.36) In RSA, depending on exactly what you mean by «private key», neither key is actually derivable from the other. When they are created, they are generated together from a common base (not just the public key from the private key). But typically, the file that stores the «private key» actually contains a bit more information than just the private key. For example, in PKCS #1 RSA private key format ( tools.ietf.org/html/rfc3447#appendix-A.1.2 ), the file technically contains the entire public key too. So in short, you technically cant get the public key from the private key or vice versa, but the file that contains the private key can hold more than just the private key alone, making it possible to retrieve the public key from it.