How to keep an open secret with mathematics.

Shamir's Secret Sharing on wikipedia.

I made the animated parabola in GeoGebra with help from my mate Ben Sparks. Here is the GeoGebra5 file if you'd like to have a play:

Read about finite fields on MathWorld:

Shamir Secret Sharing used with Bitcoin:

And for balance, an argument against using Shamir Sharing with Bitcoin, but rather Multisignature.

CORRECTIONS
- None yet, let me know if you spot any mistakes!

Thanks again, as always, to Jane Street for supporting this channel.

Thanks to my Patreon supporters who help make these videos possible. Here is a random subset:

Michael Lehenbauer
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Filming and editing by Alex Genn-Bash
Music by Howard Carter
Design by Simon Wright

MATT PARKER: Stand-up Mathematician

[rq]

Teachers would have a much easier time getting their students to care about quadratics if they told them that they can solve polynomials to access someone's financial accounts

[nickmartin]

Matt: This number is random and has no meaning.
Everyone: That number definitely has meaning.

[lexingtonbrython]

Matt's valuables are: a business card Level 2 Menger sponge, a ream of brown paper, a copy of Humble Pi, and a framed picture of the Parker Square

[jaxielrivera]

Matt: There is no meaning behind 41, 366, 362
Me: No, there has to be.

I googled the number and one of the things that came up was an adobe file image (with the number as its file ID) and it’s a 3D animated couple kissing and hugging, so the secret meaning is that he loves math. There it is. I got it guys, you’re welcome.

[Yoshiiro]

The clever-one : My password are the last 6 digits of Pi.
The mathematician : It's impossible to guess.
The engineer : I'll iterate from to should take a couple of seconds.

[faastex]

By assuring that number had no hidden meaning, I'm now even more convinced it has a hidden meaning.

[GammaFn.]

That's your password? "sums"?


That doesn't add up.

[hismigj]

That's complicated. I think I'll stick with my trusty '1234'. Nobody will guess that.

[yuvalne]

Referring to Tom's video without risking your brand deal.
Clever.

[arnet]

Shamir secret sharing is such a brilliant and beautiful idea.

[lolledopke]

I logged in to Matt's bank account, but because he's a mathematician I couldn't steal anything :(

[MephieStopheles]

41.36, 63.62 are Long/Lat's to a location in the desert of Uzbekistan

I think he's telling us where he hid the bodies.

[cosmicdeven]

Toms really out here risking all of his friends sponsorship deals😂😂

[astropgn]

9:30 "And they said no."

Hahaha matt's timing is really funny!

[robertwiesner]

Thank you so much for this video. We talked about this in one of our university courses and I didn't understand it very much. Having it explained like this with pictures makes it a TON more understandable.

[djones]

Thank you for clarifying the VPN claims. I'm sick of all the false advertising in VPN ads.

[konstantinkh]

It gets better. You aren't restricted to prime-sized sets. Any finite field will do, so you can use splitting fields. These can be p^n, where p is prime and n is any integer. And yes, 2 is a valid prime for this purpose. So if you need to encode, say, 256 bit key, there's a field over which you can define a polynomial that will admit any 256 bit number, and you'll need exactly the right number of people to come together with their parts of information to know it. The algebra of such fields gets a little intense, though.

[robnorris]

Now Matt has to change his password to something else we could never guess, like “muss”.

[wolvenmoonstone]

video aside i really appreciated the honesty of that ad spot. VPN companies tend to be really manipulative and oversell themselves but not this time it fits the rest of the video better this way

[lierdakil]

9:23 "The only people who will see it [data] are you [...] and ExpressVPN"
Not strictly true. Once the tunnel terminates -- and it eventually has to -- "the data" travels through the Internet unencrypted (unless it would've been encrypted without VPN also). Which means that once "the data" left the relative safety of the encrypted tunnel, it can (in theory) be seen by any number of third parties. In essence, using a VPN is trading your ISP for your VPN service. I mean, if you don't trust your ISP, or if you want to circumvent geographical restrictions, sure, VPN services are great for that. But those otherwise offer no more security than there is already there. In fact, those offer arguably _less_ security, since (a) VPN services are kinda shady with their stated no-logs policies often being in direct conflict with local laws, and (b) VPN services can be a prime target for malicious agents and/or government agencies -- if a VPN is compromised, it's statistically speaking less "secure" (in terms of possible data leaks) than not using a VPN at all.