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The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high-quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. TADGE DRYJA: OK, so today I'll talk about CoinJoin, signature aggregation, well before that privacy, but privacy, CoinJoin, CoinShuffle, signature aggregation, and how these all connect. It's a little bit of a leap to put these both in the same class, but not really. They're connected. But they are somewhat separate things. Today, I'll talk about privacy, CoinJoin, and various ways to do that, and then aggregate signatures, so Schnorr multi-signatures, and then aggregation, and attacks on the system. OK, so the idea is privacy. And there's a bunch of terms we can use here, like anonymity and fungibility. And whatever the term for this, I don't need any, because I have nothing to hide. So I don't need any privacy. I don't need any anonymity. I'm a good person. I don't break the law. I'm a boring guy. I don't do anything crazy. I'm joking, but-- no, I'm not joking about being boring and not doing anything crazy. That is actually pretty true. I mostly just work on this stuff. But, yeah, that's a fairly common thing that people say. And the sort of clearest example is if you don't have anything to hide, you don't have any bitcoin, because literally, if you don't hide your private key, someone will just immediately take your bitcoin. So you do have secrets. Your secret is your private key and your password. And if bitcoin and these types of systems really take off, potentially most of your money and a lot of your wealth could be tied up in what is a secret. So if you're not able to keep your secrets you could lose a lot of money. And larger, I sort of think that going forward-- this is very thought leader, future kind of thing. But going forward, it seems like sort of all you have is your secrets. To the extent that you can own anything, the thing that you really have control of, you're like, OK, I got these things in my head that no one else knows. And maybe I own my car. But that's also sort of property rights, and legal systems, and maybe you can get repossessed. Maybe I own this land. But, again, that's sort of this thing with the state. But I definitely really have the stuff in my head. And I can at least try to keep that. So even if you think you have nothing to hide, you do have your private keys to hide. And that's sort of the obvious one. But larger, you want privacy because, in general, you don't want to reveal stuff about your coins. This is specific to bitcoin. But my philosophy is I generally don't want to reveal stuff ever. And it's...