 Some crazy speech on Are you still in slides? Who's got it? What the fuck? Oh, right. Okay. Okay. Ha. We'll start with Hi, Bill. We'll start with the basics. All right Do you guys know what big-o notation is like everyone? Is there anyone who doesn't know? All right. Great. That's great. All right. Do you guys know? This is going great. Do you guys know the greatest common divisor and the Euclidean algorithm? Everyone? No? Okay. I can do Euclids really quick. Okay. The Euclidean algorithm is you got... Everyone knows what the greatest common divisor of two numbers is, right? Okay. The Euclidean algorithm does that in log base 10n. That's the big-o notation. I glossed over that before. And the way it does it is you take two numbers, it's called a and b, and the bigger being a. And you do a modulus b and then the remainder goes into r. And then you shift those over so b becomes a and r becomes b. And do it again. And you keep doing that until r equals zero. And when you're done, b is the greatest common divisor. It's really fucking fast. Like log base 10n, right? Great. Oh, modular math. Do you guys... I want to be able to show this to you. Hey, Trace, pass it around. Yeah. I'll pass it around. Ask if anybody just has a really long RCA pass cable. Does anyone have a really long RCA patch cable? Nick, far wonders. This is great. Okay, well, modular math. Do you guys know what like... If I were to say 27 has kind of grew into 3 modular 12. Do you guys know what that means? Okay. It looks like 27 and an equal sign with three bars. And then three and then a parentheses and then modular 12. And it's written in... Like if you're writing in C, it would be 27% sign, 12 equals 3. It's basically like, think of it like an if-case statement. And I really need an overhead for this. Because the next thing I was going to go over was Euler's Toten function. And... It looks like a... It's a great character, Phi. Alright, someone try and make that work or do something? I don't know what the... Alright, did you find DT? Yeah, I found DT. So what's up? Alright, well... Alright, well, they do whatever. Do you guys have... Do you use your imaginations, okay? Does anyone have an RCA, female to female gender changer? Because Nick Farah wants one. Yeah, why don't you sit here here, do your scribble and bounce back up on stage. I mean... Someone... Someone figure something out, I don't care, but... On what though? What are we going to write on? I'm not going to type latex. Do you guys want to just... To do what? Yeah, do whatever you want, move that shit around. I just... I just want you people to see this over and... It's all in one. What? What do you want me to do with the ten minute break? I'm going to entertain you? Would you like me to sing? What? I can sing. Is that all you people want? Alright, whatever. Let's skip over what's called a quantum bit. Alright, so there's lots of different ways to do that, using physics and all sorts of other crazy stuff. But for the time being, just like whenever I talk about any quantum physics, just forget all physics and imagine that it's magic. Because it is. Oh, it is. Okay, first thing, superposition. A quantum bit, like it can be a zero or one, or it can be what's called a superposition, which is in between state between the two. And it's only a one or zero if it's... It's only a one or zero if it's already decohered, which is making no sense right now, because I don't have any overheads. Okay, so... What's that? Couple minutes, great. What's up? What do you want me to do? I can sing Peter Gabriel pretty well. It's a song I used to always sing. What do you want me to sing about? I'm gonna sing about... What? You guys are all talking. What? Alright, I got a joke for you. Alright, so this grasshopper walks into a bar and the bartender's like, hey, we got a drink named after you. And the grasshopper goes, really? You got a drink named Lenny? What's up? Very delicate operation. Alright, is this a hacker convention or what? What's up? Alright, well, we still have the problem that, like, I wrote these while I was really fucked up last night, so... Alright, no, we're good, we're good. No, just don't die on that thing and duck, duck. Great, okay. So... Yeah. So, um... What the... You've got great timing. What? Are we gonna do this thing or what? What? No, we'll do the over. Just plug that fucker in. Alright, I'll start on this thing. Alright, you guys can see that, right? Alright, going back to math all the way back... Glossed over a big O and all that shit. Or just total function. Basically, phi then, it's the number of numbers that are between 1 and n minus 1 that are relatively... Do you guys know what relatively prime means? Okay, it's... It's a credit scam divisor, yeah. Okay, and so that's phi right there. And then Euler also had a theorem, which is right there. If t and r are relatively prime to each other, and t's the bigger one, then t phi r is congruent to one modular r. Which means basically... If you take t and you multiply it by itself by r times, and divide the result by r, you will always get one. So that's all that says right there. And they're still doing overhead shit. So what that's used for is... What in the... Oh yeah, no, no, no, I remember what I was doing here. Alright, check this out, check this out. Hey, give me that... Give me back that oiler's toad and... I couldn't move my stuff around. Alright, great. Check this out. Die! Alright, great. Can I pull this mic off? That's all the slack you got. Put the fuck up in my note cards. Would you quit moving my shit? Alright. Yeah, now we don't have to actually speak, huh? Alright, so... So we got the oiler's toad and theorem, right? And this is what RSA is based on completely, basically. So we start out with that theorem right there in general. And like by just basics, math, we can multiply it by itself on both sides, right? Like, do you guys... What time is it? Do you guys really want to see me derive this or not? It doesn't matter. Alright, no, okay, that's great. The end product, just the RSA in general. No, this is fast, this is fast. Yeah, just for you, Bill. If you guys don't know what I'm doing here, just stop me. Like, this combines... Alright, and you see how you can keep repeating doing this? Like, you just keep multiplying by t, pi r, and since you're already doing it... Since it's modular arithmetic, you can do that as many times as you want. And it doesn't matter, because it's modulus, right? The third line has to be a plus. Where? The who? Oh, yeah. Great. No, it's right. And so, anyways, yeah. So, you get that, right? So, you can keep doing that, and... Let's call this an s. And that's any integer, right? So, that's like our first modification to that. And then, the second thing we do is we've got t, s, trunks. Multiply both sides by t. Just gives us mod r. And then, like, we can keep... Okay, we've got a times t here, times t at, like, exponential math, right? Great, right? Everyone got that so far? And then, like we did before, we can keep doing that. We can keep multiplying t by both sides. And, uh, stop moving. Yeah. So, we can keep doing that, and we can make this an e eventually. But, really, the one we want is the one with the, uh, plus one, because we can take t, s, phi, r, plus one, can go to t, mod, r. Let's just see that. Great. And, uh, we take that, and then, this part right here is what we're interested in. So, we take that, and we create... Take that, and we create a... All right, great. So, p times q equals that, right? And, uh, s, phi, r, plus one. So, those are our p and q, which will be our two prime numbers that we generally key with. So, we substitute that in. And then, from that, we can get... Let's just squeeze it on. Great. They're, uh, right here. Uh, oh, over, right, great. Uh, yeah. So, there's, uh, there's your encryption and decryption algorithm, respectively, for RSA. Uh, basically, RSA works on... If you don't know the basic principles, it's, uh... It takes really big, uh... The product of two really big, uh, prime numbers. And, using that in Euler's totem, uh, function, you can basically do the inverse modulus of... You can do an inverse modulus operation, which is crazy if you think about it. And the encryption does the normal modulus, and the decryption does the inverse modulus, and it makes it really hard to decrypt, because the only way you can do it is by guessing p and q, which also happens to be the Euler totem function of, uh, p minus one times, uh, q minus one. All right, whatever. Uh, so that's RSA. What's this thing? That's... I don't want that. Uh, oh, go over this. Let's see what I can talk about. Oh, where is quantum shit? Uh, all right, qubit. Uh, run over that a little bit. It's just a quantum bit. That's what it's called, whatever, right? Uh, oh, superposition. Okay, with quantum bits, you can get, uh... It can be one or zero or something in between. And the something in between is called superposition. And when something's in a superposition, let's say maybe a 75% chance of becoming a one and a 25% chance of becoming a zero, that's called the superposition. And, uh, it has to do with, like, the way quantum mechanics works. Like I said, it's magic. Uh, well, I'll go to EPR state. EPR state stands for Einstein and Podesky-Rosen. They're the guys who researched it. And that also has to do with entanglement a little bit. You get two qubits together and you use a Bel-State analyzer and you check them out. And they will, um... You can get them so they're both in a 50-50 superposition. So it's got a 50% chance of becoming a one and a 50% chance of becoming a zero. And, uh, that's called the EPR state, when everything's got equal chance of becoming whatever. Which leads us to decoherence, which is what becoming is. Uh, when something's in a superposition, it's, you can't read the data. The second you read the data, it will snap into one of the positions, one or zero. That's called decoherence. And, like, if you're in an EPR state and you read the bit, uh, it will decoher to a 50% chance of being a one, a 50% chance of being a zero. And, uh, using that EPR state, you can, uh... Oh, also, with the EPR, I glossed over this again, but the entanglement between the two qubits that you have in EPR, uh, there's a control bit and the... whatever, not control bit. And, uh, when you read one, the other one will decoher to the exact same value, uh, based on what that is. And that's what entanglement is. And, uh, it's pretty crazy like that. Like, let's say I decoher, or I put two qubits in, uh, EPR state and I give one to him over there somewhere, and I give one to someone on the other side of the world. Uh, he reads his. The next time he reads his, it'll be the same value. It's like having, uh, it's like having two linked coins and you flip it a bunch of times, as long as, you know, they're entangled. Uh, and you get a sequence of heads, tails, tails, heads, whatever. The other one will do the same random sequence. Um, oh, but anyways, with that, you can create a controlled not gate, which is, you know, if you don't know what a controlled not gate, that's the way it maps. Uh, do you get a controlled bit? If it's on, it does a not to the second one. If it's not, it does nothing. And, uh, you can make every other type of gate that you need out of that. Yes, uh, any questions on that? Anyone? All right, no, great, that's perfect. Okay, so, what's all this? What's up? Where? Who? Yeah, go. Shout loud, please. Uh, this question was, are they teleporting with entanglement? No, the way those teleportation things work is they transfer the information using keywords and they still gotta transfer, uh, entangled photons, which, you know, it can only go speed a lot or whatever. And, uh, it's, like, unmapping of the information and it rewrites it. Right. Right. Those. What? Oh, he said, what? Why? Shut up. All right. So, any other questions on that? What? Go. Had, what person? Uh, there are a couple ways to, man, I'm not, okay, well, there's a couple ways to do it. One way is you just read them with the bell state analyzer and they entangle with each other. Bell state analyzer? Something bell made up? Does anyone have any? What's that? No, it's not at all. Oh, he's got information about bell state analyzers. Oh, entanglement? Right, whatever. Same deal. Right. Right. No, you're right. But it doesn't matter for what I'm saying. Like, does anyone have any questions that aren't like physically related? Like, this is an algorithm speech. Okay. All right, great. So, what this is used for now, getting to algorithms, which I kind of lost over, is remember I talked about RSA and how factoring really big numbers, does everyone understand that factoring the product of two really large prime numbers is a hard thing to do? Yeah. Okay, just want to make sure. All right, Peter Schor, he made this fun little algorithm that will break RSA in two steps. RAR. Basically the way it works is you... Oh, what ended I use? I had a demo example with all the math done out already, but I don't have a calculator on me. Hold on a second. Keep on entertaining. I just put someone's calculator in my mouth. All right, so anyways, okay, let's say our N is 15, right? That's three times five. They're both prime. It's really easy to do. Simple for us, right? So, the first part of the algorithm is you choose an A, which is less than N. So, let's say A equals seven, all right? Then we create a function called f of x. Oh, I might have glossed over this also. With quantum computers, anything that you do with one qubit is like a massively parallel operation to everything else. So, basically you can... If you've got two qubits... Yeah, two qubits entangled, you can do four operations at the same time. It's two to the number of bits you have. So, anyways, you can... And a superposition can store that much data also. Two to the number of qubits you have entangled. So, two qubits entangled can store four lines or superpositions of information. So, what you do is first you load up everything, the superposition with all the numbers all the way down or whatever, right? And you apply this function to all of them, which will give you... Well, in case you need that, whatever. That's where the math works, all right? I did them ahead of time. And what you want to do is then after you do that, you've got this whole sequence in the superposition. So, what's called a quantum fast Fourier transform, which will find the period of repeated sequences here, which happens to be four, right? So, r equals four, which is the period. And there's actually an old member theory problem that's based on. And the fact that we just solved that in one step with fast Fourier transform is like extra diffusion sort of. What we can do then is take the greatest common divisor of n and a to the r minus two plus or minus one, which will give us, we put a four in there, 50 for the plus, 48 for the not, which gives us five and three. Which are the original theories, right? Yeah. And you can do that with really big numbers and it doesn't matter. You don't have qubits to support all that stuff. So, we've still got to make really big quantum computers for that to work, but, you know, when we do, you've got, you've got RSA broken. And so, does everyone see how that fucks with RSA? All right. Then, this other guy, Love Grover, he made himself an algorithm too. And he's just for searching. And, okay, basically, he made a search algorithm that says, let's say you want to search sample space n. Normally, you've got to search everything, so your average case is going to be n over two, right? You can do it in square root of n, which is still in the same, still in the same complexity class, but hey, it's faster, right? Like significantly faster. The way it works is sort of do it up here. Let's say you've got yourself a, well, all right, you've got a two-qubit machine, and those are your ends, or, you know, whatever you've got in your superstitions, and it's a search algorithm. So, you're searching for a specific item, and, right. So, let's say we're searching for, like, three, right? Two, whatever. Star is zero. So, the way it works is, it works with probability amplitudes. Like I said, with, like, it's really easy to find it, anything in a quantum computer, but if you try and read the data, it'll destroy everything that you found. So, it's like, the find's really easy to do, it's just getting the data back out, which is the hard part. Finds easy to do, you found it, piece of cake, whatever. But you still can't see it yet, so it uses what's called probability amplitudes. Like I said, right now, each one of these in EPR has one-fourth chance of becoming whatever, you know, one of those, one of deco years. So, I'm gonna zero, one, two, three. I'm gonna sort of label and make a little graph here. Zero, one, two is actually, oh, two, three. They all start out like that. Then you can do a, you can invert the phase of the found one, really easy, almost easy. Boom. So, we inverted that, like that. That's an operation you can do pretty simply. Then, what's that? Where? Yeah, sure. Like I said, I did these when I was fucked up, so leave me alone. So, what was I saying? Oh, right. So, this is the found one. You invert the phase, and then you do what's called an inversion around the average. So, one-fourth, one-fourth, negative one-fourth, one-fourth. Like I just swung out. Fuck, I'm wrong. These go all the way here. Because EPR is one-half per bit, whatever. So, you got one-half, one-half, one-half, one-half, and the average turns out to be one-fourth, which is what I completely missed. So, the average is one-fourth, right? So, you find the average, and then you flip around the average. So, like, how do I put this? Like, this guy's here, right? What's that? Yeah, yeah, exactly. I just want to make sure people can see this. All right. So, this one flips around to here. This one flips around to here. This one flips around to there. And this one flips around to there. And since we've only got a four or two-qubit machine, we only have to do this one square root of two, whatever, one step. And now, our found one has a hundred percent chance of becoming our found data when we read it, and it decoheres, and everything else has a zero percent chance. And, like, if we had more, like a bigger system here, we would have to do this approximately a square root of n times, those three steps, inverting around the average. But eventually, everything else would go to zero, and the one that you had would go to one, and you're good to go. So, that's fine and great, like, for searching a phone work, you might think, but, like, you've still got to put all that data into those, into the superposition, which is going to take n steps. So, it might, you know, n squared of n. What's the point of that, right? But what this actually can be used for is, again, since we have massive parallelism of a quantum computer, we load up all the states with all of the numbers, zero to two to the 56, and then we run a DS decrypt on all of them, and, you know, it's one step, so it takes, it's the same as one decryption operation, and you've got everything on, you've got every possible decryption, and then you do a search for the plaintext, and you filter it to the top, decrypt your state, and you've got the plaintext. So, yeah, well, basically, you can brute force anything in square root of n with this deli here. Yeah, any questions on that? No, this isn't that new. And Peter Schor's algorithm certainly speeds things up pretty quick. Oh, she's wondering if this is a new algorithm or not. Actually, recently, he revised it, so there's, it's faster now, I guess, or a little bit better. Did that answer your question? Good enough? So, it worked again. Well, yeah, it's the same, yeah. You've got that one step, and then it's the search. So, you know, it doesn't matter. Yeah. So, you're saying that that provides all of the, all of the sub-axes. Right. Well, it's not this operation. Like, quantum computers can do that just by string together controlled negates. But you're still, like, very, very, very, very nice, and you're still having to search through all of my mail to see how this really is helping to enforce a search on a plaintext. Right, it's still a brute force, but instead of a brute force of n, it's a brute force square root of n. What's the bigger number? 2 to the 56 or 2 to the 28? The thing is, it does all of its stuff in one step. Right. Oh, is that what you're asking? Yeah. No, okay, I see what you're saying. Exactly. No. When it does its stuff, when it's magic, right? When it does its stuff, it does it to every single thing at the same time. Every single item in the superposition at the exact same time. It's massively parallel. So, you can have it... Let's say it was something that normally takes, like, five minutes to do, right? And you're going to do it on a thousand things. It takes five minutes to do. Okay? If you're going to do it on a million things, it takes five minutes to do. It's the search that takes the time. Right. Yeah, it's coming up. Do you want me to go over there? I'll go over there. I'll go over there. I'll go over there now. Okay. Right. Well, quantum computers are very delicate babies, and you don't want to be storing anything on them, really. Like, they got a very delicate thing on them, really. They got them in crazy underground places and away from electromagnetic radiation. Like, little disturbances will completely destroy them. Like, that's the way they do this stuff. The way they send something to an EPR status, they just shoot it with a little bit of electromagnetic radiation, and anything outside will completely fuck it up. Right. It's 10-2. I'm going to go over this really quick. Do you want me to go over quantum encryption? Okay. Okay. This is a BB-84. It's made in 1984 by Charles Bennett of IBM and Kyle's professor of University of Montreal. And, all right, I'm going to... I'm almost fucked up. These are... This is Alice and this is Bob, right? And, so, Alice creates a random string of data first. Start sharing out ones or zeros. I'm here... Oh, damn. Okay, so Alice creates a random string of bits, right? And then she... All right. She's creating these in photons and photons can be polarized. And those are... These are the polarizations right here. That's the up and down polarization in the slashee polarization in this one and that one. And the ones can be one of those and the zeros will be one of those, right? So, she knows what the polarizations are, too. We'll just make these random also. But make them match up. All right. So, she knows the polarizations and she sends these out over, you know, a quantum communication channel, like a fiber optic or whatever. And, Bob receives them. And Bob, he's got these two filters. One looks like a plus and one looks like a multiplication symbol. And the plus lets through the vertical horizontal ones and the other one lets through the diagonal ones. So, he creates a bunch of random, like randomly picks these things, a bunch of filters. All right. And the ones that work out great, they work out great. The ones that don't, you get some random thing, like maybe a zero, I'll mark it with a little red thing. Maybe you get a one. Oh, who's calling me? Let's see if you get a zero there. Hold on a second. Okay. So, let me finish this up. Do you guys see what I'm doing here? This one is so long. All right. So, I marked the little ones with the little thing in the corner, the ones that are wrong, but Bob doesn't know that yet. So, then what Bob sends back is Bob sends back the sequence of filters that he used. He's called technically. And Alice uses these and compares them with her set of polarizations that she used. And then, she tells them which ones are right. So, he knows that this is good, this is good, or he tells them which ones are bad. How's that? So, they know the bad ones, right? And okay. So, then what they do is they use this sequence, these random bits, as their key. So, if someone's trying to eavesdrop, Alice creates all these bits with the random polarizations. If someone's trying to eavesdrop, first off, by reading the decoherence, we'll destroy the data. But even if somehow they manage to figure that out or whatever, they've still got to use some random filters or analyzers to read the polarizations. They're screwed. And then, Bob sends back the analyzers and it's really hard for Eve, or the eavesdropper to figure out what's going on. I kind of glossed over that, but trust me, it works out that way. And if you use a one-time pad, everyone know what a one-time pad is? Everyone know they're unbreakable? Right, it's totally random. Like, if it's a real one-time pad, it's totally unbreakable, right? Well, you can figure out how to do that and like, nothing gets more random than superpositions. Then, boom, one-time pad, great. Uh, yeah. Okay, so any other questions or do you want to hear more about a completely skipped over complexity theory? Uh, any questions? Someone there? Oh, yeah, the eavesdropper can get that, sure. You assume that he's always in the middle and can figure out everything, but even if she gets all the analyzers that were used, it doesn't matter because after the fact and she's already analyzed her stuff. So, she's got you see what I'm saying? Uh, like it's a one-time operation analyzing the things, so there's no way to even if you've got that information, it's too late. Uh, any other questions? I could understand three words you said. It was filter, results, and bad. Ha, ha, ha. You're going to arrest yourself. Right. But the important thing is you can't use them again because it's already been read. Okay. Any other questions? Are you there? Uh, well, last I heard they had a seven-cubit machine somewhere. I don't know. I was someplace in California and I felt mine sometimes. I don't know. I don't know how it works. All right. What's that? I got five minutes. Any other questions? Anyone? Someone there? Who is in the hand? No. Oh. Well, you guys can both talk at the same time. Steel cage match? Okay. What's up? Yeah. Yeah. Does it work for what? No. No. One-way hashes? If you do a one-way hash, there's no way you're getting your stuff back, besides brute forcing it. No. It's why it's a one-way hash. It's more than a clever name. Well, RSA can because it's based on factoring the product with two prime numbers. What's that? Yeah, that has to do with quadratic field. What's up? Yeah. It doesn't matter because anything can be reinforced with love grovers. Just searching for the plain text. Yeah. That's not as fast. No, but still, it's... What's up? Right. Yeah, I know. It's the same complexity, but still, it's a lot faster. What's up? Yeah. It's still quantum computing. You're still using a quantum computer. All right. Anyone else want to say anything? All right, great.