Okay, good morning, everyone. This is Melissa with the Stock Swoosh Show Live. I'm here in the room and I'm going to go over the market. So anyone can ask me questions, even though I'm doing this recording here, I'm talking about the market. I'm going to say what I was thinking this morning when I saw this and then I will answer any questions for anyone. Actually, when I got up this morning and saw this, I was ecstatic, elated. I mean, almost to the point that it was amazing. Actually, let me talk about the cues. Let me talk about the cues first because this is really what the first thing I looked at in the morning when I got up, whatever time it was, I mean, it was early. And I had seen the market close strong yesterday in the cues, got up almost to one ten, one to nine fifty-five, pretty much right at a day, but then in the morning, guess what? We gapped up over one ten over the next number in the pre-market. This is the pre-market of the cute, cute cues, okay? So we gapped up this morning. You can see it right here. Now, is this an ideal gap to buy immediately, aggressively in the sky? Not necessarily, but it proves the strength in the market. And that's when I saw that made me feel ecstatic this morning when I woke up because I realized then that it just gave me the confirmation that in fact we are higher and we'll make a new high and we will do that before the end of the calendar month, which I said that we would. Now, whether we close today with a red body or a doji or a green body, it's neither here nor there. We are just continuing higher, okay? So let's look at the whole big chart here actually. Let me go back. Here's where we are in the biggest game of things. Okay. And this is what everyone is seeing here, the extension here of the market running all the way, well, pretty much since 2011. So pretty much since 2011 and some people are even looking back since 2009, but this doesn't count for anything for me. But really here where we started holding around 2011, it's been about three, three-and-a-half years that the market has made a consistent bullish continuation move higher in an uptrend. And that people think or feel is extended. Look at how this is rallying. Anyways, this is what people are saying is extended, but it's not. So I'm telling you that this is not extended. If it gets up to 120, will it be considered extended? By me? No. 125 and makes an all-time brand new high, which we really haven't done yet here in the QQQs, although we have in the spy. Will I consider the market extended then? No, I still won't. Now I have been talking about this recently since I saw it, which was just within the last 30 to 45 days, that I realized that not only will the rally continue in the bullish trend of the market through 2015, which I knew and saw in the gap from October, but that this could continue for quite a long time now. Like I don't know how long exactly, but it's definitely going to continue into 2016. And it could continue for years because it's so unexpected what is going to happen here that people are not going to be prepared for it. And then they're going to realize that they actually should have bought in here, right here, right now, like in the last month, or even here now, that this is still okay to be long the market. Your stop will vary for it in here now if you haven't taken it, but it's still a great long because there's a new buying that's coming in the market. And that is what is lifting it higher. And as we've discussed about how institutions present themselves in the market in money, they don't take a position and exit immediately. So there's a new buying that's happening here. And therefore there will be no exit at 120. So you understand what I'm saying? And for new buying to be coming in at this placement here, that everyone is seen as extended is how I'm calling what the market's going to do to be phenomenal for the rally that will flow through it. Because this is actually a place that I am seen as being bought with new positions of consequence that will not be lifted out soon. And yet this is a place that many, many people professionals are saying that the market will either rally will sue me over or is done and extend it. Like even the people that are calling the market higher think 120, 125. But I'm saying 150 in this QQQ, so that was the number I gave for that. 130, 132, 135, 150. Let me write that down before I forget them. 145. Anyways, getting back to what I was saying, I was ecstatic when I saw this this morning because I knew this would happen. And even though this isn't a great grab to buy necessarily on the live day, although if you bought it and have to stop where I told you to put it, you're in it and it's holding and you're in it. And it's not going to break now. And if this doesn't break the low end here by 12 o'clock noon, it won't today. Which is pretty phenomenal. Because this is not a gap that I would have necessarily aggressively bought here. Like if this was a stop, would I have been in love with this today? The answer is no. No, I wouldn't have. But it's still showing and giving a confirmation in the bullishness of the market. What I find really amazing, and again, I looked at this again this morning when I was doing my stuff really, really, really early, was the fact that I saw it here. Like everything that this is happening right now, I saw on this day. It was a Saturday that I looked at this. It was November 1st. But it was Friday on October 31st that this gap occurred in the market. And then I sat down on Saturday morning and I saw this guy here. And I realized and I called the whole following year of 2015 and I saw on my, I just saw it. I just saw what it would do and it's doing it now. But I mean, the fact that on this day that I could see that this would happen here and that I can see past this to even tell you the other stuff. But from this one little guy, this is a red bar, by the way. It actually didn't even go anywhere in the day. It has a tally thing. The actual length of the body is like less than 70 cents. It's red. It didn't go anywhere in the day. But it's all because of the gap. So I read in this one little person here of no significance that anyone could even see what this would, that this would happen. This is how I see all this for the whole year. From that one little guy there. Now there's other things too. But this is the main, this, it was the day that I saw this or the day after because it was a Saturday. I sat down and just, I just saw it and I said, oh my lanta. And I guess the most powerful thing that I want to describe to you here today in the video and just for the room is that support and resistance are areas number one. Targets are areas number two. But there's nothing more powerful than the gap. There is just nothing more powerful than gaps that I could see and predict 12 months out, even five months out now, one, two, three, four, five, six months out, that I could see six months out, that I could see that far out and ahead of time. The great thing about gaps is you could play them on the live day, which is in the live moment for the cash. But it could tell you long time out what something's going to do. And that to me is genius. I mean, that's to me is phenomenal. And it's all in the power of the gap. But it's really the reading system that I teach in the class to know what a good gap is. Because there's the market gaps almost every day. And 99% of these gaps are worthless, up, up ones and down ones in here. But the fact that I saw this one, which doesn't look like anything of any consequence, to know, to see this today from this and even beyond, which I realized this morning when I saw it myself and I realized that I could see this from this thing here. It just came to the confirmation again of the power of the gap. I think this is where the passion for me to teach really takes hold and grabs people. And why many of you are here is because I truly, truly believe in what I say. Otherwise I wouldn't trade or miss my own money. Yes, I'm making money trading and all of that is great. But the passion that drives me to even do it or even teach is not just to make money. It's the idea that I know that this is so phenomenal, that it's almost like I feel like you need to know it. Like I feel like people need to know how phenomenal this is. Now, is everyone going to believe me? Absolutely not. And that's why there will always be a market. There will always be a market because there will always be people that just don't get it. And there will always be more people that don't get it that do. And this goes above and beyond people's psychological issues and problems. In other words, there will be people that get what I say, but can't pull it together because they have serious issues about money. And therefore they can not get their head on straight to trade right. Now, can they be overcome? Sure. Will everyone overcome them? No, they just won't be able to do it because they won't want to do it. They will not want to change. And you have to change if you have issues about money and risk and loss and fear if you want to be successful in the market, even after you learn a strategy that works. But I'm telling you of all the people on the planet, even if I teach all the people that don't have psychological issues, some will still just not get it. We'll insist that the market is going to break. We'll insist that the market is extended. We'll swear and short the market at 120, 125. Or even after it makes a new high, they'll short the market and say it's extended. People did it back in here and it is already done. And I'm not talking about baby people. I'm talking about people that actually have real money have shorted this market. Why did you think we had some of these red bars in here? I mean, this didn't happen just by happenstance. This was real selling that occurred in here, shorting too. So there are people that have traded longer than I'm alive that will not conceptually grasp or understand or even believe what I know, even if I taught them. So that's what makes me passionate about telling you this and pointing it out and saying it every day and trying to teach you to reinforce it with you. Does it make a difference to me in the end, whether you believe me or not, or even trade or take my class or make money with me or even do exactly what I tell you to do? In the end, not really because it's on you whether you're profitable or not. And my life will go on. I'll continue to be successful and make money in the market and do what I know forever. But I actually think that I'm helping you and people who want to get it when I tell you these things. And I know that it will be meaningful for the people that get it in a way that I will impact your life if you listen to me financially and emotionally and spiritually and physically, because I will have a major impact on your life. Okay. And in fact, Tom is a great example of this. Tom, are you listening? Are you here? Yeah, you are here. Are you listening now? Tom, are you listening? I'm going to say something that I want you to hear. Surfdog, why are you even looking to short anything else today? I will look at it, but Tom, are you listening to me or ignoring me? Surfdog wants me to read another guy. It's 10.30 in the morning. What I was going to say was that, look at this here. Jen or Paul actually went long this. Did anyone else go long this before I finished my thought here? Aye, aye, aye, aye, aye, aye, aye, aye, aye, aye, aye. As I'm sitting here talking, as I'm sitting here talking right now, look at the market. Jaguar pot, are you still in this? Did anyone else go long the market?  I mean, this didn't have to hold here today at all and still would have been great, but it is. That's it. This is the low of the day. And if you took it and told you, I told you to put the stop at 10990, you're in it. Anyway, Tom is a great example for this because I've impacted his life and his trading. I've impacted his life and his trading. And he has been trading for over 20 years. But I have had an impact on his life emotionally as a friend, as a person, and I've impacted his trading by things that I have said to him. Even though he's a very independent thinker and he doesn't listen to everything I say and we disagree on some things catastrophically, and our personalities are complete and other opposites to the point of ridiculousness.  So it's a great example, but we've kept in touch. So even if I've had an impact on your life now and you're seeing the fruition of it and you're making money and you're here with me and the things that I'm saying to you are grasping and taking hold right now, go with it.  The impact may have an effect at some point where you decide to do the class and you want to actually learn it. And then it comes back around for you. But I don't think that anyone that comes in contact with me in any way, shape, or form will ever forget me. And it's not just really my personality, which is very, very strong. It is the fact that I am saying things that are very different about how to treat and meaningful. And sometimes it takes longer than other people to really get that. But there will always be a market because there will always be more people that just don't conceptually buy into what I teach. Because it is so unusual and so unique that to many people it just simply doesn't make any sense. Because to many people it just makes no sense how that I could get up in the morning on November 1st and see this red bar with no momentum and a tiny tail. And to see that, that I could see this and beyond from that one thing. But I did. And it's because of the power of the gap. And it's not just any gap. It's golden gaps and gaps that rate 20 points or more. So there were some people that just won't get that. But they will put all kinds of indicators on their charts. They will buy a million systems and platforms and they will believe in moving averages and they will look at volume and they will look at Fibonacci's and they will buy into lots of things that seem to make sense. And then on paper seem to make sense. And that seemed to make sense. But I'm telling you what I do actually makes sense. You may not get that until after you take the class. After you take the class you realize that it does make sense. But obviously you have to pay for the class before you take it. So you don't really know it makes sense until you learn it. Okay.  But either way people hear me talk even if they listen to me, conceptually some people still won't get it and therefore won't never take the class to learn it to really know that it works. But conceptually people just won't ever, it will never be swayed to the point. I guess this is what I'm trying to say. That everyone in the world will get what I do. Because the market is set up for the people that are special to make a lot of money. And it is a special, special thing to see this. So I guess I'm trying to teach you that I want you to be special. I want you to be with me. I want you to be special. I want you to listen to what I say. I want you to get it. And until you do just do exactly what I say like today. But I think you people are special that have found me that have paid for the class because you took a chance because you didn't know what you were getting into. But everybody that takes it realizes after the fact the level of information. And that's why I have a successful business. And I also came up with a new word. Yeah, that's the new word here. I started using that with someone else this week. It's called VSP. This is what it is. It's VSP. It's more than VIP. It's called a very special person. You people are very special persons because you're here with me, the people that have taken the class that are with me. You're very special.  I'm letting you into my world. I don't have to let you into my world.  I'm letting you into my world here. When I fail, it's right in your face.  And you hear the frustration of my voice that we take a trade doesn't work. And then you hear the days when we make money and we succeed.  One in Tuesday, Wednesday, Thursday, Friday. So you are very special people to be here with me. And I'd rather be a very special person to someone than a VIP, which is a very important person. And how this came up this week that I just, I made it up when I was talking to someone this week. I've been meeting some extremely, extremely important people. But actually, some of them are very special too. And that's where I came up with a term when I realized that one of the people I met was very special. And then I made up the name BSP, but the person's a VIP too. And then I realized that I am probably going to meet a lot of very important people with what I'm doing right now, which I'll tell you more later. But they will not all be very special to me. So you would rather be someone that's very special to me than very important. Because there's lots of people out there that are very important.  I think that's all I have to say today. Does anyone have any other questions about anything else? Surfdog, I don't feel like I'm reading anything else today. I'm exhausted. It's 10.30 and I have to put my game face on in two hours in a meeting. And I have to look fabulous doing it. Does anyone have any questions about the market here? Or anything else before we break for today? You're all BSPs. Everyone that's here with me every day. I'm going to start using that term more. It is meaningful. Target for the QQQs for today. One 10.50, one 10.75, one 10.60, one 11 is a dream target today. I don't think the market gets over one 11 today. That is the dream target today for the market. I don't think the market gets over one 11 today. I don't think it does. I really don't think it does. But you know what? I just saw here, we could gap up Monday morning. I just saw that right now this second I just, as I'm talking and you're asking me the targets. I wouldn't be surprised. And I wouldn't put it out of the realm of possibility. And I have no idea what the future is due over the weekend. But I'm telling you, the market could gap up again Monday morning. We can actually do this. We could just gap up Monday a little bit again. And then hold it here. We could just go poot, poot, poot, poot. We could gap up again on Monday morning. That's crazy. But I'm saying it's not out of the realm of possibility. I don't think we get over one 11 today. We could gap up Monday morning. I'm just shorting the wind everything the next week. We're going to get tons and tons and tons of great gaps. Earning season is upon us. I picked the perfect one yesterday. Today we did two things. I did, you just got it. You just have to do exactly what I'm doing. You're welcome. Okay, good. All right. Have a great day, everyone. Have a great day. Have a fabulous day. Good job today. If you did everything. If you have any questions, email me. If you want to sign up for the gap class, email me. Deadlines this afternoon. I guess that's it. All right. Have a good weekend, everyone. You're welcome. Thank you, frequent flyer.


Hello. I'm going to be talking about non-interactive zero-knowledge arguments for QMA with pre-processing. I'm Tina Zhang and this was joint work with Andrea Colodangelo and Tomar Wittig. So I want to motivate a little bit the problem that we're going to try and study and to do that I have to remind everyone about interactive proof systems and what they're used for. So let's suppose that we have a graph X and let's suppose that today our purpose in life is to decide whether X is three-colourable or not three-colourable. And by three-colourable of course we mean that a graph can be coloured using only three colours such that each edge connects to vertices of different colours. So of course three-colouring is a problem that's complete for MP. So if we can decide this problem we can decide any problem in MP. So the setup we're going to use to do this is that we have a weak probabilistic polynomial time verifier and an unbounded but untrusted prover. We're going to try and design a protocol that this weak verifier can use to interact with the untrusted prover and at the end of the interaction the verifier should know whether X is three-colourable or not. So formally we want two protocols, two properties from this protocol. Soundness and zero knowledge. The first one is soundness which means that the prover even though it's unbounded can't convince the verifier with high probability that X is three-colourable if it's not. Well, this is pretty easy to achieve. There's a trivial protocol that achieves it, which is which is simply that the prover sends the colouring. So in this case the verifier would receive the colouring and check that each edge joins two vertices of different colours. But okay, we're doing cryptography and so maybe we don't trust the verifier either. So maybe this three colouring encodes some sort of state secret and we don't want the verifier to know the colouring and we only wanted to know whether X is three-colourable or not. So that brings us to the second property which is zero knowledge and zero knowledge just means that in the protocol in which the verifier makes use of this untrusted prover to decide whether X is three-colourable or not, the verifier should not learn anything except for the fact that X is three-colourable. So I'm going to quickly go through the sort of quintessential protocol for deciding NP problems in a zero knowledge way, which is the gold-dry Nikali Wictusen protocol for three-colouring. So firstly, we have to label all the vertices and all the edges of X which have done here. The vertices have numbers and the edges have letters. So the first message in the protocol comes from the prover and the first thing that the prover does is permute the colours of the three-colouring randomly. So here we had, you know, red here, white here and blue here. Here it's just a random permutation of those three colours. Then the prover sends a commitment to that colouring. We should think of a commitment as a safe. So the prover can put anything at once in the safe and then it locks the safe and it sends it to the verifier and the prover can't change its mind about what's in the safe after it has sent it to the verifier. But the verifier also can't open the safe unless the prover gives it a key. So what's in the safe? Well, I drew only one safe, but you actually should imagine that there's one safe for every vertex of the graph X. So in this case, there should be five saves. So for each vertex, the prover writes down the colour of that vertex. So for example in the first safe, the prover will put red because the first vertex is red. The second save, the prover will put blue and so on. So the prover sends this collection of safes to the verifier and that's the first step in the GMW protocol for three-colouring. Okay, and the second step is that the verifier sends a label of an edge which constitutes a challenge to the prover. So this is edge F over here. Then the prover sends back the keys to the safes for the vertices that are connected to that edge. So in this case, the third and the fourth safes because vertices three and four are connected to edge F. The verifier can then open those safes and check that the two colours that the prover put inside are different. So intuitively we can see that this protocol satisfies soundness because if X is not three-colourable, then one of the edges at least will join two vertices of the same colour. So then the verifier will look at that edge with some probability. So if we repeat the protocol many times and X is not three-colourable, then the prover will eventually get caught out. But the protocol also satisfies their knowledge chiefly because of the random permutations of colours that the prover chooses. So you might imagine that the verifier could try to deviate from the protocol by running it many times and each time trying to learn the colours attached to a different edge in hopes of reconstructing the entire colouring. However, this won't work because every time the permutation of colours that the prover chooses will be different. So the verifier will just see each time that the two colours attached to any given edge are different. So hopefully this example gives some intuition for why this protocol is their knowledge. So now I want to talk a little bit about non-interactive zero-knowledge proof systems, which are really the focus of the paper. So in the previous protocol, there was a kind of back-and-forth between the verifier and the prover. The prover had to send a commitment and then the verifier had to send a challenge and then the prover had to respond. So we might sometimes wish because for some reason communication is expensive, we might wish that the prover can just send a single message to the verifier. Now, if we saw that if we don't require zero-knowledge, then this is fine for MP problems since the prover can just send, in this case, the colouring. But that is not zero-knowledge. So the question is, can we do that in a zero-knowledge fashion? And the answer is no. It's impossible for languages outside of BPP. So for three colourings, since that's a problem that's complete for MP, it's impossible to have a protocol to decide three colouring that would only use one message from prover to verifier. So this is why people consider extended models and one popular extend model is the CRS model, which stands for Common Refit String. And it just means that in addition to the usual setup where the instance X is known to both prover and verifier and so on, there's a trusted third party which samples this string from a specified distribution and makes it publicly available. So this is not achievable in the standard model because we can't trust the verifier to generate the string and we can't trust the prover to do it either. But if we assume that this string can be obtained somehow and maybe that's not such an unreasonable assumption in the real world, then we can do it. So we can indeed have protocol where with the CRS, the prover only sends a single message to the verifier. So okay, then there's a question of what happens in the quantum setting. And the first thing we want to look at in the quantum setting is post-quantum security, which is where the verifier is now allowed to be a potentially cheating quantum device. So the prover was unbounded anyway, but if the verifier is allowed to be quantum, can we still make the protocol's error knowledge? And the answer is yes, and in particular it's known to be possible in the CRS model under LWE so learning with errors, which was proven in 2019. But okay, post-quantum security might not be the only thing that we're interested in in a world where there are quantum computers. Maybe now that there are quantum computers, we're not only interested in mp problems, but also problems in QMA, which is the quantum analog of mp in the sense that it's the class of problems that can be checked efficiently by a quantum computer with access to a quantum witness. So in this case x, which was a graph before because three coloring is complete for mp, would be replaced with some instance of a QMA complete problem, such as the local Hamiltonian problem, which I'll talk more about later. And in this in this case, in this situation, we might also want to allow the message that the prover sends to the verifier to be quantum. But we want to achieve the same thing we did in the classical setting, which is that the prover sends only a single message to the verifier. So this problem is perhaps still unsolved. We in this paper don't achieve something quite, there's a deal, but we achieve something that's almost what we want. So instead of exactly one message, we have two messages. One from verify to prover, which contains a quantum part and classical part, and one from prover to verify, which is actually entirely classical. So the thing that allows us still to claim that our protocol is non-interactive is that the first message is independent of x. So in a sense, it can be thought of like the CRS, in that it's part of an instance independent pre-processing phase, which can, if need be, be completed ages in advance of the actual protocol before the instance is even decided. So we just need the verify to send this message at some point to the prover so that it contrasts that it was sent properly, and also for the CRS to be generated at some point. Then after the pre-processing is complete, the prover only needs to send a single classical message to the verifier. Okay, so I want to go over how we achieve this. And to do that, I need to explain a bit an interactive zero-knowledge proof system for QMA, which inspires our protocol. So let me talk a little bit more about the instance here. So in the NP case, we had a graph because the coloring was complete for NP. So in this case, we have a local Hamiltonian, so a measurement operator. That's the sum of Clifford terms, these terms here, which are called CI. And the problem is to decide whether the Hamiltonian H has the smallest eigenvalue that is smaller than sum number A or greater than sum number B. So you'll promise that it's one of these two, it can't be in between. And this problem was shown to be complete for QMA by Broadbent Z Song and Watrous, these guys, in the same paper in which they propose this protocol. So I've drawn a scale here, that's because the Hamiltonian represents a measurement, it's a measurement operator. So we can make an analogy where the question is, is there an object that I can place on this scale which will make it read a small value? Now, obviously, this is a trivial question with a normal scale, but we can imagine that maybe the scale is weird, it doesn't respond in the way we think it should, and so the question is, can we make it read a low value? Now, because the Hamiltonian H is a sum of terms, a particular state, so a particular object placed on the scale in the analogy has a small eigenvalue with respect to the Hamiltonian H. If and only if it has a small eigenvalue with respect to each of the CIs that make up the sum. And each of these CIs is a Clifford and is also a measurement operator. So this gives us a convenient way to make an analogy with the classical setting. So in three colouring, the verifier in the second step of the protocol chose a random edge from the graph that was the proper instance, and that represented its challenge to the prover. So here, the verifier can choose a random term from this Hamiltonian H and measure that, and that's kind of analogous to the verifier in the previous setting choosing a random edge. So now there's a question, why don't we just measure the whole Hamiltonian and that will become answered shortly. So let me describe the first step of the BJSW protocol for QMA. So the first thing the prover does is to choose an encryption key, K. Now this encryption scheme acts on quantum states, we want to imagine. It takes quantum states as input, encrypts them, and then outputs quantum states. And so it sends, it puts K in this safe and sends commitment to K to the verifier. Sort of like how the prover committed in the beginning of the GMW protocol. And it also sends, so recall that the prover has, it's supposed to know this witness. And in this case, the witness is a state because QMA is a class of problems that can be checked by a quantum computer and efficient quantum computer using a quantum witness. So in this case, the quantum witness is a quantum state. And this quantum state allows V to check if it had access to that state that acts as indeed a yes instance. And remember that X being a yes instance in this case means that there exists some object we can place on the scale such that the scale reads a low value. So this state is just some state we can measure with respect to this Hamiltonian which will have a low eigenvalue with respect to that Hamiltonian. So the prover is going to send an encryption under this key K that it just committed to of this witness state and send that to the verifier. And intuitively why do we want to encrypt this state? Well, it's so that V when it receives this message, this quantum message, it can't learn anything about the state by looking at the encryption of the state. But this encryption has one more special property which is that it allows homomorphic applications of Clifford gates and so homomorphic measurements of Clifford operators through the encryption. And that why this is important will become clear in the next slide. Okay, so this is the first step of the interactive BJSW protocol for deciding problems in QMA and in zero knowledge fashion. So the second step is that the verifier is going to choose a challenge rather like in the second step of the GMW protocol. So the verifier chooses an index J uniformly at random and it takes the term in the sum here that corresponds to that J. So basically it chooses a random term of the Hamiltonian H and as we said before it will measure that term of the Hamiltonian and now, but it will measure that term of the Hamiltonian on the encrypted witness state that I just received from the prover and not the actual witness state because we don't want it to have access to that. So now it becomes clear why we need this encryption scheme to have the homomorphic property with respect to Clifford gates and that's because we need the verifier to be able to homomorphically measure this thing through the encryption. And okay, it does that and what happens when it does that, it gets an encryption, you know, it gets classical outcome and the classical outcome exactly represents an encryption under the key K of the outcome it would have gotten if it had measured W directly under CJ. Okay, and I will just make one remark here which is that this term CJ does not depend on K. This should be obvious because, you know, the verifier does not have access to K but it will become important later that we don't need to know the key in order to perform this homomorphic measurement. Okay, and so now, you know, in the original GMW protocol for NP what happens next is that the prover reveals it opens its commitment, it opens the safe, sends the verifier the key to the safe so that the verifier can check essentially that the prover was not cheating. Now here maybe you'd imagine that an analogy would be that the prover would open the safe, the commitment to the key that it sent at the beginning and allow the verifier to use the key K to check, to decrypt this encryption and check that Z in fact corresponds to, you know, a low reading of the scale. But this might not be a zero knowledge or at least it's hard to argue that it is zero knowledge but there is something else the prover can do and that is that it can use an NP zero knowledge proof system to prove the following statement. There exists a key consistent with the commitment that was sent in step one so, you know, the commitment to key here such that the outcome that the verifier got in this step is an encryption under K of an accepting outcome. So this is essentially saying, you know, verifier if you had the key K, you would accept at the stage and why is this an NP statement? Well, it's an NP statement because it can be efficiently checked with a witness and the witness is simply the key K. So if the verifier had the key K, it could check. Now we don't want to give the verifier the key K so we're just going to prove to it in a zero knowledge fashion using a zero knowledge proof or NP statements that in fact basically the prover's behavior has been honest. So, okay, we want to make the BGSW protocol non-interactive. The first thing we can do, the obvious thing is to replace the zero knowledge proof that the prover sends at the end of the BGSW protocol with a non-interactive zero knowledge proof. But the real obstacle to compressing the three steps of the BGSW protocol into one is that the prover's proof in step three, this one, depends on the verifier's challenge of measurement outcome from step two, depends on these, which in turn depend on the instant-dependent witness state that the prover holds. So we can't have the prover do step two, that would clearly violate soundness, but we also don't have enough messages for the verifier to do step two. So our first main idea is to get around this using quantum teleportation. So notice that instead of directly sending the verifier to the encrypted witness in step one, the step here, the prover could equally have used quantum teleportation to teleport the witness to the verifier, provided that they share APRs. So this would generate a string D, representing the one-time pad that gets applied to the teleported witness state after the teleportation. And the prover would need to send this to the verifier as well so the verifier could undo the one-time pad and carry out the rest of the protocol. So far we've just complicated the protocol without buying ourselves anything. But now notice that the prover's teleportation measurement that teleports the witness state to the verifier over here and the verifier's measurement of CJ on the teleported witness state commute. If we ignore for now the issue of the one-time pad string D that the prover has to send to the verifier. And this is because, you know, this and this are both just measurements on different halves of their shared APRs. So we could switch the order of these actions without affecting the protocol. Okay, so here's a modified protocol. Firstly, we assume that the verifier prepares APRs for the teleportation and sends the prover its halves. It turns out this is okay for their knowledge. And the verifier then chooses its challenge as before and measures that Clifford operator on its halves of the APR pairs as if they already contained the teleported witness state. Now note that CJ doesn't depend on K so it's fine the encryption key K so it's fine that K hasn't even been chosen yet. The verifier gets, you know, some measurement outcome M which it sends to the prover and then the prover creates the encrypted witness state and teleports this to the verifier. Now this results, as we said, in a one-time pad string D and if you think for a second you'll see that D XOR with M will end up being the encryption of Z the encryption of Z under K where NKZ is just the thing that the verifier would have gotten in the BGSW protocol. So for the final step the prover sends the commitment to K that in the BGSW protocol it would have sent in the first step. It sends D the one-time pad string and it also sends an NIZK proof for an NP statement. Now this NP statement is a little bit different. Now it will say something like verify if you had K then you could XOR D to the measurement outcome that you got in this step and now what is step one? M, you could XOR D to M and then decrypt the encryption remember that D XOR M is equal to NK of Z you could decrypt the encryption to get an accepting outcome, Z. So are we done now? That's not quite. There are a few holes in this construction. The verifier can't measure CJ yet in this step because this step is meant to be instance independent and CJ is part of the instance X. So I won't go into details of how we get around that but it can be done. Secondly, the verifier can't just send CJ and M to the prover before the prover has sent its witness date. Otherwise the prover would know the verifier's challenge ahead of time which is like knowing the edge to be checked ahead of time in the GMW protocol which obviously violates soundness. And thirdly, the prover gets to report D. So maybe if it was clever it could misreport it and make the measurement outcome, the verifier's measurement outcome M look like an accepting one even if it wasn't because after all D controls D XOR M. So to address these problems we add one more ingredient we use homomorphic encryption. The idea here is pretty simple though it's a little delicate to implement. So basically we have the verifier homomorphically encrypt CJ and M. So notice after we do this the prover no longer knows the verifier's challenge because it's encrypted so it can't get away with teleporting a state that's not a witness. And it also wouldn't know what D to report here to mislead the verifier and to thinking that M was accepting and it wasn't because M is now encrypted. However, if it behaves honestly it can still compute its NIZK proof at the end by homomorphically encrypting K, this K its own encryption key. Under the verifier's public key for HE the homomorphic encryption scheme and computing this whole MP proof homomorphically and then the verifier can decrypt the proof that the MP proof is valid. So I've basically just stepped through the soundness argument for our protocol. Note that our protocol is an argument, not a proof meaning that it's only sound against computationally efficient provas and that's due to the homomorphic encryption. So I'm basically out of time so I won't go through the zero-knowledge proof but if you're interested you can check out the paper there are a few subtleties to be worked out there as well. We also define in this paper jointly with Anne Broadbent and Alex Grillo who published independently the notion of a proof of quantum knowledge in analogy with the classical idea of a proof of knowledge. And we show that this protocol I've been describing is also an argument of quantum knowledge. So once again, feel free to check out the paper if you're interested and thanks for listening.


sold for $3,399 free shipping, less than 12 hours after listing. I found these at an estate sale for $15 and sold them for $1,225. $15 into $1,225. I mean that's not a Bolo, right? Hey, Bolo buddies, thanks for watching. Amazing, right? All right, let's get started. Hey, Bolo buddies, thanks for watching. All right, we are gonna talk about big money Bolo's items that you can pick up cheap and sell for a profit. Do you know that people do this full-time? If you don't, it is definitely possible. I am a full-time reseller. This is what I do. I buy stuff cheap and sell it online, but in this video, I am gonna share with you sold items from other resellers from my Bolo buddies Facebook group, which looks like this. If you're not in it, definitely go join. It is in my link tree down below. You can click on that and it's gonna show you all of my links to include my Facebook groups, Instagram, all of that stuff. But in this video, I'm gonna tell you where they got it, what they paid for it, and what it sold for. And this first item is a Build-A-Bear.  Well, let me tell you, some of them sell for big money. I have a video that looks like this and I talk about Build-A-Bear. One thing that I learned when I was doing this video is that a lot of times Build-A-Bear sell for more on Mercari.  I have a link down below. If you use that link to join, you're gonna get $10 to shop. You're gonna get another $20 to shop when you sell $100 worth of stuff. But this video right here, I mean, I was like, I couldn't believe it. I just could not believe it. So I know that things that are saturated on eBay do better on other platforms from time to time. But Build-A-Bear is definitely one of them. This one is a Powerpuff Girls Blossom Plush Build-A-Bear that sold for $90. She says, the buyer told me that she had Build-A-Bear Powerpuff Girls sold for 90. I paid only 90 cents. The buyer told me that she already has the plush and bought it to just have the dress. Wow. She bought the doll for the dress. She paid $90 basically for the dress is what I'm hearing. Yesterday, somebody contacted me asking for the buyer's contact because he would like to buy the dress. So if you see the dress somewhere, it is a bolo. Huh. So that's funny. The person buying it only wanted the dress and then somebody reached out to her asking for the buyer's information, which I would never give out. If personally me, I would not, I would not do that. And that person wanted the dress. So the dress is a bolo. I wish I had a close-up of the dress. It looks like it's pink and black there. I pick books up regularly at the bins for 25 cents a piece. I always keep my eye out for Vintage Sweet Valley High. Chapter books. This was a lot of 11 that sold for $55 full asking price plus shipping. Fun and nostalgic bolo. This is what they look like right here. Sweet Valley High bought for $3.95 at a thrift store and sold it for $40 plus shipping. I've had it for about two months, but puppets sell well for me. They have to be in great condition though for me to buy them. I have sold puppets that are not in great condition. So I just say puppets do really well. They range from bread and butter to big money, but I usually pick up about every puppet I see as long as it is a good price. And I just did a video on puppets. So check that out. I'll link it down below. I found this at the Goodwill, paid a dollar, great bolo. It is a Gory Cats Paper Dolls by Edward Gory Trumbador, Trumbador Press. First uncut, $41.40. And this is what it looks like. Paper dolls definitely can be a bolo. I found these at an estate sale for $15 and sold them for $1,225. $15 into $1,225. I mean, that's not a bolo, right? Oh my goodness. They're two inch chrysloid bacillite, bacillite. Oh my goodness, bacillite. Baggam and checkers. I put them on an international auction and minutes I was getting so many offers I actually had to go write in the description that I was not taking offers before people stopped. The offers were around $500. Glad I held out for the bidding more. So, bacillite, definitely, definitely can be a bolo. Jewelry comes in bacillite, but also backgammon, checkers, they can be bacillite. Now, are they common? I would say no. I have found a, what was that game called? I sold a game. I cannot think of what it was called right now. You guys help me out. They're the rectangle tiles. Oh my goodness. It's one of my best bolos ever and I cannot think of what the game was called. But anyway, that game also has them and they're incredible. But if you want to learn how to test if something is bacillite, I do have a video. Type in bolo buddies bacillite into the YouTube search and that will pull up. You can use something called semi-chrome. I think that's how you say it. It's really cheap. It comes in a bottle. It lasts forever. Okay, it doesn't last forever, but mine does because I don't use it very much. And it's a great way to test and it's really easy. So, check out that video. I love this next one. I found these vintage Playtex Nurser Baby Bottles. My mom used these for my brother. They were 99 cents. I picked up all they had. My total was $9. I looked up comps, saw they were selling high. I put them on eBay for 160 plus shipping and they sold in about a month and they sold for full asking price. This is what they look like. How awesome is that? Hi, Courtney. I watch your YouTube channel faithfully and I wanted to post a first time bolo. I found this at the Goodwill Benz for $1.70. I listed it for $89.99 plus shipping and it sold the same day for my full asking price. The buyer was all in for $106.57. Next time I will do what you recommend and start it out at an auction first and list it even higher. I was okay with my profit though and so thankful. I'm hoping for many more. This is what it looks like. It is a Go Games Tan Brown Plush Floppy Stuffed Wolf Realistic Animal Collectible. So really awesome bolo. But yeah, I definitely, if you can't find any like it, start it at an auction and start it high because you just never know. This one comes from bolo buddies member the Kitchy Kansen and she said, I bought this lamp lantern at a garage sale for $5 and I listed it for $50. Three days after listing I took a best offer of $42.50. Gotta love garage sale season. Thank you, Courtney. This is what it looks like. It is a vintage cobalt blue glass globe hurricane light railroad lantern lamp Hong Kong. I love that blue. This one comes from Bolo Buddies member Piece of Scrap on YouTube and this is her YouTube channel. So you're hearing me say Bolo Buddies member. That means they have joined Bolo Buddies memberships on this channel for perks.  If that is something that interests you, you can join Bolo Buddies memberships. If not, no worries. My channel is completely free. Memberships is for perks. So Piece of Scrap. Check her out. She's linked down below. She has an awesome YouTube channel. She sells a lot of clothes and you guys don't get that from me. Clothes and shoes. So sub her up for some different type of content. She paid $3.75 at the Goodwill and sold it for $60.04 plus $7 shipping. It is a Nike Team MLB Major League Baseball. Yeah, it was baseball. 2X Chicago White Sox Black Windbreaker and I think that's an eBay sale. Be on the lookout for this small Squishmallow Panda with Hearts. I found this one at the Goodwill Benz. It's only five inches tall. So it must have cost less than a dollar. Turns out it is super rare addition in high demand with collectors. Sold even without its tags for $185 plus shipping in three days. Wow. The buyer was very happy and said it was a college graduation present to herself. Look at him. He's from 2022. He's not even like super old. He's just probably one of those that is maybe discontinued. Hug Mies. He's only five inches, $185. Incredible. Bolo Buddies member, the Kitchie Kansen, bought this. It is, she bought five Bratz dolls for $3 each at a garage sale. Listed them, listed all, but this one for $25. Found high sold comps on this one. So listed it for $100 and then within less than a week it sold for full price. Wow. So this one is called Express It Rena Doll Rare Freckles Blonde Hair Green Eyes 2001. So you can use Google Lens to figure out which doll is what. It's really, really helpful. Sometimes it works, sometimes it doesn't, but Google Lens is free and I recommend it for every reseller. I do have a video of how it works and how to use it. So check that out. It is a free reseller resource. Okay. Pick this up at a garage sale for $500. They paid 500. Woo. Did a ton of research on the item and after contacting the owner of the National Lunchbox Museum in Georgia, I was confident that it was real. Listed it high at $4,799.99 and had three offers by morning. Sold for $3,399 free shipping. Less than 12 hours after listing. Find of a lifetime. But you know what? He paid $500 for it, but he did his research and this is what it looks like. Toppy the Elephant 10 Lunchbox Original 1957 Lunchbox Rare Kroger Promotion. Wow. I would have looked at that at a garage sale and been like $500. What? I wouldn't even have looked twice. I wouldn't have looked it up. I wouldn't have researched it. I definitely would not have called a museum. So props to this guy for doing his research and making a huge profit. That is incredible. I bought these belt buckles at a yard at a yardage. I'm guessing that's a yard sale for $2 each. I sold one for asking price of $110 and the other gorgeous for a best offer of $55 to the same buyer of the other belt buckle. They are Pacifica. Yep. I've sold these. I actually have a video on these. I got a bunch of these at a garage sales also and I've done really well. This one's 1976 Pacifica Peter Frampton sold for $55 and the other one is Rare Genuine 1975 Pacifica Rolling Stones and that one sold for $110. These are typically belt buckles with bands on them. Like rock bands. This one comes from Bolo Buddies member childhood finds and this is her YouTube channel. Definitely check her out. She has great Bolo's and a great YouTube channel. She said I picked up this board game for a dollar at a garage sale last year and finally got around to counting the hundreds of pieces. It's sold within a week of listing for full asking of $109.95. It is Napoleon in Europe Epic Strategy Board Game Soldiers 2002 Eagle Games No Dice. So I thought it was a puzzle but it's a board game. Wow. Yeah. Counting the pieces is no fun but when it's worth a hundred bucks it's kind of worth it. This one comes from Bolo Buddies member Dolo Deals. She said so I always pick up old cookbooks at local bends for 15 each. 15 cents each. On this particular day I found a trashed antique cookbook that was missing several pages. The cover was hanging on by a thread. I searched for the missing pages to no avail, listed it and sold it within a week for $51. My eBay and Etsy store are both Dolo deals. I find better luck selling antique books on Etsy. So the thing is trashed. She paid 15 cents for it and sold it for $50.99 on Etsy. You gotta love that. Antique modern home cookbook with helps and hints for the household 1890s to early 1900s. This is my best sale to date. My husband came sourcing with me which he usually he usually does or usually doesn't. I'm not sure. Let's see which he doesn't. Oh I read it wrong. My husband came sourcing with me which he doesn't usually do. He found a tote full of Star Trek stuff for $40 at Desert Industries. It was taped up so we couldn't see much of what was in there but we took a chance. I just sold this lot of figures for $575. I've sold all but one Starship to the tune of about $800 so far. Not bad for a $40 chance. This lot sold on eBay. This is what it looks like. So it says Star Trek, TOS, TNG, Enterprise Art, Asylum, Diamond Select Action Figure Lot. Nice. I wanted to give this time in case there was a problem since the books were moldy. No issues so far so far anyway. Paid 69 cents at the Goodwill outlet. So I'm not sure if they smelled moldy or if they physically had mold on them. Do you guys sell things that have mold on them because I have a tendency to not do that because I'm afraid somebody would have like a mold allergy or something like that but stuff that just smells moldy like it's been in a damp basement. I have sold items like that but I have a tendency to also usually just stay away from that stuff. So this could be a good learning experience for everyone. Let me know down in the comments what you guys do if something smells moldy like do you have a tip or a trick to make it not smell moldy. If it has mold on it do you list it? If you have a mold allergy what are your thoughts on this? I mean we could go all kinds of places with the mold issue but it is a 1990 Microsoft QuickBooks still sealed new three books have mold. So if it's still sealed what I'm guessing is the person is probably buying this going to throw away the packaging pull the stuff out of the sealed stuff and it's going to be completely fine. So yeah I'd love you guys's feedback down in the comments it looks like it sold for $149.99. Paid $1.25 at a thrift store when all their stuff was marked down to 75% off after Christmas. They had tons of ornaments since they had most priced at $5 or $10. I bought a bunch of ornaments most were bread and butter only three of these have been on ebay in the last year none currently so I priced double what the last one sold for and took a best offer of 80. Yes I like your thinking it is a 1992 through 1994 insco treasury a child's Christmas books baby mouse ornament and this is what it looks like yes price it high guys keep those comps high while this is a bread and butter it is just a sponge for a certain cleaning system bought at the Goodwill outlet so probably 25 cents or less can you believe $25 for a smiling sponge it is a scrub daddy daisy dishwasher or wait dish wand system sunflower replacement head so I have a funny story about this I picked one of these up at the Goodwill bins outlet also but mine was not I don't know if it's the same brand I think it is but it was not in the packaging and something just told me you need to keep this and I will tell you it is amazing for spot cleaning like plush and stuff like that because I don't know if this is the same type that I'm showing you but mine is soft on one side and it has a scrubby on the other side so I can really like scrub those plush and get those spots off it is amazing and a lot of times I'll do that and then throw it in the washing machine but you want to get that stain off first and that scrubby side really works great so there's a little tip if you ever see one of these keep it oh boy let me start by saying thank you for all you do for the reseller community I'm new to reselling just started in in November I clean out abandoned storage units for inventory and without the things I'd learned from watching you and other YouTubers I would have thrown away so much money I would like to share my best Bolo to date thank you for watching and I appreciate the shout out very much she said I found these Birkenstock sandals in a box of actual garbage in a unit I was cleaning out I thought they would be worth saving because of the brand and they were in decent condition boy was I surprised when I looked up comps and saw similar sandals selling for 150 to 250 however all of the sold comps and currently listed sandals and this style were brown and mine were black I searched Terapecan found only one black pair that sold for 280 free shipping I figured black must be rare so I priced mine at what I thought was high at 299.99 plus shipping they were listed for five days and had over 60 views and 11 watchers all of whom I sent offers of 269.992 I woke up Sunday morning to Cha-ching and it sold for full asking price of 299.99 the buyer was all in for 347 who 300 for 30 year old use sandals I am still amazed wondering now if I should have auctioned them but still super happy with what I got especially because they were so close to ending up in the dump want to look for Birkenstock's women's slides with flower cut out brown or good but black or better the flower cut out style with a strap on the back seemed to do pretty good and this is what they look like and she is calling them Birkenstock's and they're Doc Martens when I saw the picture I'm like I don't think those are Birkenstock's she's got it right in the title they're Doc Martens you guys and yes vintage Doc Martens definitely do well and oh my goodness they're a size six that is a super hard size to sell so if these would have been a bigger size she probably could have gotten even more so but Birkenstock's are a bolo also but Doc Martens if you find the old ones they can do really well bought this old wood carving wall art at an antique mall for five dollars everything there was so expensive so was surprised at the price I thought it looked like the Madonna and mentioned that in the title but misspelled it still sold on auction for a hundred and thirty one fifty is very different from other listings of wood carving spirits by felt it fit but felt it fit the category and this is what it looks like and this one comes from YouTube channel Thriftaholic and here is her YouTube channel I will link her down below definitely go and give her a follow she has reseller content so this is what her little she called it vintage wood carving spirit Madonna not head tree log home cabin folk art this next one comes from Bolo buddies member YouTube and eBay is resell and donkey yells and this is what the YouTube channel looks like bought this very heavy frog vase from a thrift store for twelve dollars it sold within three days of listing this was one of the most difficult packaging I have had to do to date it was delivered and I haven't gotten any notification from the buyer to arrive damaged so fingers crossed thanks for all you do you are a very hardworking lady and we appreciate you all thank you so much I appreciate that so let's look at her item here it's an art pottery urn vase 3d applied frogs lily pad ref flowers 12 inches tall and earth tone wow that would be hard to show very cool item and this is also from the same YouTuber resell and donkey yells this is just a vintage baby blanket that was probably handmade I picked it up at a thrift store for a few bucks bread and butter but it was so cute thanks so much appreciate you vintage Noah's Ark baby crib blanket hand quilted ruffles satin trim pastels animals 2995 on this now keywords that she used satin trim definitely use that in your title quilted very very good also if it has that quilted pattern this one also comes from reselling donkey yells pick these pillows up at a goodwill for half price color of the week paid two dollars each took about four months to sell but a win in my book pair of lorenne ralph lorenne floral throw pillowcases sold for 64.95 bought at a church rummage sale for one dollar sold within a week on mercury for full asking price this comes from bolo buddy's member halin vintage and this is what her ebay store and youtube channel look like this is a 1996 molly dolly from the big comfy couch original clown doll with vinyl face sold for 84 plus shipping on mercury this one comes from franklin hill ventures he is a moderator of the facebook group he also sells on what not under the same name and he has a youtube channel so his etsy store is fh ventures this is a 1975 avalan hill wooden ships and iron men fighting sale game paid three dollars and 98 cents at the thrift shop and sold for 72 plus shipping on etsy in general any old avalan hill games are bolos this is what it looks like so he sold it on etsy now franklin hill ventures sells on what not and he does a ton of ephemera on what not so if you want to buy ephemera if you want to learn how to sell ephemera on what not definitely go and give him a follow he has been doing it for a long time if you're not on what not already let's try that again i do have a referral link down below if you use that you will get 15 dollars to shop that's free money go buy yourself something and follow me i'm bolo buddies over there and franklin hill ventures all one word that is his what not so give us both a follow and use that link below to get that free money oh my goodness this next one i love it i found this vintage rubber face rushed in bear at the goodwill bins what thanks to this group i knew what to look for i paid approximately 45 cents i listed it high at auction on ebay and had many watchers changed it up to buy it now and took best offer of 500 so 45 cents into 500 and she got it at the goodwill bins talk about a big money bolo it sold end of april i am so excited and this is what it looks like it is a vintage rushed in bear plastic face red white crying for you plush sorry it's really really small but i'll pop it up you guys will be able to see it better i found this book at the salvation army for one dollar i listed it for 275 and took a best offer of 250 it is edward pernkopf did i say it right atlas of topographical applied human anatomy volume one 1963 would you have picked it up or walked past it let me know down in the comments thank you guys so much for being here thank you for watching this is a whole playlist of videos that go on and on for each month of the year uh come share a bolo over in the facebook group go to the featured section and post a screenshot tell me where you got it what you paid for it and what it sold for and i will feature it in a video like this i hope to see your bolo in a future video if you want to join memberships for perks level two gets you the pop-up and the link down in the description that is optional my channel is completely free memberships are for perks but level two will get you that so thank you guys so much for being here thank you for watching be sure to like comment subscribe and share and thanks for watching