Hello everyone, welcome to lecture on Introduction to Information Theory. At the end of this session, students will be able to articulate the amount of information per symbol and rate of information. Now before starting with the actual session, let's pause the video and recall what is a mean by a communication system. It is nothing but a transmitter, a channel and receiver. So here, this transmitter is nothing but the source of the information which generates information which is communicated to a receiver through a channel and at the receiver it is nothing but the destination of the information which receives the information which is coming from the channel, right. Now let's start with what is a mean by information. If it is generated in the several formats by the source as we seen in the communication system, the first block is nothing but the transmitter which generates the information. So it generated in several formats, it may be English, Marathi in the any regional language alphabet series or it may be a binary input sequence which is generated by the computer or it may be the analog waveforms which is nothing but the audio and video signals. So now can we measure it? The answer is yes. So for that let's take an example. So there are two sentences here you can see that. The first is that there is a traffic jam on National Highway 5 and the second sentence is there is a traffic jam on National Highway 5 near tunnel number 3. So if you compare these two sentences, from which sentence we will get the more information? Obviously, it is from the sentence number 2. So as compared to sentence number 1, sentence number 2 gives me the more information about the traffic jam at the tunnel number 3. So from this we can conclude that we can measure the information. So for that the basic principle which helps for measurement of the information is uncertainty. So what is mean by uncertainty? It is nothing but the unpredictable of the event occurrence. So for example, when you throw a tie a dice there are six outcomes but you can't confirm that which will be the outcome whether it is 1, whether it is 2, whether it is 3, whether it is 4, 5 or 6. So there is unpredictable output. So that helps to find the amount of information in the communication. So for that let's take two example.  So occurrence of this event or probability of occurrence of this event is more which will give you the less information. There is no information in that. Second sentence a man bites a dog in that this event occurrence is less means probability of occurrence of this event is less rarely happens. So obviously the information in this event is more. So comparing these two you can say that a quite amount of information is communicated by the message a man bites a dog because the occurrence of this event is rare. So you will get the information in that. So using this you can say that there is a inverse relationship between the probability of occurrence of the event and the amount of information associated with it. So for example, more probability you will get the less information associated with or less probability you will get the more information associated with it. So let's take this as a in the form of equation. So you can see over here this i of xj is equals to function of 1 by probability of xj. So xj is nothing but the event which is occurring and p of xj is nothing but the probability of associated with that event. So as we said in the previous slide the relationship is a inverse relationship. So that is i of xj that is the information associated with that event is equals to the inverse of probability of that event occurrence. In the similar case there is another event which is happening that is yj yk and the condition is that these two events xj and yk are independent. What does it mean by independent? Independent is nothing but there is no relationship of the event occurrence xj is occurring differently yk is occurring differently. In the same manner what is the information associated with the event yk i of yk equals to function of 1 upon probability of yk. Hence we can say that if these two events are independent so total information associated with these two events combined that is called as a joint event is nothing but the probability of xj, yk equals to probability of xj and probability of yk. So total information associated with that combined event is nothing but the ixj, yk equals to nothing but the function of 1 by probability of xj, probability of yk. Now we already said that these two events are independent means xj is of event is separately occurring and yk event is separately occurring. So whatever the probability of these two events having and the joint probability is nothing but the sum of these two individual information associated with that. So on this arreches of this equation is having a multiplication but we want the sum. So how are we going to convert that multiplication into sum? So whatever the function over here is supposed to be convert this multiplication into the addition. So how that is done? For that we have to use log that is logarithm is one of the function which can convert the multiplication into the addition. So by using the logarithmic we can say over here that is information associated with the joint event equals to log of 1 upon probability of xj into probability of yk. Separate out these two terms we get log of 1 upon probability of xj plus log of 1 upon probability of yk. So this individual term is nothing but the information associated with the event xj. This is nothing but this I of xj and this individual term is nothing but the information associated with event yk. So that is why I yk and the summation of these two adding of these two either is gives you the nothing but the information associated with the event joint event that is a xj comma yk right. So from that you can derive the basic equation of the amount associated with event occurrence is nothing but the log of 1 upon probability of that event occurrence. So in this case for xj you can write information associated with that event xj equals to nothing but log of 1 upon probability of that event occurrence which is also can be written as a minus log probability of xj. Here it is 1 by probability of xj here it is only the probability of xj so that is why the minus sign is over here. Now let us take a so there are different units of the information defined for different basis of algorithm. If you already seen the equation for the information associated with the event for that the unit is depending on the log base whatever we are using. So if the base is 2 the unit is bit and if the base is e the unit is not and if the base is 10 we are using the unit is decade or hardly. So for that amount of information i of j xj satisfy the following properties. So first properties i of j xj equals to 0 when the probability of that event occurrence is equals to 1 means you are definitely know that there is one output is going to be occur. For that we will get the information is equals to 0 because log 1 equals to 0 so information associated with that is equals to 0. Second property is that the information associated with that event is always greater than or equals to 0. We already seen in the first one that i of xj equals to 0 when the output or probability of event occurrence is 1 in that case it is 0. So it is supposed to be minimum 0 or it should be greater than 0. So it is not a non-negative value it is always positive value which is 0 or greater than 0. Third one is if as we said in the previous slide it is having inverse relationship and if the probability is less you are getting the more information and if the probability is more you are getting the less information associated with that event. So in that here it is right. Now let us see what is mean by average and mutual information. So average information is nothing but it is also called as an entropy and it is nothing but the uncertainty in a random variable. We already see what is mean by uncertainty. It is nothing but the unpredictable of the event occurrence. You cannot predict what will be the output of that event we already seen the example. So entropy is nothing but the average information per individual message means whatever the events occurred and whatever the output you are getting you make the average of that I am saying average but if it is it has two types. One is arithmetic average second one is statistical arithmetic average means you have the fixed output deterministic output event occurred and you can make the arithmetic summation of that and you can take the average. So that is why that is called as a arithmetic average. Statistical average means you cannot predict the output the numbers whatever the output you are getting is unpredictable. So for that the value is always changing and it is random. So for that you can get the average is nothing but the statistical average and the entropy is defined or denoted by the h of x over here h of x equals to summation. Summation is means it you are performing an average of that summation of probability of x into the log of probability of x which gives you the entropy and the unit for that is nothing but the bits per symbol. The last point is a mutual information. The mutual information is nothing but the amount of information which is obtained by one event with respect to the other event. You already seen in the previous slide there are two events we consider x of j and y k but in that case both are independent. In this case we are taking the output considering the second event. So that is why the mutual information is nothing but the i of x over y equals to entropy of x minus entropy of x by y. So this one is h of x is nothing but the initial entropy which and h of x by y is nothing but the final entropy. So whatever the difference between these two you will get is nothing but the mutual information that is the amount of information which is obtained from one event with respect to observing other event. These are the references. Thank you.


That's right I switched it up just a little bit to Narbash this match I will say that Narbash is a better support overall than Richter if you manage your mana well Which is difficult because he's been nerfed to all hell by strange matter But he's still enjoyable to play and once again teamed up with the bearded Wolverine His twitch channel will be linked in the description below and I'll toggle back and forth between our views I also added some captions here and there throughout this match Let me know what you think of that in the comments like the video if you enjoy it sub if you want to see more gaming content But for now, let's see some big daddy bashal and bash gameplay Together and he sent me a message.  He's giving me a lot of great advice over the over the time that I played fault I Love armadillon great guy, but he gave me no advice there. All he says it made me hurt He didn't say hey, man. I will throw it as a jet literally just gave me Unconstructive criticism I'm like interesting. All right Thank you. I mean your build made him hurt inside. I guess I Would have loved to know undead fun. What's going on brother? How we doing? I Would I would love to know what why it made him hurt inside? You know, like maybe it's something I can fix maybe like the build I was doing is just Had no benefit or something, you know You can say to your ward. I'm gonna drop my ward first right here Then you can put whatever award you want it's gonna be easier for you to get back in here than it is for me So we need to watch for early gang since they're coming from Redside. Yep. That's what I was thinking I'm gonna bangle it up over here. How are things in the Wolverines then doing great doing great God that takes so much mana.  Oh, yeah, and I don't have enough mana to Of course you're good. You're good. I was just thinking as a man. I was like, do we have a ward up and then Soon as you said that you like watch out. I'm like, no It adjusts went down when it came over.  Are you just back? No, I died, too Okay, that looks like they're going for gold. Did they not get gold? No, they would you get they went to gank mid lane. Oh There's gold still up. Yeah, they're no gold trouble. Oh, we're not going. Okay, kind of pins on this Rocks, oh, he didn't seem very committal.  Ooh Sounds like fun, but also You know could be stressful Get on kai get on kai Raptors coming up soon. Yep Oh, yeah, nice stand. I may get a couple more No, can't do that We hired Gwen Stefani for a private concert.   I just missed my last auto. So it was bad on my part there Definitely on me holds up and let us start getting it low All right, all right, let me know what's one hit. It's one hit. Whoa. Hello, buddy Oh, you got kai coming at you and I'm all out of mana. Yeah, dang dude Oh, there goes someone forgetting that gold So much for getting the gold An enemy has been slain Sparrow just backed. I'm gonna go ahead and back I'm gonna push gold this bad Yep. All right, ultimate's up. I want to drop a ward I love nabash's little pitter patter when he wins Other than that got a kid on the way and just found out. It's a girl. Let's go. Hell yeah My first kid was a girl too. You know nabash's pitter patter feet. Yes. Yeah, he's level six. So watch out I'm close We'll get you there. All right, let's wait for him to miss a funk Yep, like that. Yep, just like that. You should start at yours first, buddy been slain Yeah, she got me. Oh, oh she got you.  Yeah My bad, man.  I got the I got her halfway down And then they finished her so Damn it.  You said okay. Whoa, they're right here. Yep. All right. All right. All right My ultimate's back up So watch for him to miss a thunk and if he does I'll go in. Oh, I need to go work I'm gonna pull ward up too Kai is the one raptor his health is probably He doesn't have smite Oh, we damn it.  I wasn't expecting them all to be here That's my bad. I shouldn't have done that.  I forgot.   I do I miss time. Just let me know.  She went in. She went in I was not expecting her to go in like that. He has been sleigh That was a good fight There are two for there.  I don't know.  I don't know I didn't think it goes that may freaking Come on now. There we go That's some ds, man. Oh bellicose coming around Yep whoop What's that? He has been sleigh Damn it, dude. I just can't do anything Hello, who love your face phoenix. Thank you so much, buddy I'm up to you're good. You're good Did you get a snipe? I did Narvae is dead now Finally got two kills.  I'll tell you that much longer No, I again, man. They just keep on Oh, I'm coming over to try and help them. I don't know if I can I just took that. I'm sorry You're good McCary Follow me not mccary They are following you too.  I'm just on to the tower Where the hell is sparrow? Enemy has been slain. Oh, she's being killed by countess. That's where she is I'm on my way to you guys Be there directly.  That's what we need to work. We should be worried about that This tower is going to be here and we'll get to it.  Seriously. I I'm not We're winning. That's all that matters to me I don't have any mana though, but I want to get some minion kills here because I need to catch up on cs Okay, I'm gonna back now. I got 25. I need two samesies My phone keeps going off makes me worried that it's something else This is doing nothing to help my reputation. What is your reputation?  You you're the carry. I'm the support. I got more assist All right Five two seven. I'm three five eight. You start building white.  It's not my fault. I kind of stuck with Hey, look at you if I'm not around you get kills She was like abit of me getting that Getting the tower so I didn't let her do it. She's dead for 27 seconds I can get a bigger wave on this tower a two-two tower And that's what I'm gonna do Okay. Yeah, take all my cs you got all the kills to count this shit You don't need the cs as well free tower Right or close to it at least Always coming from the front. Oh, we got another minion wave. I'm gonna. Okay. Yep. Oh, okay.  Why we already have the tower down There's no reason They're pushing hard. Yeah, they're still chasing us. That's her by herself. That's her by herself. Her by herself She kept chasing nobody else did That was weird Right Yep, I'm backing I got 19 to stand. I'm pretty sure I can finish my item Yep, I definitely can Oh Let's go Oh sparrow. Yo, how's it going? It's going great sparrow entered the lion's den over there Oh, damn Yeah, she's uh, she's kind of an ending after she had a good start and now the team's been doing what they're doing. Yeah I mean, she only had a good start because of the chimera right Careful you're only Ah Waving on my bot d and nothing to happen. He has been slain Oh dang We made out for the best so far.  I hate when that happens. I would rather play very much though That she was uh beating you pretty good destroyed Man, we got that tears too. Oh, no Those two won't have to do a bid. Okay. They're not even chasing him. I'm not even worried. No, they're not chasing them There's some deep deep boards. Look at that in there Left. Yeah We haven't even been over there since we took that zero two down.  I was gonna grab some jungle, but uh I'm sorry. You are the carry support here. I guess you should take jungle Give me that red buff I'm gonna go help countless. Oh, that's our inhead.  Interesting. We lost all those minions that quick. Damn. Well, he played that right Whoops Well, I'm fucked.  I was gonna get away, right? Dude, we still have we still have our tier one's mid and Yeah Left me has been slay Wraith stuck. Where are you going gray? Gray, I had you.  I started mine after him Got room.   Yeah Are you playing goose or Yeah, playing no, no, he's adc nardash Oh, I got more kills than him now. So maybe he's not my bad. I didn't know what I didn't know what narvash that was that came around the corner.   I know he's pretty good. He had some pretty good zigzags there Only you would see Is it right?  I got my buck shot. You're dead But he uh, I mean he absorbed quite a few shots there too Let's see if we can get uh attack camps prime See if we can get prime They're all left. So We should be able to do this Worked out for us.  Yeah, maybe that uh, because that uh Several he's seven two and four. He's only got died twice.  Uh, you're not gaming at this time of night Don't even this is my normal game time. You know where to find me at this time. Don't come at me like that, bro Nice The core goes down you sniped it again.  What do you don't have access?


Hello, my name is Thomas Prest, and this is joint work with Shuichi Katsumata, Chris Kredgowski, and Federico Pintore. So the main question that we are concerned with in this work is how efficiently can we share one session key between n plus one users. And the use case that originally motivated this work is secure group messaging. If we consider n plus one users that wish to communicate together in one group, then a simple way to realize that is for all of them to share a session key that they can use to encrypt messages using symmetry key encryption with each other. But first, they need to agree on this key. And one naive solution is that if all of them have a public key, then we can use public key encryption schemes and send and one of the users will generate a session key and encrypt the session key to all of the other users and broadcast all of the cipher text. So if we use that with El Gamal, since each cipher text has two group elements, then the quantity that will be broadcast by the sender user will be two n elements. And in 2002, Kurosawa did a nice algorithmic observation, which is that in El Gamal, actually you can do some sort of randomness reuse that was the term that was used. So if you consider the left part of the cipher text, so g to the r i, you can see that it does not depend on the public key and it does not depend on the key. So what we can do is reuse the same left part for all the users. And then it's only the right part, which will scale in the number of users. So in this example, what this would amount to do is to send g to the r, then pki to the r times k for all the users i. And instead of sending two n elements, then this user only need to broadcast n plus one elements and asymptotically it saves a factor 2. In terms of terminology, besides randomness reuse, we have seen the term cipher text compression or at a more syntactic level if we consider the syntax of describing the security notions that we are trying to realize. We have seen the term multi-recipient chem or multi-recipient pke or aka mchem or mpke. And since 2010, there has been a lot of papers considering this problem. But to the best of our knowledge, there is almost no post-quantum proposal. We have seen one paper trying to propose a construction from the LPN problem. But we also found that this paper was broken. So as far as we know, there is no post-quantum secure proposal. So this work aims at revisit the notion of mpke and mchem. So a first contribution that we do is to propose a more natural definition. And this definition is more natural than the previous ones in the sense that it captures classical assumptions that were captured by the previous ones, but it also captures post-quantum assumptions. And in addition, this new assumption and new definition is amenable to an efficient curum proof. And we also do this curum security proof. In the second part of this work, we instantiate our constructions from post-quantum assumptions. So from lattices, from isogenes. And something that was a nice surprise to us is that the efficiency that gain that we obtain is one or two orders of magnitude. So we obtain a communication cost that asymptotically is one or two orders of magnitude smaller than what we had previously. And then finally, we apply our techniques to TricM. So TricM is part of the MLS protocol, which is a protocol for secure group messaging. And TricM is the bottleneck of MLS. And what we did was, we observed that there is a simple but powerful interplay between the notion of M-CAM and between TricM, and that basically combining the two of them together allows to divide by two the communication cost. All right. So first, I will talk about revisiting MPKs and M-CAMs. OK. So first, I want to talk about the abstract notion, the abstract assumptions that once is realized, it allows to construct M-CAMs and MPKs. So if you look at previous work, for example, a work by Bellarre, Boldireva, and Stanton, the notion that they put forward is the notion of full reproducibility at the top of this slide. So if we consider a ciphertexte, which encrypt a message M under the public key PK1, full reproducibility assumes that you have a polynomial time algorithm A that takes the ciphertexte as input, takes the public key PK1, the second public key PK2, the private key SK2 associated to PK2, and a second message. And this polynomial time algorithm transforms the ciphertexte into a ciphertexte of M-prime under the public key PK2. And in this work, we put forward a more natural assumption, at least in our eyes it is simpler and more natural. So we say that a ciphertexte on encryption scheme is decomposable. If it can be split into two parts, so the first part of a ciphertexte will only depend of on domain's coin R0, so it will not depend on the public key and it will not depend on the message. And then the second part, which we call CTI hat, it will depend on the public key PKI, on the message, on the randomness R0, and of a second chunk of randomness R1, RI. And if we look at the example of El Gamal, then El Gamal satisfies full reproducibility as well as decomposability. So if you have a ciphertexte GRPK1R times M, then in the example I have shown, this ciphertexte can be transformed to encrypt any messages under any public key for which we know the private key. And it is also decomposable because you can see that the left part does not depend on the public key and on the message and only the right part does. And how do we exploit that to achieve mchem or mpk? So a ciphertexte with n-recipients will be CTRO, which will contain CT0, and then it will contain CTI for each eye. So the left part of the ciphertexte will scale with the number of users and the left part will remain constant. For key generation and decryption, they remain the same. The second contribution is that we propose a generic transformation which takes as input an ncpa mpke and transforms it into an ncca mchem. At the technical level, we don't propose any new technique, but rather what made our life simpler is that if you look at previous works, previous works took as input an ncpa mpke. So it did not consider that it was decomposable and it did not consider that it was an mpke. And so we start from a somewhat stronger assumption, but something that is really nice for us is that this assumption is actually verified by several pke's. And this is something that we will show in the rest of this talk. So it's actually a very natural assumption to start with. And our transform is simply a variation or a generalization of the Fuji-Zaki-Ukamoto transform. So in the sense that when we are going to, so we will generate a random message and then we will use this message to generate the random coin for CT0. And then we will also generate CTi by taking pki, the message, g1 of m, which will be a random coin generated by m, and g2 of pki m, which is a random coin generated by pki and m. And then the session key is going to be the hash of m. And for the encapsulation, well, it does the same as what is done in Fuji-Zaki-Ukamoto. So you do the encryption and then you do re-encryption. And you check that your safer text is equal to the new safer text that you computed. And if not, then you're going to return bottom. And something to take into account is that you have to be careful that when we do the re-encryption, it should not, the time of the re-encryption should not be linear in the number of users. Because if we do that, then you will lose a lot of efficiency. And so a simple way to achieve that is simply to, in the same way that we have a decomposable in CPA MPKE, we have a decomposable transform. In the sense that here you can see that CT0 does only depend on the message. And it's only CTi that will depend on the public key as well. And this is nice because when we do decapsulation and we do re-encryption, then CT0 will not depend on the public key. And CTi will only depend on the public key i. It will not depend on the other public keys. And this means that when you receive the safer text, you only need to receive the part of the safer text that is relevant to your public key. And this makes the whole algorithm faster. So in terms of the security proof, we use classical existing techniques. So we use compressed oracles that were introduced by Zendry. And so in this example, we achieve explicit rejection, but we can achieve implicit rejection as well. All right, so now I'm going to show how we can instantiate a decomposable MPKE from post-contum assumptions. So first, let's look at the Lindner-Pikert framework. So I'm going to assume that the audience is familiar with LWE. So in the key generation, we generate LWE samples. And then in the encryption procedure, we generate an LWE sample U, or other A and U is an LWE sample. And then we generate V, and V will contain the message M. And this framework is very generic and it encompasses several schemes, such as the NIST, Round 3, Finalist, and Alternate Candidates, Frodochem, Entrelprime, Kiber, and Saber. And what is interesting for us is that the Lindner-Pikert framework is actually decomposable. So one mild restriction that we have to do in order to do that is that the public key, the public matrix A should be the same for all public keys. And this is something that is not done in the schemes that I mentioned, but you can do that and the security remains the same. And then what is happening when you do that is that U becomes independent of PKNM. C, here U is equal to RA plus E prime. So that means that the scheme is decomposable. And then you can apply the generic framework that we described previously and obtain a multi-encryption scheme. So here you can see that you will compute U only once, and then it's only for the part V that you are going to repeat it N times for the N users that you have. And in terms of efficiency, a nice surprise that we had is that each VI is much smaller and faster to compute than U. This is due to at least two reasons. So first, it has shorter dimensions. And second, you do some sort of bidropping on V. So what you're going to do is that you're going to drop the least significant bid for each coefficient of VI. And this is again a nice for efficiency. In terms of security, the security of this variant reduced to the original variants of LWE, which in the sense that it is LWE with many samples. So it's different than the variant of LWE that the original schemes that I described rely on because they rely on LWE with a limited number of samples. But it's still a very standard version of LWE. We also did consider the SIDH scheme and its successor psych. So again, I will assume some familiarity with isogenic-based cryptography. So E is in elliptic curve and then we consider torsion subgroups that are generated respectively by PAQA and then PBQB. And the encryption procedure is what is the most interesting for us. So we are going to sample an isogenic fee of kernel RA. And then we will generate CT0, which is E quotiented by RA and then fee of PB and fee of QB. And for the second part of the safer text, we compute the J invariant of E quotiented by RA and RB. And we call it J. And J can actually be computed from the public IPK and from the ephemeral secret isogenic fee. And then CT hat is going to be JxM. And again, what is nice here is that we have a decomposable flavor because CT0 does not depend on the public key. It only depends of some random coin. And so we can apply the same framework as before and we obtain this scheme. And we show in our paper that the security of this scheme reduces to a decisional variant of the SIDH problem, which was introduced in a paper by DeFeo, Jaoh, and Plu. And finally, we did also apply our framework to C side, but this is in the paper and not in this presentation. All right, so now in terms of impact, what we did is studied the computational cost of using the normal scheme, the initial scheme, and our M-chem variant. And what we found is that our M-chem variant is significantly more efficient and consistently more efficient than the regular schemes. So in the case of C side, if you use C side for a group key exchange, as I described in the beginning, with a large number of users, then the cost per user is going to be 80 bytes. And if we use the M-chem variant, then the amortized cost per user is going to be a communication cost of 16 bytes. And for C side, we have even more impressive gain because it's 20 times more efficient in the compressed situation. So when we use M-chem, and the most impressive in our opinion is the case of Frodo-chem because we get a gain of a factor more than 60. And this is all only for the NIST level 1, which is 128 bits of security. And for example, in the case of Frodo-chem, the gains are even higher at higher security levels. All right, as a final application, I will show you how to apply M-chem to TRI-chem. So TRI-chem is a sub-protocol of the MLS Draft IETF protocol for group messaging. And it is a particularly important sub-protocol because it is the bottleneck in terms of communication and computation of MLS. And the reason behind that is that when you're using TRI-chem, you're sending and receiving a lot of public key material. So let me show you why. So consider we have N-users that are the N-users of a group that wish to communicate together. So these N-users are arranged as the leaves of a binary tree, as you can see. And every single node of this tree, including the leaves and including the root, is going to have associated to itself a public-private keeper. And all the users will know the public keys, but the TRI-chem invariant, which is very important for the security properties of TRI-chem, states that a user will know a private key if and only if it is in its path. So for example, the user at the bottom left knows only the private keys that are in orange on the figure. And an important operation in the context of TRI-chem is a user, the operation where a user that is compromised, so its private state will be compromised, will refresh all its private key material and then broadcast the relevant information in order to maintain the TRI-chem invariant. So what is going to broadcast is an update package that contains for each level of the tree. So it will contain one public key and one cipher text. So it will contain one public key for each node in its path except the root. Because actually, everyone knows the private key of the root so it doesn't make any sense to broadcast the public key of the root. And it will send one cipher text for each node in its scope path. And the cipher text of a node will encapsulate the seed that allows to generate the public key of its parent. And not also that when a user does some refreshing, the private key of a node that he refresh will be used as input of a PRG and the output of the PRG will be the private key of the parent. So this means that once you know the private key of a refresh node, you know the private key associated to all the parent, all its ancestor nodes. And so something that we try to do is to instead of using a binary tree, we use a NAMARITRY. And if we do that then, if we do that naively, we are going to send log M of N public keys and M minus one times log M of N cipher text. So at first sight, it's not obvious that this is going to give us a gain. However, something that was very interesting is that all cipher text has the same level encapsulate the same key. So for example, all the cipher text at the bottom left, they will all encapsulate the private key of their parent. And this is interesting because this means that we can use one single N cam at each level to encapsulate the same key for all the public keys that are concerned by it. And if you do the math, then you find out that compared to standard tree cam, we have a gain because here, if you look the formulas for standard tree cam and MRE tree plus tree cam, instead of having log two of N, we got log M of N. And then once this is chosen, we have the same proportionality of public keys and of CT zero. But in the case of MRE tree cam, we will have a number M of CTI hat at each level. So this means that you cannot make M too large because otherwise the size of your update package is going to be linear in M. But still, now we have a leverage in the sense that we can play with the arity of the tree and try to achieve some efficiency compared to binary tree cam. And in practice, we do in effect have a gain. So in this slide, we plot the size of an update package in kilobytes as a function of the number of users. And if you consider, for example, 65,000 of users, then if we use tree cam with size, in the binary case, each update package will be 10 kilobytes. But in the case of MRE tree cam, each update package will be less than four kilobytes. And similarly in the case of Frodo cam, instead of having 300 kilobytes, we will have an update package which is less than 70 kilobytes. So more than four times smaller. All right, so that concludes my talk. If you want to see our paper, it is on this link. And if you want the slides, it is on this link. And thank you for your attention.


hey friends and welcome back today we're doing well first let's show off this new b6t and she's temporary because I'm waiting on one from mystical gifts the really the one that I really want but this replaced the other one and I'm excited it's usable I still may find a way to use it and I did a flip through a bit of how I set it up so far on my Instagram if you're not following Instagram why not you should be I am Norris Cove on Instagram as well also on Facebook which I'm gonna work on my Facebook so last week let's look at last week's spread I ordered another insert and I kind of want to try it out let's see where are we here we go this was last week's spread today is Sunday so basically is it I made it through the week I've been working on something and I can't wait to share with you guys so I'm a bit behind in posting up excuse me recording and uploading so most of my posts will probably be a little late this week excuse me so this is how the week turned out my b6 I looked at it every day first of all it was so pretty I got a lot of compliments on it and it was just so so pretty the only thing is because the week was busier than I anticipated I ran out of room to write so thank God I had my classic so I was in both of these this week this week which I am and you see how it turned out so whenever I ran out of room and there I carry this I was carrying both of them just to kind of see which one I liked I love this spread you all didn't see me do this spread because I did this at a meet-up and let me tell you something I have turned into a freaking printable paper crackhead okay because this paper that my planner bae gifted me oh my god I just kept looking at it and I just kept doing this all week and I was like oh it's so pretty so the name is this kid here is from Sadie's plans I went on there looking she was closed thank God she opened up on Tuesday and I reordered some more I started by the same exact kid but in needless to say let's jump right on in so what I was gonna do this week was just lay this spread out but what I found is that I kind of need notes so I want to kind of keep this going so I'm gonna keep it going and then I may just do a practice spread in the four-page one so I will let you all know sit that aside and the dollar pin is back so so this week what week are we in this week so the days are 12 so that should be the 13th through the 20th so I got these I printed these printables off with my printer and use my silhouette and this from the planner shack this is called the farmhouse look how pretty this is I've been putting I've been downloading print all day this is what that looks like the kid is huge just humongous hold on you got my son so as I was saying I knew what I could hear him coming so this is that and it's so pretty and like I said you get so much look at this let's look at that real pretty look at it look at that oh my god I can't wait to use it so that is that so let's get started I'm not gonna hold you any longer let's jump in this is what it turned out like I got a little disappointed kind of sort of say realize that these printed off that's what's been happening here with the printer and I've been printing stuff all day and I noticed that's like the bottom half will be off and they didn't print correct and I was really looking forward to using this sheet so now I gotta reprint it and I want to use it hopefully so look at it I really wanted to use that and I really wanted to use this a candle right here let me see you mess the candle up I want to use that I mean I was gonna go in but I'm gonna do like I did last week since this such a big kid I'm gonna try to put some in my happy planner or we'll see where else it goes alright thank you all so much for watching so we've been doing after the pen so I'm gonna try to remember now the dates that's the only thing this kid did not have any dates but I have my own stickers I'm just gonna use mine I normally use the I would already had a girl in here but I wanted to put another girl so let's do a quick after the pen Saturday I have a bridal shower to go to I thought I'll get Saturday I thought I did and then I work bridal shower I don't have the time let me see it's in a text it's five o'clock kind of know what a place is you know also I put my clients in so let me do that I just didn't want to forget that because it's in a monthly when I got a whole lot of stuff I got it let me get my clients in first because this is gonna be something else because I have a lot of sticky notes down of things I need to do so I'm pretty much off Monday Tuesday until Wednesday then Wednesday 15th I could just want I just did this lady's hair maybe I'm tripping losing it Thursday so this week appears to be slow but we'll see so I'll put down this work sticker cuz I'm not going into nine at day so so far this is what we have but you see how last week turned out and it ended up being more what else let me whip out all these stickies that I laid for the month of man I kind of did a little pre-planning you're like big for the dentist appointment and I did not keep it I canceled it because I didn't feel like I was trying to go to Hobby I know it's bad so I paid for my daughter's storage I need to remind her about her storage which I'm pretty sure she hasn't forgotten because she had to have to put her stuff but I've signed her lease that was on there I have to check for Bentley's next appointment that's my dog so I want to put that oh and Bentley needs some dog food destiny storage I got the sticker there for that look into a bigger battery so I'm gonna do that on Tuesday I need to get a bigger battery for my camera because I have to to me is this too much I don't get a lot of filming time and it seems to die pretty quickly stickers yeah so what I'm trying to do I got two carts but I want to organize my stickers so that I can just pull like maybe a compartment off on my desk here and you know just flip through it instead of having to reach over stuff falling all out okay what else I forgot to get to the car wash I pray it stops raining I'll put that down on Tuesday or Thursday my son has a concert on Thursday at six o'clock so I'll be getting some happy mail this day but I have the sticker up so I can take that off I'll just leave it there car wash Erica's bridal shower Jaden's concert okay what else am I missing my destiny's lease okay and this week y'all needs to be a no spend week I lost it okay as they say I lost my shit I lost all of it I lost all of it last week I don't know what happened okay oh also I need to look into a I'm looking to a laser printer and possibly the mink machine because I'm also getting some new sticker paper I can't wait to try I forgot to take a before-the-pin Lord Jesus and else is going on this week I want to be all Friday something else is going on but I'm generally have to you'll see how it goes the week start off slow and then it just booms it's busy okay all right you guys so for right now that is it and thank you all so much for watching there we go so we can get a better closer look at this week's spread so this is for Monday May 13th through the 18th and I hope you guys enjoy this video thank you all so much for watching bye


G'day, Greg Moethe here at Targo Rotorua having a great time out, having a bit of a fang I suppose you could call here in the HSV R8 LSA, so it's got the 400 kilowatt engine and it is an absolute trooper of a thing and loves just tearing up the roads here around the beautiful part of central New Zealand. So having a ball, taking a few people for a few rides which is always entertaining, get a few different reactions from it all and just enjoying the sunshine and what we've got around us. I had the pleasure, well I think it was, the pleasure, of taking Darcy Watergrave for a bit of a spin as well and he I think had a pretty decent ride. Good expressions on his face you could say at moments during the 20 odd K's that we did out in the back there wherever it was. I think he was a bit shocked and blown away by just how good these modern cars are these days out there on those roads. Great of him to be a part of, I'm in between the tour and the competition cars, the tour guys are having a ball, the competition guys are having a ball and there's no doubt about it, we are having a ball as well cruising around and probably doing things you want to do day in, day out, you can't do because the rules and regulations, well they're all out the window at Targo Rotorua and we're having some fun.


Hey what's up you guys and welcome back to my channel if you're new here hi hello I'm Lydia and today I'm coming at you from in a car this is uh it's odd this is weird so today I wanted to make a video talking about coping after a flashback episode this video was requested and I figured hey why not make it because I feel like this is going to be a really helpful video to anyone who's new hi I'm Lydia I'm diagnosed with PTSD I have experienced multiple forms in my life the main one being my ex committing suicide in front of me I've had my fair share of trauma and I experienced flashbacks so over the years I've come up with a fairly okay way of coping now so first of all let's talk about what flashbacks are and how they affect people flashbacks can be anything sensory so it can be visual tactile auditory someone's playing now music because they're a dickhead flashbacks affect people differently so what is a flashback a flashback is a vivid experience in which someone relives a specific traumatic event and it can feel although that event is happening in that exact moment flashbacks are not like watching a video it's not linear it's not watching something from start to finish it can be absolutely anything related to that traumatic event it can be a feeling it can be triggered by someone touching you in a certain place so now let's get on with the video so coping after a flashback so you had a flashback what do you do my first advice is to take a minute I don't care what you're doing where you are what's going on please take a minute give yourself time to come to terms with what you've just experienced take a breath and try to remind yourself that the next thing would be to remember some grounding technique when it comes to this please remember your five senses so so sight touch hearing smell taste remember all the senses and try to stimulate each one in a way that distracts from what you just experienced my next bit of advice would be to just keep telling yourself that you are safe now you are not in that moment and you are you are not in that moment anymore you have moved you've moved forward you're not there you are safe reminding yourself the next bit of advice that I have would be to get some pressure take a step outside have a minute eat grants in our focus on the surroundings where you are what's going on how hot or cold is the next thing would be to journal what you've experienced when it comes to therapy it's quite hard to talk about what you're experiencing flashbacks and something that I found helpful the rest of the credit list is I write everything down that happens and that's been really helpful in the respect that I'm able to then hand it over there you go that's what I've been going for my next bit of advice is if you have them and you feel like you need them take prn medication prn stands for take is it is for take when needed so if you have that I would advise doing that if you feel like you need to the next thing again involves a notebook and that would be to try and work out what triggered that incident and write it down and the more you know about your triggers the more you can prepare yourself and make yourself feel safe and put yourself in a situation where you just feel safer because you know what's going to trigger you and you kind of valued them triggers you can work on them triggers knowing your triggers is some really important isn't that want to make a whole whole video talking about another one would be to talk to someone whether that's a close friend family member so yeah talking to someone is definitely a good coping skill and something that I think most people would suggest doing however I am aware that not everyone has someone's thought to win that everyone feels comfortable talking to people so please don't feel like that's your only option there are things you can do that can help like recording a voice note to get things out filming a video phoning someone texting someone writing a note writing in a notebook these things will help it's a way of releasing what you just experienced and the last thing I want to say is distraction techniques distraction techniques I only a best friend I always carry stuff to distract me with and a lot of times my fidget queue of my puppet thing that mean let me have my puppet out my puppet thing this my puppet thing so I always have stuff like this on me as a distraction and I would highly recommend it if you have any other coping skills for flashbacks let me know in the comments down below because you know I want this channel page whatever you want to call it to be a helpful community so yeah that's all I've got for this video thank you for watching and if you're new hit the subscribe button while you're here give a little tickle say hello in the comment we don't buy a prize and I will see you guys soon in the next video peace


Okay, welcome to today's show. I have one of the most special episodes for you. I have Brock Pierce here who, if you don't know, is I consider you one of the OGs of cryptocurrency, Bitcoin, he is the chairman of the Bitcoin Foundation. He's humble, so there's about 30 titles I could give him, but if you know anything about Bitcoin and cryptocurrency, he is one of maybe the most well-known person in the world, number one expert, been into virtual currencies since the 1990s. He is the co-founder of Blockchain Capital, which is the biggest crypto blockchain venture fund. He's the co-founder of EOS, which is the largest ICO in history. I did the math, it's probably over $700 million raised.  You asked me one of my sort of favorite questions lately. I've been putting into all of my talks that a billionaire isn't someone with a billion dollars. A unicorn isn't a billion-dollar company. A real billionaire, in my opinion, is someone that has positively impacted the lives of a billion people. A unicorn, in my opinion, is a community or an organization that has positively impacted the lives of a billion people. I think one of the kind of misconceptions and a lot of what's leading to the world in which we live is this kind of misunderstanding of money. Money's a bad thing, it's just a tool, but that people spend a lot of their lives in pursuit of it thinking it's going to make them happier and it's gonna provide them with something they need. And all they have to do is ask themselves, why do they need something? And then they'll learn maybe if they'll discover whether or not they really need it. And so they'll go through a lot of their life thinking that money's gonna bring them happiness and then if they're lucky enough to eventually get it, a lot of those people end up staying unhappy for the rest of their lives afraid to lose it. Cause it's all about being in the present and living in the now and in the now, you don't need very much. And so I think people are thinking about money and clearly, well, we're attempting to reinvent it. So the old adages of money is power, that paradigm is going to come to an end and it's gonna be technology is power and consciousness is power and all sorts of interesting changes to come. So if you're watching my target audience in this conversation, he's jetting to Columbia. He's speaking at the number one Bitcoin conference at all South America. So I want to get as much, I want to respect your time cause you're a super busy guy. I got back into LA this morning. We got into this morning. We were supposed to meet up on Friday and it was like, we might have to helicopter him in and I was like, all right, let's just, let's put it off to today. So for people not familiar completely with cryptocurrency, blockchain, Bitcoin, in one sentence, if I have to explain to somebody what Bitcoin and cryptocurrency is, what do you say to them in a one or two sentences?  There you go, magic internet money. But no, it represents something far greater than that. And that is that it's a monetary system that is based on math and cryptography. And so, and it's open source and it's transparent. So it's governed on a peer to peer basis. So it's a system that can't be corrupted. You know, it can't be cheated. It's a system kind of for the people. Do you think big picture, there is a potential that Bitcoin, cryptocurrencies, blockchain will take down the Federal Reserve, US dollars, pounds, euros. Can you see that in a world in 20 years? Or does it compete? No, I think that there's uses for both. And what Bitcoin is, isn't a currency. It's not a transactional currency. It's far too expensive to do transactions. What it is, is it's a store of value, meaning you're better off thinking of it as gold 2.0 or digital gold. And when you think about it from that perspective, you have to ask yourself about the history of money. And so for the last 5,000 years, the primary form of money was precious metals, gold, silver and copper. And those three, you know, after 95,000 years of experimenting with everything, were selected because they had specific attributes. It was sufficiently scarce so that you didn't need a truckload of it to buy a loaf of bread. You know, you can transport it. It had to be malleable. You got to be able to take it apart, put it back together again. It had to be fungible, like diamonds. It has to all be the same. It can't be like diamonds. Nonspoilable, you wouldn't want to put it in a safe. Go get it in a year and it's rotten. Right. So these precious metals have very specific attributes. Bitcoin possesses all of those attributes except for it's a lot better at all of them. And the other big difference is gold is physical. Bitcoin is intangible and the intangibility is a positive trait because you can send it from anywhere in the world instantaneously and it's just, you know, gold actually, it's easier to club you and take it off you. Yeah, PayPal, Western Union may be a thing of the past. So. It's more gold, I think that's the. You think gold. Now gold, no more question that we have. I asked just some beginners on the drive over here. Is Bitcoin a bubble? I know you're probably sick of being asked this. Everybody's been saying it's a bubble. You see big bankers saying this. The more they say it, China's banned ICOs, Russia's banned cryptocurrencies, the more it's going up right now. What's your answer to that? Is this a bubble? Yeah, of course it's a bubble, but, you know, what are bubbles? Markets and this one in particular, the price, you know, sentiment is the primary barometer, you know, of the price right now.  We had lots of like, you know, movements during that phase. And so this is going to be no different. So the data point I would give you though that's most interesting is we're calling it a 300 billion, you know, we're, we can get $400 billion market cap sector more or less right now and you know, kind of doing this in this period. How big do you think the internet was during its heyday? In 1999, it got to over 7 trillion, the internet tech stocks. And so, 7 trillion, and that was when it was an only a Western phenomenon and this is not adjusting to inflation. So I could argue it would be a 50 trillion or 100 trillion dollar market today. So relative to that market that was betting on the future potential of the new technology, which is inferior to what this is. This is 10 times bigger. I think, yeah, we're in maybe a temporary one, but it will go far from being even anywhere close to where the internet got. And so the thing that I would argue is the biggest bubble today is the stock market. So you think cryptocurrencies, Bitcoin at 300 bill, 300 to 400 billion dollar market cap is not nearly the bubble as conventional S&P 500 regular stock market, what people have their 401k. I think the stock market's more of a bubble. So you could see that crashing, a bigger crash than you could see crypto. Of course, it's a bigger market too, so obviously, I mean. So would you recommend people listening? Should be starting moving a little bit of their money from conventional stocks over into Bitcoin, Ether, things like this? Yeah, so I don't ever like to give anyone investment advice. And I don't think that if someone tries to tell you you should do this, you should invest in that, always be very skeptical. Because a good teacher doesn't say you should do this. They give you information, they transfer knowledge to you so that you can be informed and get more informed if it's inspired you in some way. And you should know what you're doing and then make decisions for yourself when you feel that you're adequately informed. And I think that's what good teachers do. These are the types of people that you should listen to, people that are trying to hawk something at you. Normally that should like put off the red flags. And so the information that I would give people is if you're doing what's called asset allocation. If you have assets, you want to try and figure out how they should be allocated and give some thought to it, have intention into things that you do. And so you can say, OK, I've now been informed enough due to my own research to inform my own opinion, to have my own view, because I'm making a decision for myself, I am choosing to do this. Once you've done that, you say, how much do I want to allocate? And that's going to be a matter of what level of knowledge you have and what level of conviction you have. Your prediction of the future. And you might say, I want 1% of my assets and something like this. You might say, I want more. I'm more or less mostly in blockchain and crypto related assets in real estate. That's where you put your money, either in crypto or real estate. So real estate is your physical asset that if something happens, you know you're balanced out here. Well, I think the real estate market's interesting because it's undervalued, hugely undervalued It's the second largest asset class and it doesn't have a matching engine or an order book. It's still running on real estate agents and talk about some draconian infrastructure, a market of this size. So as soon as real estate title gets put on the blockchain and where it becomes digital title, it becomes fractional. The stuff that's going to come out of that is going to be utterly insane. So imagine if you could say, I want to buy $100 in every house in the neighborhood or $1,000 and it's all fractionalized and it's a whole market that's trading all the time in fractions of home ownership. If you make it truly liquid, markets have liquidity discounts. Yes. Bring liquidity to the market and you will cause them a huge increase in price. So you think theoretically, so this is a whole thing for those of you who don't know. You have cryptocurrencies and they're built on a type of technology that's broadly called blockchain and there's different blockchains. There's Bitcoin is on one technology and Ether is on another one. You are the co-founder of potentially one of, well, EOS is going to be or is another technology. You're saying real estate is gonna go up on this technology and no longer just be realtors with titles in old fashioned 1800s methodologies. Yeah, I mean, this is the technology that will have that big an impact. It's gonna affect everything, so to help. Yeah, what else will it affect? What are the huge things? Let me take you down to the foundation. So the internet itself, if I wanted to describe the internet in three words, I would call it a data transport protocol. Okay. It's a system for moving information. Now the problem is it's an insecure data transport protocol and that's because back when the internet was first being designed, we couldn't, we didn't have the processing power to run the types of cryptography necessary to do this. And so the foundation of the internet was built wrong and then we just kept building on top of it. But the problem is when the foundation of a system is wrong, meaning it's insecure and the way that it was constructed, it'll never be secured. The internet is essentially broken. What the blockchain is doing is it's going to bring and create the secure data transport protocol. And so the internet is only fulfilling one small part of its potential because of the security flaw. When you fix security, the internet is gonna reach its full potential, which is gonna be, I think, 10 times greater. Every industry in the world is going to be affected and it's going to be a beautiful, beautiful thing. See, are you saying the internet will be gone as we know it? Yeah, this is the new internet, it's the upgrade. Huh. So the entire internet's gonna go, I think. So will websites like Amazon, like Google, disappear, or they'll have to go on the blockchain? Well, they're gonna have to go through their process of upgrading. And anytime you have a big transformational event like this, read the innovator's dilemma. You know, you've got the incumbent and you've got the new entrance and there's gonna be a meeting of the minds there. But my view is I help the incumbent industry as much as I can and I help the startup community as much as I can because if anyone is successful in changing the world and making it a better place, we all win, so I help everyone. I don't ever ask for anything. I give everyone in the industry, I can't help every person that I have as much time in the day to do. I don't sleep because it's such an inspiring thing to do. You're doing this free, thank you for that. I believe we have an incredible opportunity here to make the world a better place. And back to that being a billionaire, this is the opportunity to be a real billionaire and when you start to understand what's going to happen in the world, you eventually wake up and you go, wow, what I'm working on right now isn't gonna matter in a little while. And then you just, people all of a sudden, I'm watching it happen in droves all over the world. Once they come to this realization, it's like they can't get up and live the life that they had anymore because it's no longer inspiring. Because they realize that whole system's gonna change and now all of a sudden they're like, okay, I've gotta really rethink everything I'm doing. And it may stay in that same industry using those same skills, they have to be the one to do it. And that can be at the incumbents level, that can be at the startup level. When he says incumbents, we're talking about corporations, large companies. Yeah, and the big companies are gonna also drive a lot of progress too. So these big banks, should they be scared?  Do you think they should be scared? I mean, I think they're doing the right thing. I mean, the analogy I like to use is we used to make our phone calls over twisted copper wires. Yes. One day it switched to voice over IP and everyone said, hey, this is gonna be the end of the telcos, and on and on and on. No, the telecom industry became the biggest beneficiary of the technology, massively cutting their costs in their middle and the back offices. And the banks are gonna do the same thing, they're smart. They can benefit greatly from this technology. And yeah, I mean, when I was asked by banks early on in the space, because I did a lot of introducing the ideas to them, they'd ask me, is this gonna be good or bad for my business? Yes. I said it's gonna be both. It's gonna be balanced.  Some portions of your business will get better.   You can't stop innovation. We are living in exponential times. So you have to get with the program and that is, you have to keep evolving. And we're accelerating, which means you have to evolve even faster than you've ever evolved before. And that's the kind of this really interesting thing about the period and time in which we live. There's this Japanese concept of kaizen, which is to continually improve. Approach every situation and don't just get the job done. Do it as well as you can and always strive to do it even better. Continual improvement.  When you stop trying to live a life of mediocrity, I mean, when we came out of World War II because we won, because you have that pyramid of good, fast, cheap. And we won the war by being fast and cheap because we were able to mass produce and that won the war. But post the war, we kept just doing fast and cheap. And we've basically started to build, we live in a world of mediocrity where people are not making things incredibly well. We don't need to be fast anymore. We can be good and we can be good and fast but it won't be cheap. We can make it good. The Japanese grows up. It should always be good. And there's this other Japanese concept of Ikigai which is when you figure out what you love, what you're passionate about, what you're good at, where you got the skills. I'm never gonna be the NBA player. Figure out what you're actually good at too. And then figure out what the world needs. In the center of that is... So what you're good at, what the world needs. And what you love. And in the center of that is what you'll find is your Ikigai, that's your purpose. And what's your Ikigai? We've got multiple, I call them superpowers as well. And so the superpower that I'm using most right now is I know how to take complex ideas and distill them down into words that are generally easy for people to understand. I make my objective being able to teach a child. And if you can do that, you've started to hopefully master a skill as the Japanese do, it's about mastery. It's an Ikigai is how you get to this point. And so I'm a storyteller, which makes me an evangelist, a first follower of Satoshi and the many other great creators like Vitalik and Dan Larimer and Gavin Wood and many others. There's a lot of incredible engineers, incredible cryptographers, people that are making the code that's going to change the world. I just try to support these people that are operating from a place of good intention. And so my purpose though is everything in my life from digital currency to everything I've done kind of just uniquely positioned me to obviously do well in this. Because you've been in virtual currency since when? 90s? 99, yeah. What virtual currency was back then? It was gaming. So I was a teenager and I was a kind of a pro-ish gamer. He was also, a lot of you will remember him from Mighty Ducks. So he's also a child actor. We didn't put that in the, just a lot of people know that. Yeah, it doesn't, yeah. I'm still an actor. I just don't do scripted things anymore.  The world is but a stage. You don't stop performing once you become a performer. You don't stop using your superpowers. You know, once you've developed them, they become part of it. Now you're using it for more powerful purposes. They become part of your toolkit of things. I mean, you just keep learning and you just kizen everything. And you just keep showing up and give everything your best. So yeah, the gaming stuff, 99, is collectible card games online. And so I was becoming the main trader and I bought, I called it in Menceller and I called the game company. I'm like, I'd like to buy your virtual packs of cards. You don't think Pokemon or Magic the Gathering? And I said, like comic book shops to do our baseball card stores. I said, that's what they do in the analog world. They're like, oh yeah, that makes sense. So I did that first deal in a small game that never got more than 5,000 users. But then I came back when the first MMORPGs were emerging, you know, all online and EverQuest. And then I built the whole sort of market for that. And I built up to buy and sell the digital currencies in games like World of Warcraft and Second Life. And I became the primary market maker for the world's digital economies or virtual economies. And I built up a supply chain of 400,000 people in China in my early 20s that were playing games professionally to mine digital currency. I did tens of billions of dollars of business, lived all over the world. Hong Kong, Shanghai, Beijing, Seoul. And we met what, we met probably 10 years ago through a mutual friend who was in Tiger 21, which is an investment group that you were in. And we went to dinner and then we reconnected almost a decade later. When did you start with cryptocurrencies? As we know it, the big coins. Yeah, so I got familiar, not as well, probably as I should have very early on. But it wasn't until 2012 where, because when I was first approached and asked what my opinion was, I was like, Bitcoin, this or something like it is the future. I just don't know if the future is now or 25 years from now. Market timing is something that I try to be aware of, because that's kind of the main thing you gotta get right. It's not hard to see the future. Getting the timing right is the hardest part. And so I got in full time in 2012. That's when I said, hey, the future's now. Yeah. Good time to get it. Done a lot of things. Let me ask you a practical question, because Zach is here. His uncle was given about $1,000 worth of Bitcoin I don't know, a couple of years ago. It's probably worth 500 grand and he cannot access it because he can't remember how to get to it. What do people know, this lesson, this is a lesson on security, remembering your hash or 10 words that was worth. This is why you have backup. She has, you need to write these things down for us. So how do you think, a beginner, what do you need to know? Well, in this specific case, does he know what wallet he had? Probably. We will find out. Yeah, but let's start, it's an investigation. What do you, what does he remember? That we was using a blockchain.info wallet. Did he have a Coinbase account? You know, try to figure out what that is. Go through his emails, see if there's any sort of. I calculated it's worth 500 grand. Any account registered to that email address and you know, with a little bit of research you may find that the answer is there. But let's talk preemptively for someone who doesn't want this to happen to them. How do you, what's the basics of storing everything? Yeah, so when you set up, security is having two-factor authentication. Make sure that you've enabled that. Use a Google two-factor authenticator. Use the Google app. That's the, Better than SMS or anything like that. Definitely don't use SMS, SMS is not secure for anything. Never use SMS again. Google authenticator is the easiest. It's an app you download and it changes and gives you new codes all the time. So make sure you, you gotta get the basics of security, right? And the new world security is important because we now have secure systems, but it does require learning a new skill. And just have it on your phone. It's like learning to use email for the first time. You know, it's just a new skill and it's gonna serve you well. So put a little time into it because it's important. And so yeah, get the two-factor authentication stuff figured out, do not use SMS. And then when you open up a wallet, it normally has a pass phrase, something of that nature, or you're gonna get the two-factor auth, QR codes or whatever it might be. Make sure you get those numbers and things, store it down on a piece of paper. Would you do it on a piece of paper? Put it on a piece of paper, put it in a safe, you know. And it's safe in your house. Yeah, you don't want to save it as a photo or a screen capture because if someone hacks into your photos, they, you know, you don't want those things. What about something like LastPass? Not for something like this. I mean, I wouldn't use your private keys there unless it's a small account for convenience. If it's in a consequential amount of money to you, then, you know, take what- Piece of paper. If you want to do things well, yeah, just make sure you store that, put it offline. And if ever you have a problem, you know you've got redundancy. Yeah. And that's why I say have, you know, multiple of the hardware keys. Yes. Have one in a backup. So everything you're doing here, Have redundancy. You want something offline and multiple places, especially if you have a lot of money because that's a nightmare. At what percentage, I've read a percentage of crypto Bitcoin that people can't access. It's a large amount that people are forgotten where they put it. Yeah, it's a large amount. I mean, 10s of millions. Probably 10%, no, it's there. Hundreds of millions of dollars. No, billions, no, yeah. Billions, oh man. I read an article, I got to ask you this. It came out today, theorizing that Elon Musk is the man of mystery behind Bitcoin. You don't have to, you may know a lot more than you can say here on camera. Any comment on that? I've never, you know, Elon is obviously doing some of the most extraordinary things in the world.  It's all blue sky above you. Anything you dream, anything you can imagine you can do. Yeah. You know, the power is within you. Yes.  Yeah, and so. You can buy a Tesla with it. I mean, doing what he's done for electric cars, looking what he's doing for solar, look at what he's doing for space, and you know, and now look at what he's doing with hyper-loops and boring. I mean, he's the man, but I can't see that has any possibility of- You don't think that's true? Well, no, he couldn't. I mean, as much as he's the man, there's only some, and SpaceX, I mean, there's just only so much one can do. So much. And he's not been this guy. I mean, but he obviously was part of PayPal and you know, been a player in this overall broader spectrum, at least the fintech part and others, and just being a great mind. I mean, in inspiration, and he's helped obviously many people. I mean, he's made a lot of the entrepreneurs in the world, you know, the entrepreneurs today because he's inspired so many. So, you know, obviously PayPal and things led and inspired, you know, some of these types of transitions. You know, we had to go from the old world offline stuff to the online stuff and then figuring out how to continually upgrade it. How do things continue to evolve? Yeah. Let me ask you this. One of the questions I did this poll on the way over here. What coins, there's so many, there's thousands, there's the main coins, the Bitcoin, the ETH, the, you know, Litecoin, Bitcoin Cash. Are there other coins people should be watching? Do you see, is there gonna be a world where there's a million coins? Every corporation, Apple will have a coin here at every place you use. For a beginning investor, let's start with this and then go big picture. For a beginning investor, would you recommend that wants to put, let's say $10,000 into crypto? Do you recommend a little bit of that into the main coins that have liquidity and then some of the alternative coins? Well, I'd say don't invest in anything you don't understand. And so start with the big coins because those are the ones with the most liquidity, they're the safest. And just work your way down the list. You know, start, go to CoinMarketCap or CoinCap or any of these sites and start at number one and just work your way down from coin number one, three, five, 10.  But I wouldn't recommend investing in anything you don't understand. So start with the big stuff and then as you learn more, try to understand that the rabbit hole runs deep. So just keep kind of learning and you'll see amazing things emerging before your eyes. Do you think people should trade coins actively? I see people there, whether it's pumping them. If you think you're a trader, if you're a Wall Street trader and that's your competency, I don't trade, but if that's what you do, I can see it. If you know how to make algorithms, if you're a quantum, whatever, if you're good at it, there's obviously money to be made, lots of money to be made in this space. I don't like trading because when I get involved in a project or I get behind a project, I wanna be fully in support of it. And to trade it is actually to kind of short the project that you believe in because I can make a couple extra bucks by riding it down and actually causing it to go down more because I added to the negative pressure. I was selling it in the market and certainly as someone of influence, I don't wanna be doing that. And so I don't trade for that reason, but I don't judge others for doing what they do if that's your talent, do what you do. But I wanna be behind a project until I'm not. What do you think of Ethereum? I love Ethereum. I've been a huge supporter of Ethereum. I'm friends with very good friends of most of the founders. My firm was the first to invest in an Ethereum venture deal. I've been one of the founding board members of Mastercoin, which was the early iteration of kind of what Ethereum in some ways evolved into. We did the first ICO. In June of 2013, I'm a huge fan. I mean, Vitalik and Ethereum has done more for the market in the last couple of years than anyone. So for people listening that don't- Other than Bitcoin. And Ethereum has done other things to expand the market. More use cases than Bitcoin. Right, the smart contracts. Bitcoin Cash, Bitcoin Gold, the classic. Someone listening that doesn't understand it.  How do you make that simple for people? People are going, what the heck? Do I bet it was Bitcoin Cash, is this what? Forking, forking is good. Forking is evolution. We're all here because of forking. We are a fork of our parents, DNA. And this is, forks are generally consensual. And for that reason, they're generally good. But then you have contentious forks. And it's the contentious forks that create a lot of the problems because you have a big disagreement in a community. And that contentious fork, watching it because it's open source, you get to see how the sausage is made is messy. And it sometimes leads to extinction, but that's sometimes progress too. I support all the forks where the people behind it are operating from a place of good intention. They're multivariant splits. And if the community wants to split, so be it. If you own any of these fork tokens, you don't have a strong opinion. I would highly recommend you don't sell them unless you know, again, have an informed opinion because you don't know if Bitcoin cash could be a winner. I mean, certainly I'm not saying that's the case, but until you have an opinion, you shouldn't be doing anything. Hold your tokens till you know. Do you think there's a chance?  Yeah, which is kind of how we align. I'm all about knowledge and learning and you're a learning machine. Bitcoin theoretically, the main Bitcoin could go down and Bitcoin cash could go up. Bitcoin gold, do you think there's a chance or very likely chance that all of them go down to nothing? Or do you think it'll be one could go down and the other would rise? I mean, yeah, Bitcoin could fail. I mean, I don't know if Bitcoin's the friendster, the MySpace, the Facebook, the Instagram, Snapchat. You know, I think it's got a much greater chance of surviving than those did, but something else could come along that's substantially better. I don't see it as of right now, but I would never say never. It'll be a binary outcome. Bitcoin will go to a million bucks if it succeeds and if it fails, yeah, it's gonna go down but it'll take a very, very long time. You think it's conceivable Bitcoin goes to a million? Yeah, I mean, if it is used enough. So let's talk, are people using Bitcoin? Like I said, Tesla is being used in countries in Africa, being used in Africa, some cryptocurrencies. Curl like wire transfers of a store of value in places like Zimbabwe, Venezuela. Yeah, places where you've got currency control, keep in mind there's three billion people on the planet that have no financial services and other two billion people on the planet with limited access to financial services. One aspect, and it's almost a small aspect of what this technology is doing is it's going to democratize the global financial system in a way where every human being on the planet is going to have equal access and the least fortunate billions of people on the planet are gonna be the biggest beneficiaries. Get involved and you will be a billionaire by my definition because that's the type of impact we're going to have. I mean, and if that's not a reason to make you want to get up in the morning, you know, I mean, come on. So you're saying that? This is the sort of stuff that you want to find joy in your life, go and when you get all these things right and you find a way to give your gift and contribute to something beautiful, I promise you the money and everything in life that you need and want will most likely come to you. Yeah, so these unbanked people, they're people in third world countries, they're people in the U.S. My dad was unbanked. My dad from Harlem never had a bank account in his life or a credit card. He didn't trust the system. He kept money in his wallet. I took him to a trip to Puerto Rico once and he lost his sock that had $3,000 in it, which is a problem with being unbanked, you know, that you can get robbed, you can have this happen to you. So you're saying this thing that we call cryptocurrency Bitcoin blockchain theoretically is going to take these 3 billion people who, did you know right now the top 10 men in the world have more money if they add their net worth together than the bottom 3.5 billion people in the world? You think crypto blockchain has the potential to change that? Yeah, I mean this is one area where it's one of my only disappointments with Bitcoin is there's still a lot of concentration, you know, if Bitcoin were to become that big thing, I mean, yeah, I'd be one of the big guys in that world, but that's the only thing that disappoints me. I really want to build a system that's fair to everyone, but I think that Bitcoin is still a big improvement over what we have and the world can change in increments, you don't have to go from A to Z and it normally doesn't. Things normally happen in more of a hybrid type of things, evolution goes through phases, as you continually upgrade, leveling up, I'd like to think of life as kind of like a video game. People ask me, is it too late to get in? Bitcoin shot to 11,000 not too long ago is at 4,000 and people go, is it too late? Oh, it's, if anything, you're too early. Really? I wouldn't say you're too late, it's called, don't get fear of missing out syndrome, don't feel the need to just dive in, make sure you know what you're doing, don't rush in and what I always tell people is, like when I'm giving talks for these days, I'm like, hey, if you want to pitch me, don't walk up to me and just pitch me your deal.   That's not how I want to transact. Right. Establish a human connection, so I think of the world as a game and I'm the game master of my game and I can give you the first tip on how to get through level one. Level one is don't start out as the first thing you do, pitch me, don't just walk up and be rude and interrupt someone else that's in the middle of something talking because you want immediate attention. Don't be a person that's like, what do you do when you're at an event? All of those things are basically saying, what can you give me? Yeah. That's people that are just basically going around entitled and just trying to take from everyone versus doing what you're supposed to be doing. So you fail right out the gate, if you pitch me, it's like thawing the first, press the button and floppy birds. Most people do that too. And so if you walk up to me and you're like, yeah, they do and that's why I don't invest, but I'm telling them now, this is a good lesson. I'm teaching you, I'm giving you the cheat codes to kind of my game anyway and this game is probably true for lots of other people. Whether they've thought it through and gamified it in their minds, it's a practice they've probably already put in place.  It's just not interesting to any of us.  If you want to talk to Brock, first go to, first definitely go to Burning Man. I can tell you that. I'm always burning. You and your wife, I've gotten married at Burning Man. How many years in a row? Remaried, or what is it? Well, we got married once there, two burns ago. This year we got married in Ibiza. Oh, okay. We get married every year, but it's a different place. So it's not always at Burning Man. What's the idea there? Is it redoing your vows? Is it just? It's called, I think it's always fun to celebrate. And so it's just another reason to party. It's a reason to throw an event to celebrate love and it's for your friends more than anything else.  What is it, a farm? Yeah, yeah. Is it one of the big, you told me it's a- 60 acres. 60 acres. We're building something magical out there. I'm working on also building a kind of a city, a big city somewhere else. Will you say where it is or not yet? A city, yeah, I can say Puerto Rico. The 51st state with like 180 billion of debt, 35% unemployment, and now a hurricane hits. I mean, it's devastating what's happened there. I'm moving right now. Really? I'm gonna be moving down there with a bunch of my friends shortly because it might just be temporary for a moment, but I wanna go roll up my sleeves and get some work done down there and help out. I think those people need our help and I think that we're capable of so much. Yeah, and it's almost become a blank slate now. Yeah, and so in these times of crisis, the Phoenix can rise sort of from the ashes. When you experience great loss, it creates an opportunity to upgrade, but where you can make these giant trans quantum leaps of upgrades because you basically lost everything and so you have to start over and when you have to start over from scratch, you would do it very differently than if you have this big thing that's kind of been building on top of itself for ages and ages. So in this horrible event that's occurred, there will be a great opportunity that emerges and I wanna be a part of helping the Puerto Rican people, helping people that are in need. I am here on this planet to live in service to humanity. I see an opportunity to make a difference in the world and I'm devoting my life to these types of things and I'm an American and I love my country. I don't love everything, but I feel incredibly blessed to have been born here and to be given the opportunities to be where I am sitting here today with you and eternally grateful thank you. I'm glad that we've reconnected and been spending time together. You do great things. I love who you are and I love what you're doing in the world, getting the word out and sharing the knowledge and the wisdom in ways that you can connect with mass. The masses is a wonderful thing. You have one of those incredibly important roles and great responsibilities and from what I see you're doing great work. I commend you. Well, I appreciate that. I'm trying to, this is the next thing that I think needs to get out there and one of the things that people are asking me is, you know, these ICOs, you've done the biggest one, right? Aren't you the, isn't EOS the biggest by far? I think that's what they say. Brock's humble, but it is the biggest because nothing's done over 500 million and you're not even done because it goes to what, May or something of 2018? June 1st. June 1st. So. Do you know what the logo is? No. Oh yeah, you showed me. It's the, it's the chest of Hedron. It's the sacred geometry of the heart. Yeah. You, you actually, he was nice enough to give me. I have it. You gave me a necklace. Thank you for that, by the way. Are most ICO scams? I wouldn't say most of them are scams. There are a lot of scams. Anytime you get this big of an asymmetry of information where the, you know, the difference between the people that have the knowledge and those that don't is so great. I mean, when you get it, you just don't understand. Yeah. You can't get scammed if you don't invest in things you don't understand. But there are ICOs we think that are solid. Yeah, of course. Yeah. Like all things, you know, some, you know, there are good deals and there are bad deals and you need to do your research and that's why don't invest in things you don't understand. You can't get scammed if you know what you're doing. Yeah.  Don't like rush in and let someone tell you what to do. What about entrepreneurs that are or yourself, take responsibility for your life. What about entrepreneurs that want to raise capital? I think it's fantastic. You think an ICO could be for them? So the ICO is basically, on a theory, and the ICO is essentially replacing most of venture capital. Yes, it's bigger than, what's the number? It's where you're crushing it. We're over 3 billion. I mean, we're doing like four or five times what the early stage venture is right now. I mean, this is going to crush it all. It's going to crush it. It's the world's changing. And there's an opportunity to get involved. If you're interested in building the city of the future, get to Puerto Rico and be a master and be ready to roll up your sleeves and build. I might come down. I'll pop Puerto Rico.  We're burners. We're guys that can build cities in the middle of desert. We can do things that very few people in the world can do. And why not go down there and construct something awesome that creates all sorts of opportunity for the Puerto Rican people? To support the Puerto Rican people and any of the indigenous tribes and old ways of being and making sure that they have the freedoms that they need to still be respected with things like Standing Rock and such going on today. I'm spending a lot of time thinking about the indigenous tribes, most of the world's resources, most of the world's minerals and water and things that we need to survive are on the lands of the indigenous people. And we think in our big cities that we're somehow superior and that you have these people that have old ways of being that are just incredibly beautiful. Yeah, Columbia, too, where you're going. And all of these places, such people that have been doing this for so long and doing it so well, that because it looks primitive to us because we don't understand their ways and they've learned how to live in harmony. They kind of have had their avatar sort of. That's where they are. We're not necessarily the advanced ones. For somebody who wants to do an ICO and they're educated themselves, do you think, number one, that this is a viable replacement of raising capital going up to Silicon Valley? You answer this, yes. Absolutely. Absolutely. Two, do you raise outside of the US? Because the US, the SEC is coming down. I know you guys did, I think EOS is outside the US, right? You've excluded everybody. Yeah, we don't even talk about the token sale in the US. Yes, we exclude the US. But we do encourage US developers to build on EOS. You don't need the token to be able to use the software. Yes. The software is an open source software available to everyone. And so we encourage you to. Do you recommend most people do that, raise outside of the US if they're doing it?  And the risks of making a mistake are really high. Yes. And so I did it with the B-CAP deal. But I generally don't recommend it, because the US is where most of your risk comes from, but only a small amount of your capital. Are you willing to leave some money on the table to sleep better at night? Yeah. And it's not that you would do anything wrong. The well-intended ICOs are doing this to the best of their abilities. And they're being as thoughtful as they can be. But the risks are high. So you have to make that decision for yourself. I encourage people to do the US if they are doing it correctly and they're properly, legally advised. But if you're doing the US, really know what you're doing. The risks of getting it wrong are severe. Yeah. It's no joke. Yeah, SEC is not. I know the orange is the new block and all. I know I wouldn't look good in that color. And I don't do anything bad. I look at everything I do. And I try to also look at it in the future with the benefit of hindsight if things go certain ways where, even though I didn't do anything wrong, it could eventually look bad. Because some sort of said, I try to think through all of the possibilities, because I just don't ever want to do something that could be perceived as bad. And it's hard. Would you do it as a utility token? Versus, because you have to securitize it. In general, do you think people should be trying to do utility token? I mean, it depends on your token. Each token sale is different. Each market is different. And you have to look at each deal on it. It's kind of individual basis. Yes. And so you have to ask yourself, this is community building. In designing your token, are your users, is your community better suited if it's a security token or a utility token? And always do what's best for your users. Always do what's best for your community. I like to call the ICO the initial community offering. Okay. Not just the initial coin. So you think, in general, there's a little bit too much greed right now? Yeah, but this is what happens when you get in these emotional cycles. And that's why you should have a little bit more. And you need that greed, though, to get people in. Yeah, it's driving growth. I mean, these are the cycles of things. This is how it goes. Yeah.