Come back to the independent investor channel here for our weekly update on Aduro clean technologies. Very important for us to continue to deliver on a consistent message here with Aduro at a time where it's probably the most difficult to do so. Even with the marked progress in the company. Over the last couple of years of covering the company, at least going back until fall of last year. It has been one of the stories that we know is going to unfold over the long term. Aduro is not one of those companies that you're going to be able to just trade around a quarter. It's not one of those things that you're going to be able to look at and catch some sort of wave height. Aduro is a value company. And I want to put that out there first and foremost, I've disclosed and for you guys that have made your way to the message. For the first time. I'm a bullish share owner the company. With that, I try to deliver upon a neutral perspective. If there is negative to report out on in my perspective, I will share that convey that to the grander audience. I don't think it does anybody any good to come online and try to generate hype around a name like this because I think Aduro. Generates enough activity and turn around the name why because their technology is that good. It is just that good. Coupled with the fact that Aduro is unknown amongst the investing community and I do mean unknown. The share volumes, albeit have increased as I have monitored the stock action over the last, let's say 18 months or so. But they are not even close to where this company needs to be to reflect the current opportunity and the value proposition that Aduro brings to the table. What does it mean to be an Aduro investor. I'm going to convey a few things for you and I share these things openly so that you can glean over a 30 minute video how I truly feel about this investment for me. And how potentially this could be viewed by you in this unknown opportunity. Unfortunately for a lot of people this will fall on deaf ears. This this will be a proven story until it's too late. It will be a too good to be true story. I totally understand the skepticisms and you're entitled to feel how you feel. I've said before, and I like to set a good baseline. My intent here is not to persuade you in any direction. I think we've gone beyond that with the social media content creators at least that I associate with. You're going to get a different viewpoint on different equities. There's a few of us in the space here. Myself and Mariush, Penny Queen, Carbononix, just to name a few who cover the space and have been trying to convey this message as objectively as we can over the last really the last couple of years where Aduro has thought that it would be or it was timely enough to actually start to present their story to the forward facing audience. Aduro is a publicly traded company. I want to remind you guys just this week I did release my video cross comparing Aduro to the other 20 companies that were named in the advanced chemical recycling space, very telling. Not so much one of those things to where I was excited to see Aduro named with some of the who's who in the plastic recycling industry, which they have earned that. I felt like the company that they were put in was very vast, which would require investors to be very careful. Be very diplomatic and very cautious in approaching this developing space. We've known that there was a need in the plastic recycling space for a long, long time. The fact of the matter is the chemical recycling and advanced recycling methods just have not existed. We have relied on traditionally ineffective ways, specifically paralysis which I've identified in the majority of the companies that I covered in that list of 20 that Aduro was named with. The problem with that method is that it has been proven out to be extremely inefficient, both on the production side, as well as the economic side. Okay, it costs too much to run that system. Why with the light regulations and oversight it it's just been cheaper to allow those hard to recycle plastics to be subjected to our landfills and our oceans. And that's just the way of things. That's the way things have transpired over the last, let's just call it 50 years and or more as this problem has compounded itself and plastic produce production has increased significantly every year which means that more of those plastics are subjected to the staunch reality that those hard to recycle plastics could not be recycled. The method by which we're being used to to actually recycle. Those those hard to recycle plastics have just been proven proven to be inefficient. And so the stock in Aduro has modestly raised this year. I think the stock last check was up around 17% this year. There's an increase in what I feel like is a little bit of notoriety on a lot of forward facing information that Aduro was released to the grander audience. Aduro has hit this thing hard. We're generating revenue on their customer engagements as we speak. Aduro sports three, not one, not two but three verticals my friends that two out of the three best of my knowledge and my review are actively generating revenue now. So revenue is not something to jump up and down about they are in the testing phase and customer outreach phase and the testing with each of those respective clients and we want to make sure that Aduro has ample time to continue with those customer engagement processes as they are in now, but to be generating revenue with such a huge adjust addressable market is promising at at at the least it is promising.  Okay. I have significant wealth put aside in investments that are in the portfolio, they'll remain there. And they'll remain there for my life and into follow on generations. Aduro for me really gives that value opportunity before the opportunity is discovered. I really want you to think about that for a moment when you are listening to my video that I did this week on the other competitors in the space minus Honeywell and Chevron I really didn't include them and I'm share owners in those wonderful companies. But the other 18 as we were able to glean through the list and parlay half of those companies as private companies. And the other half having gone public here into public markets and have just been on an absolutely atrocious ride, subjected to yeah, headwinds in the macro economic environment as disclosed by most every CEO in their CEO comments. And I think furthermore, there was a timeframe and 2020 and a little bit before that, where that we were, we were unfortunately subjected to market hype. And a lot of these companies just thought that they could just get in and acknowledge that they were getting in over their skis financially, and that that would somehow make it up and the environment has has flipped in that these are very very difficult markets. Now, companies are not being given favor, they are being provided scrutiny in in in scrutinize their individual ability to stand on their own. Now if they want to seek out financing a lot of these companies are actually seeking out financing rounds and the tunes of hundreds of millions of dollars and in some cases that matches or almost matches their total market cap and valuation at present. So many times, if you're looking at it from an investor's perspective, I mean you could be investing in a vacuum for many many years with such high cap X, and OpEx to support these initiatives, all the while, the purity of the initiative is quite good. The promise of the plastic recycling space is quite good. I just fear that a lot of these companies have got in way way too quickly and and subjected themselves to, you know, massive, massive debts, and to service those debts some of those contracts I mean I look at pure cycle and the debt servicing on those contracts that I've written are scary and, you know, the bowls of those companies are going to say well they're going to make up for it in the right in the right time by selling their product. As a lot of the themes of the companies that I reviewed over the course of that review would suggest that a lot of those companies have finalized facilities that are actually producing that can be sold and reused to the to the circular economy. My friends that's a fact and that's an exciting fact. Okay. Whether or not those systems are going to play out in the long term by deploying what what I contend to be those more legacy types of technologies. The process being that in in that the high energy and high input, and the high cost to run those operations, even make sense economically. Those numbers are not disclosed to share owners to understand how much how efficient they're actually being by deploying this process is they just want everybody to understand that they're going to continue to spend hundreds of millions of dollars somehow some way sometime down the line that it's going to pay off. And a lot of these companies shoot I saw revenues on one of the companies at $56,000 they had losses of 5.75 million. That was a reoccurring theme where they were just dabbling in making a little bit of top end revenue by selling their product, but the but the bottom end was mounting losses to the tune of multi millions. So they can flip the script on this I wish them all the best me personally I'm not invested in those companies, but I look at it from a diplomatic eye because I was attempting to compare what they had with what Aduro has and quite frankly I was able to make no real comparison and it was quite frankly unfair to Aduro to to include some of those other companies that were listed in that that group some actually being subjected to current litigation.  It's up to you to do your own due diligence on this but certainly looking to gain consensus on whether or not I'm completely off my rocker and looking at this opportunity and looking at the value proposition which in my mind looks very very rich at this point. Now, I'm on an island with that perspective and there's a few within the network who would share in the Aduro clean technologies opportunity being very very bright, but it is the most difficult time to do that when there is no organic churn in the company. There's no buying interest right now per se on the environment. Okay, the last stock transaction that I heard just came as early as this week with the CEO exercising his right to 650,000 more stock options that he had from from many moons back I'm happy for the guy offers done a fabulous job with this project being co founder CEO, along with Marcus and I think they deserve everything they've got coming to him. You know you start selling stock on the open market I might take a little bit different of a twist here, but as long as this man is accumulating shares in his own company I think that's a bullish sign, all the way across the board and it's not just the top guy. It's the upper management across the board that just over the last six months have been doing nothing but accumulating shares and to my knowledge, there's not been one red cent sold on the open market of this company I think again that speaks to the conviction of the management and how hard they're working, but also, it's kind of easy to glean their belief in this project going forward, and the mission kind of speaks to itself on what aduro is trying to do and tackling this this this plastic problem here. I've made a couple notes here and I want to get this in under the wire and share with you guys. What will move the needle for aduro. Okay, a lot of people will come to the channel social media and I take a lot of scrutiny on social media. I take a lot of positive and that's just part of the territory that comes from putting your opinion out there on social media and trying to generate some churn around a topic that I do believe is is is warranted. But what is going to move the needle for aduro. I think what we have been subjected to over the last three years has subjected investors to be a little bit gun shy, I am one of them. You know, there's been a lot of bad beats coming out of you know the SPAC era where the vast majority 99% of the SPACs no longer exist or they have just fallen on such hard times that they'll never recover. Furthermore, coupled with high interest rates, the perceived lack of availability of financing on the markets and really just the the dry up of pure animal spirits in the market that we enjoyed in the back half of last decade. It has just not materialized here in this new decade. Do I think things are slowly starting to transition toward a more positive vibe in the market. I do. I do. I think eventually these good companies will win out and it's not going to matter what the environment calls for but I tell you what good companies will get scrutinized in unfavorable markets as opposed to be given favor. If if investors are a little bit on the fence as to whether or not something is going to materialize or not and I tell you everything in the microcap space is getting scrutinized there are good companies doing good things right now that are not being provided do favor for that I actually think a lot of people are going to be doing good things. I look at the performance this year I'm happy about it but 17% it really does not speak to the opportunity it does not speak to the technology and it does not speak to what over and the team have done in 2023 in way of building out the baseline for the company and really accelerating their customer engagement program and I think 2024 is going to provide some of those aluminum catalyst I'll talk about that in just a moment. I think a duo really could and will over the coming 12 to 24 months provide a little bit more color around their status financially and their inability to seek out new debt financing on the market. Aduro really separates itself. I, you know, Mina Bache, I think is one of the best in the industry. I'm not alone in that opinion. It's just an absolutely phenomenal job of navigating this company through what I feel has been tough markets now a duo has really performed well. I will say that it is, it is upheld its stock performance of the last, let's say 12 to 24 months going forward I don't expect any less from from from from our CFO in in navigating and really looking to put financing where it is necessary to do so, but to do so carefully and calculatively I've been given no indication that share owner value isn't right top, if not the top priority of upper management. And it is in it is really reflected in the company's performance in establishing a baseline and hope for the future in putting themselves in this position in not having to seek out financing in a market that may be may view that as a as a negative attribute that may be perceived as, you know, more desperate or needing that financing. Those companies that I reviewed in that list of 20 some of them are desperate. Like they have to have the financing to continue to operate. And some of them are within 12 months of going illiquid. That that's a scary thing. So looking at it from an investor's perspective, I would like to see more fortification on the bottom line. I mean five six million bucks or whatever I duo has on the books is a far cry from what I want to see for available cash on the books certainly, and they're not in a time right now where, you know, expected revenues on the top line are coming from multiple multiple sources. We'll talk about that as well. What is their ability to navigate what I would consider to be fairly lean times they've been successful, you know, in their stock offering packages and getting private financing along the line here to kind of help a duo make possible what they've been able to do in the open market so far. I see no reason for that to actually not get easier into the future. So those are a couple of things that I think may end up moving the needle in giving the share owners and the grander financial some sort of, of pause in being hyper critical over a duo's current financial position. Alright, the last thing I will talk about is what I expect of the next 12 months for a duo this can be fun. This is going to be a little speculation. It should drive a little bit of discussion and I invite you to leave that discussion in the comments below where do you think a duo is going to go. I mean, this is part of the fun of investing investing is fun. You know, making money as a byproduct I've invested my whole life have made a lot of money investing. It's a byproduct of investing yada yada. Okay. There's no guarantee in investing. But I tell you what when I look at this a duo opportunity top to bottom I don't see a lot of negative. And the deltas that I will share with you now because I think sometimes I watch a duo videos. You know, we're positive across the board top to bottom. And I've always been taught to try to use your imagination in trying to apply the what if what if a duo can't do this what if the technology isn't as prescribed. What if they do incur a situation where they need to raise financing during a lean time what if what if what if now this is somewhat speculative and somewhat presumptuous on my part but I think it really speaks to kind of the not the bearish thesis but the other side of the coin when we're looking at evaluating a company fundamentally. Okay. And fundamentally, I saw some things out of that list of the companies that I looked at and I was like man I wish a duo had that right now. Now I give a duo a pass now based on the timeline that they have provided to share owners in really just kind of understanding that those those things are forthcoming, but they are not here now. And they have been disclosed by other companies, even in the private markets right which means nothing for me as somebody who wants to get a hold of a privately publicly traded company as early as I can in the game because that's where the money is made. Let's be real, those private companies, they're going to come public someday if they ever do. And those are going to come public at multi billion dollar valuations because right now they have plants established they're making revenue. They're making product, however efficient that might be right, but one company specifically I believe it was plastic recycling. Yeah, I believe it was plastic energy that when I went on their website, I saw there was 10 products that their circular plastic made by plastic energy was contained with. And that was something that kind of set me back and put me at pause a little bit you know that'd be awesome to see a plastic product right as much as the plastic products that we have in our environment and how how much we rely on plastic, it'd be awesome to see plastic produced by a duo right this plastic is circular plastic produced by a duo. I just think that'd be awesome validation because I think right now we're stuck in a little bit of a, I've done my due diligence up down. I've visited the facility at a duo for crying out loud, and I would venture to guess that I don't think it's common knowledge out there for the would be even share owner in the company, let alone people who are making their way to this technology for the first time, and can explain with some level of accuracy what hydrochemical technology is. And I think everybody can wrap their mind around even a vial of produced product on the back end of the reactor. But I think when it really hits home and really kind of brings home that circular economy that we're all seeking. You can look at a product, a plastic product and say, Okay, this was as a result of the aduro process. And I think those things are inevitable and certainly not to rush things along. But some of the companies out there, especially on the private side are are in that scale. And it's up to you to delineate whether or not you think that those are worthwhile processes, whether or not by rushing to market was in their best interest. But I think for aduro, if I was going to be a little bit critical, I would say to drop the hush hush. Okay. Now, I say that tongue in cheek, because I want to Duro to exercise their right to hush hush right now, release information when it is appropriate to do so. So, over vikas has talked about this and I respect that 100%. Here's the thing, you got public companies out there announcing finalization of full scale production facilities you're talking about private companies out there that are sharing information on the public forum, even though they're private companies with regard to their approach to bringing in waste plastics to a facility and turning out that waste plastic to their proprietary technology and then rendering a product that can be sold and is being sold on the back end. When I look at aduro, it's not quite as defined for me. Now, this is my objective opinion, and I would put this into let's see category. And when we start to see these customers that, you know, half of the customers are secretive that we that we actually come out and both parties feel comfortable making that solidification in public markets and what that's going to look like in real time I really think is going to embolden this message. So, albeit that we in 2023 have been very, very hush hush, especially about the game changer program I totally get it. I would look for those to start to blossom and materialize as we're being provided more color as opposed to less going forward and I think that's really going to solidify the aduro clean technologies, technology, and more real people can look at it say okay yeah I get it I don't get hydrochemolytic, but I get it I see aduro's name on the side of this big company. And here's the process from a to z. This is what it's going to render on the back end, and this is exciting stuff. We are void of that right now my friends and when I look at it, I look over the next 12 months to maybe get a significant more color around those pending initiatives with the company. I look at or materialize partnerships. Right now I see a few. I looked at some of those private companies Lionel Bacell, Dow Chemical, many, many others large chemical companies large oil companies that are doing business with these other companies. You know, I appreciate the shell game changer program but what what has that truly meant for the company has that that been the reason for the 17% increase in presuming that that's somehow going to materialize into something. What about the secret multi billion dollar company we don't know what's going to materialize out of that. We know that there's been a 450% increase in infusion into the R&D, or the customer engagement that they've got going on what. What's that going to mean for a duo in real time and I, I think I have more questions than answers on that. And I give a duo a pass on that because they are not in that time where they can actually announce those things to the greater audience and grow client list I think we need to have, you know, 1020 2530 50 clients you know once we start to embolden these commitments with the duo and and start to subject the technology to multiple customer engagements I really think that's going to continue to fortify and add merit to the technology. I really continue to grow revenues. My friends their revenues right now are pretty light. They are making those revenues from two out of the three verticals I believe the last revenue stream that I saw was around $58,000 that's pretty light right for a company that, you know, okay, it's a $60 million valuation they need to fortify that that top end they need to start to bring in some significant revenues now as we progress to those significant revenues I understand that there's going to be off quarters. I understand that there's going to be revenue drops and revenue fluctuations. This company is just getting its bearing and going full force into an addressable market to the tune of $200 billion. So it's expected that they grab big swaths of it. And then while they're working on those big swaths are going to potentially even miss out on some of the other low hanging fruit. All right, but they need to fortify that top line. They really do. That really when you look at the financials and you put the aduro clean technology, the story aside, that balance sheet and those income statements and cash flow statement that those really have to shine. And right now we're in the early stages of solidifying those relationships that are going to add value to the top line. And that's what I foresee in the next 12 months coming down the pike is a fortification of the financial statements with the I would like to end the video by just saying this, we're going to end 2023 up on on the stock on the opportunity. I'm eagerly awaiting some some words from the CEO about what he expects in 2024 he typically tries to coin. What we're what we're forecasting for the following year. I cannot expect based on this baseline that's been set of the last 24 months that 2024 is going to be anything less than exciting. I just don't see it because they've really started to accelerate in the back half of 2023 with their customer engagements. I'd like to understand a lot more color on the interest in the program where their focus is is it to complete game changer and what's going to come out of that. Will that open them up will it close them up. Will they get bought out, you know, these are all justifiable questions for a retail share owner in the company that is looking to convey their story pay it forward. Again, I've declared my share position is set I'm long the shares. I'm not looking to get a bump in the shares to, you know, two or three dollars in the share and sell out of the company I'm not looking that my first look comes at $10 a share, which is quite frankly where I value the company now, especially based on the competition that I read that aduro was placed within company yesterday. Right. I think aduro sports, a significantly higher valuation than the 60 million that it sports now. This is the calm before the storm, my friends. I'll continue to pay forward my information that I have at the time of sharing it. We will continue to look for new information. We will discuss that and we will pay that forward through the channel as appropriate going forward as aduro continues to evolve in this story. Going into 2024 exciting times, my friends, stay with the message. If you enjoy it, hell subscribe to the channel, man. Leave your comments at the bottom of the video, hit the notification bell. You may notified of new content put online by the independent investor. I'm glad to be with you guys. I'm glad to be delivering this front.  There's no doubt about it. Guys, thank you so much for tuning into the video and good luck in your investment future.


Autistic shutdowns and not internalised meltdowns. It might be a good way of explaining the concept, but my shutdowns are often protective and much less intense. What about you?


Hi, I'm Dima, a fourth year PhD student at Stanford working with Dan Bonet, and today I will be talking about private information retrieval with sublinear online time. This is joint work with Henry Corrigan-Gibbs. Thank you for watching this virtual presentation, and I hope you enjoy it. In this work, we present a new method for making PIR faster. Specifically, our new PIR schemes push the bulk of the work to a preliminary offline phase, during which the client fetches a short string from the server. In a subsequent online phase, the client can privately query the database, and the server can respond to the query very quickly, in time sublinear in the database size. Moreover, our schemes do not require any additional storage on the servers. First, let me give you a little bit of background about PIR. Private information retrieval, introduced by Shor, Goldrach, Kushi Levitt and Sudan, is a cryptographic protocol between a database and a client that allows the client to read any record in the database without the database server learning which record the client is reading. And throughout this talk, we will model our database as an n-bit array, meaning each record is only a single bit. However, using standard techniques, PIR can be applied to databases with larger records, as well as to key value databases rather than plain arrays. PIR is useful in scenarios where the user's query contains some sensitive information. For instance, a query to a database of medical conditions might reveal some information about the user's disease, and a query to a database of stock prices may contain information about the user's financial interests. And in both cases, the user would ideally want to keep his query private. PIR is also useful as a building block in larger privacy-preserving systems for applications such as private messaging, search, or DNS. More formally, a PIR protocol has to satisfy the following properties. First, correctness, meaning that an honest client interacting with an honest server should learn the correct value of its bit of interest. And second, security, meaning that the server should learn nothing about which bit the client is reading. And as always, learning nothing means that the view of the server when the client is reading bit i should be indistinguishable from the view of the server when the client is reading bit j. And actually, there's a trivial protocol that meets both of these requirements. The client can simply download the entire database and perform its query locally. However, downloading the entire database is impractical in most settings, so we would want the protocol to be efficient, meaning that the total communication between the server and the client should be minimized. And indeed, these requirements can be met. The same work that introduced PIR also presented a protocol that achieves sub-linear communication by replicating the database on two or more non-colonial servers. And ever since, there has been a long line of work improving the communication complexity of multi-server PIR. And today, the best PIR protocols have communication complexity and to the little of one, and they provide information theoretic security. Moreover, if we settle on computational security, recent protocols achieve logarithmic communication just from one-way functions. In addition, soon after the original multi-server PIR paper, Kuszy Levitz and Ostrowski showed that one can build PIR with only a single server, but here computational assumptions are necessary. Today, we know how to build PIR with polylogarithmic communication complexity in the single server setting from a wide range of public key assumptions. So it seems that in terms of communication, our situation is actually very good. However, the situation is not as good if we look at computation. In fact, in the protocols on the last slide, a server needs to scan the entire database to respond to a query. And in practice, doing linear work on every query is very expensive. It turns out this is in some sense inherent, since the expected server work in any PIR protocol must be linear in the database size. The intuition is that a server must touch every bit of the database, since if it doesn't touch one of the bits while it is responding to a query, it can guess that this untouched bit is not the bit the client is attempting to read. And although it is not at all trivial, it also holds in the multi-server setting. There have been several approaches to reduce the server work in PIR by somehow circumventing this lower bound. A very promising approach is called PIR with pre-processing, where the basic idea is that the servers store the database in encoded form, and using this encoding, they can respond to user queries much faster than in linear time. The catch is that now this encoding of the database, which the servers need to store, is much, much larger than the original database. So for instance, to get query time and to the .6 using this approach, the servers need to store code words that have length larger than n cubed. And this is not very practical for databases that are gigabytes in size. There have also been other approaches that reduce the server's work in PIR by batching queries, sharding the database, relaxing the privacy guarantees, or moving the more expensive part of the work to an offline phase. However, the overall amount of online work in all of these approaches is still linear in the database size. So the plan for the rest of this talk is, first I will define the offline online model, then I will present our results in more detail. Then in the main technical part, I will explain the main ideas behind our two-server PIR construction. In the end, I will talk a little bit about the single-server setting, and then I will conclude. But let's start by defining the model. For simplicity, we will be working in the two-server setting, and we will refer to our two servers as the left server and the right server. And crucially, we assume that the two servers are non-colluding, meaning that the adversary controls at most one of the two servers. Our scheme starts with an offline phase. In the offline phase, the client interacts with the left server who provides it with a hint, which is a string that depends on the database itself. The length of the hint has to be sublinear in the database size, as otherwise the hint could just be the entire database. And to give you a preview in our constructions, the hint will be about square root n bits in length. To produce this hint, the server does need to perform a linear amount of work, but the key point is that this phase can take place before the client has decided on which bit it wants to read from the database. So the server has much more flexibility to perhaps run this phase overnight and without any strict latency requirements. So after completing the offline phase, the client stores this hint and waits for the online phase to begin. And know that unlike in the PR with pre-processing approach, the servers don't use any extra storage, and in fact, they just store the database in its original form. And then the second phase is the online phase. Here, the client decides on the actual input index i, the index of the element from the database it wants to read. And it uses the locally stored hint to generate the query to the other server, the right server. And the response to this query together with the hint allow the client to recover the bit of interest x sub i. And crucially, the servers work in this phase, as well as the communication between the client and the server has to be sub-linear in the database size. I should mention that an offline online model has been considered in the past, yet previous schemes in this model either have linear online time or require additional storage on the server. So now we can state our results in a bit more detail. Our first result is a two-server offline online PIR scheme with square root communication and square root online time. And for simplicity throughout this talk, I will avoid explicitly writing factors that are polynomial in the security parameter lambda and polylogarithmic in the database size n. So when we talk about square root of n, what we really mean is o tilde of square root of n times some polynomial in lambda. And this construction uses only basic symmetric key primitives, so it is concretely efficient. The construction also has the extra property of allowing to execute multiple online queries without having to redo the offline phase from scratch each time. And this means that the linear cost of the offline phase can be further amortized across multiple queries. Our second result is a single server offline online PIR scheme, which uses n to the two-thirds communication and n to the two-thirds online time. In terms of assumptions, what we need here is black box use of any single server PIR scheme with low communication and additively homomorphic encryption. And both of these can be built from a variety of public key assumptions. If we are willing to use heavier tools, namely FHE, then we can recover back the square root of n running time. And an extra property of our single server scheme is that it doesn't require any public key operations in the online phase, which makes the online phase even faster. A drawback that our single server scheme has is that unlike the two-server scheme, it requires a separate execution of an offline phase before each query. And finally, we give a lower bound for offline online PIR schemes in this model, where the servers need to store the database in its original form. Specifically, we show that the product of the communication C and the online time T must be at least linear in the database size. And this matches our two-server scheme and the FHE-based single server scheme. And I should say that this lower bound holds even in the computational setting. So now we proceed to the main technical part of the talk and we'll see how the two-server scheme works. So let's start with the offline phase. Here the client chooses m random subsets for a parameter m that we will set later. So these are m subsets where each subset contains square root n independent random elements from the universe of one through n. And then what the client does, it sends those sets to the left server. And naively sending this amount of information would take too much communication. So we could either generate those sets using some shared randomness between the left server and the right server. Or we can just use a pseudo random generator and then the client only needs to send a seed to the left server. So yeah, when the server receives these m sets, for each of these sets it computes the parity of the database bits that are indexed by the set. So overall it computes m such parity bits, one for each set, and sends them back to the client. And what the client does, it stores the collection of this set and their parities as the hint. So the hint contains a collection of sets and their parity bits. And that's the entire offline phase. Notice that there's no index i in the picture, so everything here is completely independent of any particular database index and this can happen offline. Now we move on to the online phase. Here the client decides which index i it wants to read from the database. And the first thing it does is to look for a set in its local collection that contains the index of interest i. If none of the sets contain index i, then the client fails and we will later see how to deal with all these failures. If such a good set SJ does exist, then the basic idea is that the client removes element i from the set and send the set as prime, which we call the punctured set to the right server. Except that with some small probability of roughly one over square root of n, the client actually does something different. It sends to the right server a random set s prime that does contain index i. And this is also considered a failure, which we will account for later. In any event, the right server receives from the client the set s prime, which has size square root n minus one. And just like the left server did before, it computes the parity of the database bits index by this set and sends back the parity bit back to the client. And now the client has two bits. It has the parity bit hj from the hint, and it has the answer bit a from the right server. So the client just outputs their sum mod 2. And note that hj is the sum of all the database bits in the set SJ. And the bit a is the parity of all those same bits except bit x i, since the client removed index i from the set SJ. Therefore, the sum of those two bits is exactly the bit of interest x i. And that's the construction. Okay, so now let's go back and look at those two failure events. So the first failure event is when the collection of sets doesn't cover all indices. And here is where we choose the number of sets little m to be roughly square root n times log n. And then by standard coupon collector argument, the failure probability of this first event would be something negligible in n. And then the second failure probability, it comes directly from our construction, which is the event that we send this random set as prime that contains i and consider this a failure. And this happens with probability roughly one over square root of n, which is also the overall failure probability. So what we do next is we actually want to drive down the failure probability even further. We want it to be negligible in the security parameter lambda. So we repeat our entire construction lambda times in parallel. And this is not the most tight analysis. But in any event, now that we have lambda instances, the probability that all those instances fail happens with a probability that is negligible in the security parameter lambda. And one point that I want to emphasize is that those repetitions, they include both the offline phase and the online phase. So in fact, the client generates lambda independent hints in the offline phase. And it repeats this online phase lambda times in parallel completely obliviously of any successes or failures it has in some of those iterations to avoid leaking anything from those failures to the server. Okay, so that's overall we end up with a negligible failure probability. This is the correctness that we want. Okay, so now we turn to doing the sketch of the security proof. So first of all, the security from the left server is actually pretty immediate. The sets that the client sends to the left server, they do not depend on the index i in any way. So they can't possibly leak anything about index i. The security against the right server is trickier since the set SJ clearly depends on index i. And here is where the non-collusion assumption and this weird looking sampling come into play, since they guarantee that the resulting set S prime is a uniformly random subset of size square root n minus one independent of i, and therefore hides i from the right server. And to see this, we can identify the distribution of the set S prime with the following way to sample a uniformly random set. So fix any index i, and then a uniformly random set of size square root n minus one should contain this fixed i with probability square root n minus one over n, which corresponds to the first case above. And with the remaining probability, the set should contain elements which are all distinct from i. And this is what happens in the second case where we explicitly remove i from the set SJ. So overall, the set S prime is independent of i, which shows security from the right server. And just one more thing, if we generate all the sets using a PRG rather than using true randomness, then we simply lose some negligible distinguishing advantage, but the argument is basically the same. Let's now look at the efficiency of our protocol. The communication in the offline phase consists of the client sending square root n random sets, which we assume we can shrink using either a PRG or shared randomness. And the server sends back square root n parity bits. So the total communication in the offline phase is square root of n. In the online phase, the client just needs to send a single punctured set to the right server and get back one parity bit. So the total communication is also square root of n. In terms of computation, the offline phase is linear since the server needs to process all the sets, and the online phase runs in time square root of n since the server just needs to process a single set. Next, I want to discuss a main feature of our two-server scheme, which is that it amortizes the linear cost of the offline phase by running multiple successive online queries without having to redo the offline phase each time. The problem in naively running multiple queries as is, is that the client must be careful not to reuse the same set as j for two different reads. If the client would accidentally do that, then from the symmetric difference between the two appearances of the same set, the server would be able to learn the client's indices. So instead, the idea is that we refresh the hint by sampling a replacement set s new and then fetch the parity of this new set from the left server. And we need to be careful to sample the new set in a way that preserves the joint distribution of the sets in the collection to provide correctness guarantees for future queries, and also everything needs to be done in a way that hides index i from the left server. This refreshing procedure can be done any polynomial number of times, and the bottom line is that now preparing for the next query only takes square root n time rather than linear time, which is what redoing the offline phase from scratch each time would have cost us. So to sum up the two server results, we show the scheme with square root n communication in online time and even amortize total time per query. The client's storage and running time in our scheme is square root n, and the scheme requires either pseudo random generators or shared randomness between the client and the left server. We also have extensions to our scheme such as trading off communication for online time and vice versa, and there's also a statistical security variant that works even when there's no shared randomness. Finally, using punctual pseudo random functions, we can have the client send only a short description of a punctured set which shrinks the communication in the online phase to only log n. The resulting scheme is highly efficient in terms of communication, though the client's running time is not as good as before. The last thing I want to talk about before I conclude is to give you an idea of how our single server scheme works. The general idea is that we want to transform our two server offline online scheme into a single server scheme by running both phases on the same server. However, this breaks security which crucially relies on no single server seeing both the offline and online queries. To work around this, the client encrypts the offline query using homomorphic encryption, and the server evaluates the offline phase without seeing the client's query in the clear. The online phase remains the same as before. And here we have two options. We could either use fully homomorphic encryption which preserves the asymptotic running time of square root of n, or we can use an additively homomorphic encryption scheme, but then having to express the scheme as a linear transformation forces us to use a less efficient representation of the sets, which results in a worse asymptotic running time of n to the two thirds. The advantage is that the second scheme is concretely more efficient. So to summarize, we have seen a new type of PIR schemes that get sublinear online time and require no additional storage on the server. In the paper, we also have a lower bound for this model, which we prove using a reduction from a classic problem by Yao. And finally, I want to mention two open problems. First, it would be great to get schemes with better running time on the client's end. In our scheme with log n online communication, the client's running time is n to the five over six. It would be great to make the client more efficient. And second, one limitation of the offline online model is that the offline phase is separate for each client. It would be very interesting to be able to somehow amortize the offline costs across multiple mutually distrusting clients. And with this, I'll conclude.


This is the most perfect lack of pronouns that we've ever seen on the panel. Can you give me just a list of a few of the reasons? Ms. Yurtie resided there, went to visit her, maybe went to talk about a document that I received. Let's break down pronoun absence really fast. It's when somebody suddenly, and remember this is about detecting changes, suddenly stops using pronouns in their language. And this is a result of an increase in cognitive load, our mental energy, that reduces our ability to think clearly and it impacts our linguistic choices.  So it's also a distancing mechanism. It's kind of like a subconscious way to reduce their sense of personal responsibility for the statements.


Hi everybody. So as a dental professional, what do you do if you don't necessarily agree with what the dentist is doing in the dental office? So let me give you some examples. Let's say they demand you take x-rays on kids every three months, even if you know they don't really need it or they're double charging people, not in a bad way, but they just charge so much more. They're still within the feed guide, but they charge so much more and they come in for half a second and you don't like that. Or maybe you just don't agree with the office politics. You come in an hour early every day because they make you, but you're not being paid for that. At least you're being organized with charts, but you're not being paid for that. Maybe you never get a lunch. So you see what I'm getting at here. You're working for an office that there's just things you don't like about it. Do you stay? Do you not say anything?  So let me offer you some tips and tricks here. So let's take x-rays as an example. If that dentist is making you take x-rays every six months because that's just their office policy and you're okay with that, well that's one thing. But personally I wouldn't be okay with that because as we know, every client is different and some of them do need x-rays every six months because they get a ton of cavities, but some do not. And what if patients are saying, I can't afford it, I don't want the x-rays, but then you get yelled at by your boss for not taking them. It's ultimately dependent on what you can handle. I was always very firm as a dental professional, so I just simply wouldn't take the x-rays if I felt it wasn't necessary. Not saying I knew more than the dentist, but I would look in the chart and say, well they haven't had a cavity for five years, they've been getting x-rays every six months, now is the time to maybe stop because their teeth are looking pretty good. So I would just simply let the dentist know why I thought that. If they were able to convince me otherwise of why they're still taking the x-rays every six months, then okay, we could at least talk about it and have that good relationship. You might be right, they might be right, it doesn't matter, but if you're not comfortable with something, it's your license on the line. I have worked for dental offices before where I would do the work, I would put the codes in, and the receptionist would literally change my codes to a two-unit scale to magically a four-unit scale. And I would tell them, I see you change the codes in the computer, but that's not what I did. You crossed out what I did in the chart. That's not right, like you can't do that. And they would say, well Andrea, we've told you for every adult patient for 60 minutes, it has to be four units of scale. And I would say I didn't do that. They had hardly any plaque. We talked about oral hygiene, we did other things, and I'm actually done in 45 minutes. So how can I charge for one hour and four units of scale when I didn't do that? That's a little bit different. I wasn't comfortable with that and I left the office very, very quickly. That was a temp position. So it depends on what's going on and what you're doing. If you're not getting a lunch ever, that's really too bad. I would talk to the dentist about that and say, listen, I'm never getting a lunch because nobody's helping me. It would help if maybe an assistant would turn down the room, or maybe you're a dental assistant never getting a lunch because the dentist is always booking into your lunch. I would talk about that. But if nothing changes, look for another office. You don't have to quit right away, but look for another office and maybe take that into consideration. So things to think about. It depends on what you're okay with. But if you're losing sleep over something, you're just coming into the office every day with anxiety. You don't like it. There's office politics. There are some amazing offices out there. You just might have to find them. Even if you're getting paid a little bit less or more, maybe you'll be super lucky. But find an office that works for you because personalities don't always mesh. We're in a small space all the time with the same people. You might not get along with the staff there and you might get along so much better in another office. We work too much to not be happy with work. So please consider it, you guys. Okay. Thank you for watching and I'll see you guys in the next video.