Get a mate 40 here So I think YouTube is down. Can can anyone even see me right now? You don't even hear me. Am I even there? Who am I talking to? I think I'm just talking into the void Sad So how long is YouTube being down? Can you pull it up on an app? So Ron Owens has a theory No, nothing's coming up and His theory about oh, here we go Apparently on a on a mobile app As you can you can see YouTube. Okay, you can see you can see YouTube on on a mobile app right so Ron Owens has a theory that That covered is a is an American intelligence bio warfare attack now. I just want to say Very clear. There is absolutely insane along with many other Ron Owens articles I think are absolutely insane and this is very different from saying Ron Owens is insane I'm saying something that he's written is insane and another thing that he's written I think is insane so he consistently produces just wacky useless just insane post But not saying he's insane But his latest is the tide finally starting to turn on covered as an American bio warfare attack So he says during the last 18 months I've stood nearly alone on the internet and arguing that late 2019 covered outbreak beginning Wuhan China was probably the result of an American bio warfare attack Conducted by rogue elements of our own national security establishment All right, this is insane You know why Ron Owens is alone in this because this is so out there that no one else would go out there So he says the individual articles in my long series have been viewed some 350,000 times yet you can get a lot of attention if you're saying crazy things and Now he's finding support from the conservative treehouse. Wow, there's a reliable source The conservative treehouse Wow Ron Owens has really lost lost the plot Right, I've had this growing discuss with much of the American populace right and Brian Stelter now Eric Wemple has a good op-ed in the Washington Post Giving more reasons why I'm so contemptuous about much of Right wing populace in these days. So what's the New York Times of the right? Well, it's the New York Times So Brian Stelter at CNN Talked on a recent show that we should distinguish between reporters people who actually dig for new information and Repeaters meaning people who simply aggregate information. So into the latter category repeaters You find Fox News. All right, Fox doesn't do very much individual Reporting it does a lot of repeating So then Stelter asked why aren't there massive American newsrooms dedicated to journalism from a conservative point of view? Why is it there in New York Times of the right? Well, there is the New York Times of the right And that's Eric Wemple and it is the New York Times Right, so it went right wing is Wanted to cite authoritative journalism. They have to cite the New York Times I don't know how you keep up with the news and not read the New York Times It simply head and shoulders the best English language Newspaper in the world and it's not even close. It's twice as good as its closest competitors such as the Wall Street Journal and The Washington Post just the quality of the writing in the Wall Street Journal The Washington Post doesn't come close to what's consistently offered in the New York Times So this past summer Tucker Carlson talked on the five about his media diet He says oh, I gave up my New York Times and Washington Post for subscriptions because they're just garbage, right?  He highlighted video investigation by the New York Times into a US drone strike in Afghanistan September 20th Tucker Carlson credits the New York Times for forcing the Biden administration to admit that a drone strike killed a number of innocent people September 22nd he quotes the New York Times report on a housing law in California SB 9 essentially and single-family zoning September 28 Tucker Carlson sites New York Times as Vindicating what we said months ago that FBI operatives were deeply involved in the events of January 6 now Let's be real the New York Times article did not vindicate vindicate Tucker Carlson's previous contentions Have I heard of an app called ground news? No, I have not it is free It is nice because it shows the media's bias in coverage of a given story interesting October 4 Tucker Carlson site in December 2020 New York Times story Questioning Anthony Fauci About the changing resistance thresholds for the country to acquire herd immunity So the New York Times Tucker Carlson says their job is to report the news right so Like many Conservatives Tucker Carlson says our New York Times is garbage, but whenever it makes a point that's convenient to him Of course, he's gonna sign and this is not just Tucker Carlson like Sean Hannity all the time citing the New York Times Howard Kurtz at Fox sites the New York Times Fox host Steve Hilton sites the New York Times First Shannon Breen credits the New York Times guest host Mike Emmanuel credits the New York Times Brett Bear is always citing New York Times Post Maria Bartiromo crediting New York Times Jesse Waters Janine Pirro citing New York Times whenever it's convenient so Eric Whample makes the point when the when Fox News isn't citing the New York Times as an authority the Authority in journalism Right is seeking to reduce that authority So Tucker Carlson will call New York Times the Praetorian Guard protecting a corrupt establishment Mark Levin says it's a propaganda organization It's just an appendage of the Democratic Party and the deep state now. It's not New York Times is a left-wing publication and once you understand that bias you can read it to your benefit So it's not a propaganda organization. It's less of a propaganda organization the Fox News and Fox News is simply recycling other people's reporting primarily so This this posture by by Fox News that oh, you know, we decry the New York Times We're above the New York Times, but then always eagerly citing the New York Times when it's to their benefit is Cynical and destructive the best that can be said for Fox News rights Eric Whample as it does nothing to hide its two-faced Simultaneous effort to drag down and pivot up a vibrant news source and Fox viewers appear just fine with it Good op-ed there by Eric Whample and then back to the John Gruden story from last night so in the NFL's Investigation into the toxic environment at the Washington football team they Uncovered something like 600,000 emails, but somehow only John Gruden's get brought to life Like if the NFL investigated the emails of its other coaches, you don't think they'd find something Why isn't the NFL releasing those other 600,000 emails? Why are we getting just this targeted hit on John Gruden? like how how does he get to be the Foreguy what's going on with that? and Remember the New York Times was absolutely fine with the racist tweets sent out by its It's employee Sarah Jong like ho hum well, who whom because she was going after white people is fine and Is it okay to mock people who have a normally big lips like why is that such a?  If you went through anybody's private communications, would you not find things that would? Shock contemporary sensibilities So some people say the NFL has become rather gay Because whenever the opposing team throws an incomplete pass within 10 years Within 10 yards of a defensive back does a celebration dance So the NFL turns a blind eye to real harms done by their employees such as Michael Vick Ray Rice OJ Simpson are in Hernandez So what what's really going on? So I wish John Gruden didn't apologize at all Should have said I have F you money. So F you I guess some rival faction wanted to put John Gruden out So they could put their own guy in The beating women and torturing dogs is okay If you want to make it in the NFL but making it mean comments about people who are black gay or women is forbidden Yeah, the NFL has become full throttle workers Like why do we have a month of breast cancer awareness? I mean frankly, I think every day should be about breast cancer awareness and Then why at earth the Washington football team have sexual harassment of their cheerleaders Sexual harassment of women who get paid to shake their groove thing while partly dressed in front of tens of thousands of mostly male fans of the humanity and John Gruden called our president a nervous clueless pussy and remember when he made these emails He wasn't employed by the NFL And he sent them from his private email address Shouldn't they have paid for the blonde Facebook whistleblower to have a little jaw reduction plastic surgery before rolling her out? Yeah, she went after Facebook because It was too open to vigorous debate Ex military dude says can I sue the United States government for the derogatory names? I was caught during basic training 40 years ago Yeah, low status males looking at women is considered harassment Yeah, we've got this mysterious sexy instant media darling brave whistleblower Facebook over and over again is chosen profit over safety and by safety She means why isn't Facebook doing a better jog of squelching vigorous discussion She wants the federal government to impose regulations On social media. Yeah, so the NFL is going through 650,000 emails. This could be the Panama papers of football so what would happen if you did a thorough search of Smartphone texts by various NFL players. You think you'd find any homophobic or Misogynistic content in there High school football coaches everywhere tomorrow will be yelling in the faces of straight white kids and sorting distressing Humiliating and traumatizing them. That's their culture That's the nature of the beast Man and Gruden also criticized president Obama during his reelection campaign in 2012 Yeah, Gruden should have hung tough called for the release of all The NFL emails. I'm a free man. I like what I like. I don't like what I don't like That goes for some people some behavior some of the nonsense of our time I said what I said when I said it if that's important and let's get it all out there The NFL should release all the emails from everyone players coaches team management But especially Roger Goodell and all the suits and NFL broadcasters. Let's have transparency That's okay for the NFL to have murderers rapists girlfriend beaters drug addicts Alcoholics, but don't dare criticize the commissioner or question his work agenda so don't radar fans Aren't they radar fans because they love blood culture. I Mean whenever you see a liquor store robbery in Southern California close-circuit camera There was always raiders gear being worn by people committing the crime What does Ron wouldn't say he says that COVID is the result of rogue elements of the US intelligence agencies But they they cooked up COVID insane How come I don't do that many live streams anymore. I'm taking a break.  Yeah Yeah, the core promise of email and general internet communications technologies that we're supposed to be able to converse easily and casually Without physical proximity All right, but instead of being liberating Now search and retrieval means that we've unleashed the school moms the lawyers the commissars into every thought and utterance a man has What was supposed to help liberate man has become a transfer of power from men and the productive To the unproductive and the tut tutters and the parasites Yeah, when are we going to get those other six hundred fifty thousand emails? From the Washington football team investigation So the league that hired AJ Simpson Aaron Hernandez and Ray Lewis is concerned about offensive language in a coach's private emails Yeah, when when are we going to get a trove of emails sent by New York Times executives? At least young grooms emails are more entertaining than the normal coach speak that we need to control the line of scrimmage Take care of the football and establish the vertical threat. By the way, was there a trove of emails on Hunter Biden's laptop? Did the New York Times report on any possibly racist or insensitive or sexist or misogynistic or misanthropic content on Hunter's trove of emails to that trove of emails contain any weft of corrupt payoffs Did Roger Goodell just want to get John Gruden because John Gruden's not with the work program So Roger Goodell instructed NFL executives to look at more than six hundred fifty three 650,000 emails during the past few months Including those in which Gruden made offensive remarks and nobody else made offensive remarks in that trench in that trove So distressing this happens for the Las Vegas readers because Las Vegas is just known for its sensitivity Man, there's no homophobia or sexism there reading from the comments on Steve Sealer's blog Yeah, so Question the wisdom of recruiting female firefighters Man, you're just relying on Endequated and discredited tropes bro about females lacking the physical strength of their male counterparts Well, maybe maybe John Gruden You know caution someone about venturing into a certain part of town Maybe employed age-old stereotypes about African-American and other communities of color being less safe than their white counterparts And too bad that John Gruden is not Hillary Clinton because then he could have had a team of interns review all his emails Delete all the ones deemed problematic then print out the rest and submit them on paper to investigators Watching the breaking news coverage of this on Monday night football. You'd think someone just died You got these former football players saying how they can't believe that they ever played for this racist Broadcaster saying that John Gruden committed the holy trinity of offense racism misogyny LGBTQ denigration and everyone nodding their heads in unison No one questioning why these emails are just now released after a decade Because of the investigation the Washington Redskins uncovered these old emails Or what about everyone else's emails This This seems like just the tip Just the tip as uh, Ron Jeremy would say That John Gruden is gone. But maybe the NFL's troubles are just beginning, right? Sam Farmer in the Los Angeles Times. Well, how many more emails are out there? Like what other NFL careers are on the line? That we didn't get to see the back and forth. We just got to see John Gruden's share of this conversation So we've got 650,000 plus emails And a summary of them was presented to Commissioner Roger Goodell and the readers last week So emails private emails sent a decade ago Roast the level of red alert how many how much more is out there? What else will be revealed? Hard to imagine any NFL team weathering this level of scrutiny unscathed so Two weeks ago. We saw urban Meyer Having a woman dance against him who was not his wife She was grinding on him a beautiful young woman when he was supposedly spending more time with his family So this John Gruden mess says Sam Farmer feels much more like the beginning than the end So who did John Gruden piss off the wrong person? Obviously, that's his real sin not writing naughty things in private He checked the emails of everyone in the NFL since 2011. You'd find worse than John Gruden's comments But my god, he said that a black man had lips like Michelin tires.  I don't fear and hate strangers Well, guess what everybody's got fear and hatred of strangers inside of them. It's just how deeply is it buried? Right. It's only a matter of how deeply is buried. We have an instinctive revulsion Loathing and fear and and hatred of that which is different from us Now we are sufficiently educated and incentivized to try to repress this But it's there inside of everyone So I wonder if the wonder if the raiders will hire a woman.  We fear those who don't believe like us Every disagreement puts strain on your relationship So Loponius and I we we had a conflict about air supply I said to Loponius air supply is the greatest Musical group in the history of the universe and he disagreed And it was really hard for me to talk to him for a few days afterwards because we had such a passionate disagreement over air supply So even disagreeing about the merits of a song the merits of a radio station the merits of a sports team That's going to put stress on your relationship Right, we feel most comfortable with those who are most like us the more differences you have with other people Whether it's skin color religion sexual preference It's just going to musical taste sporting preferences Income differential The more differences the more strain on the relationship Yeah, we need a masculine presenting non-binary omnisexual palestinian latinx trans woman It's the next readers coach Then we can achieve peak Workness Yeah, thank god. Loponius and I we agreed to disagree about air supply now. We're just the best of buds We got over it We were all out of love. We were just lost without you But here we are What do I think about Rabbi Mizrahi and Rabbi Rubin? I think they're They're uh, quite uh, they're quite compelling All right It's uh, it's low IQ content, but it's incredibly entertaining So what do you guys think about John Gruden getting fired for? Logical song from super tram. Yeah, the questions run too deep. Good point. So what do you guys think about the? The firing of John Gruden for insensitive comments Made 10 years ago. Yeah, brutish and compelling. That's a good way to describe rabbis Rubin and Mizrahi now You don't personalize business. You don't criticize people personally in business, especially in writing. Yeah words to live by If I renounce my love of John Gruden, will I be free? I think he's got a coach again in the nfl Let's go brand and Let's go brand and Just seems crazy on the face of it that we're cancelling people over 10 year old private emails as refereed by the new york times All right. Okay. These aren't tweets. These are private emails But uh, once this stuff is out there then a team and an owner has to act in its own self-interest and the reader's owner Mike Davis got in Got in a little bit of trouble for posting a tweet Now I can breathe right after After George Floyd died Do he died complaining? I can't breathe. Mark Davis appeared to mock him by saying now I can breathe Yeah, the the new york times makes it seem like John Gruden's ripping just ripping on women gays and blacks But when you see the actual transcript realize he was just using crass language Someone like the shift from using word prostitution to human trafficking. It just makes it seem so much work So do you think the emails of the dark lord bill bella check are getting scrutinized?


Hi everyone, I'm Joana from Inaria, and I'm going to talk about latest savings via quantum variables. So, first of all, I will introduce some notions about the latest sales and quantum computing. Then I will explain how our algorithm works and give some results about the complexity. So, first of all, the latest is defined that way. It is a set of all integral inert combinations of a given basis of vectors. And from this, we can define the shortest vector problem, SVP, which is given a latest. We have to find the shortest non-zero vector in this latest. So, here in this example, we have the basis P1 on B2 in blue, and the latest vectors are represented by black dots under the shortest vector problem. Ask us to find the shortest vector of the latest unsoldered by P1 on B2, which is the vector in red. So, why do we want to solve SVP? Basically, from a cryptography point of view, it is an NP-hard problem, and it is hard in average. And there are several problems which derive from SVP, such as SIS, LWE, or NTIU. And there are several quantum-resistance cryptosystems which are believed to be quantum-resistant, which are based on these derived problems. So, from a cryptanalysis point of view, all of these cryptosystems are broken if we can find a reduced basis of the latest, which is used. And the BKZ algorithm finds a reduced basis on using an overcome that solves SVP as a subroutine. So, in a nutshell, the security of these cryptosystems directly relies on the complexity of solving SVP. So, there are several methods to solve SVP. The two main practicals today are by elimination and by saving. And today, all of the methods we know to solve SVP run in exponential time. So, in this presentation, I focus on the saving method. And it is a heuristic method that means that we use heuristics. And the main of them is that the latest vectors act as random vectors. And this implies that vectors of normed atmosphere are lying on the border of the sphere of radius air on dimension D. This heuristic has been very dated by experiments, so it is not far from the reality to consider that the latest vectors act as random vectors. So, this is the algorithm for the saving. So, the idea is that we begin with a list of n-latest vectors, which are of normed atmosphere and air. And we take a parameter gamma strictly if I have to run. On the output, the algorithm will return a list with n with the same n as before, with n-latest vectors of normed atmosphere and air. So, the output vectors are shorter than the vectors in the input. And through this, we can simply check each pair of vectors in the list. So, and we check if the norm of the difference is inferior to gamma air. If it is the case, we add v minus w, so the difference to the output list. Here we see the shear of dimension D on radius air. We have our vectors all over the sphere. And we see that if we have v on w-latest vectors, then v minus w is a combination of two latest vectors, so it is also a latest vector. And if we have v on w, which are close at angle, then v minus w can be shorter than v or w. The limit angle, so that is true, is when we have v on w, which forms an angle of p over 3. So, if they have a bigger angle, then they will not reduce. So, to serve SVP using this algorithm, we begin with a latest, so it is defined by a basis of vectors. On the output, we want to have the shortest vector of the latest. It is a probabilistic algorithm, so it will probably return the shortest vector. To do this, the first step is to generate a list of n-latest vectors, for example by Planck's algorithm. Here, the value of n is the smallest value such that we have at least one vector, which reduce with another vector in the list of n vectors. So, it is the smallest value such that we can have n vectors in input and n vectors in output. So, we have our list. While the list does not contain a short vector, then we apply a steep step on it with a parameter gamma being close to one. Then we return the shortest vector we have formed with this method. We see that at the beginning, when we have just generated the list l, the norm of the vectors are at most r, for certain r, which is the maximum of the norm of the vectors. So, after the first iteration in the while loop, the norm of the vector are at most gamma r. After the second iteration, we win again a vector gamma, so it is gamma square r. After only a polynomial time in d, the dimension of the l-t, we have a gamma power polynomial of d times r. So, it is exponentially lower than the first r we had. So, we can expect that there is a short vector in the sphere of t's radius. So, the complexity of t's algorithm is in n square because we have n square pairs in the list of size n to check. So, it is t's complexity. For the space complexity, it is just n because we have to store the n vectors of the list. So, t's algorithm can be improved by using a filtering. So, the idea is that we only want to check pairs of closed vectors because all of the vectors which are often more than p of s3, they are not interesting us because they are not reducing each other. So, to do this, we use filters. So, a filter is characterized by a center s which is basically a vector of the sphere and an angle alpha. So, here we have the sphere. We have a filter of center s and angle alpha. And here v is of angle at most alpha with s. So, we can say that v is in the filter of center s and the angle alpha and the value is outside t's filter. So, to improve the sphere using this, the first step is to generate filters all over the sphere. And through this, we consider a code and we consider that the code works as the center s of the filter. Then, we add each vector to its nearest filter of angle at most alpha with z. So, to do this, we use the list decoding algorithm which is provided by the code structure. And then, we search for reducing path. So, for each vector, we search reducing one within its vector. So, it is instead of checking in the wall list, we only check in the filters. So, for this third step, we can do it classically by checking each vector one by one, or we can do it confidently by approval search. So, about the complexity, for the original sieve, it was this, and we see that using LSF, it reduces a lot the time-exponent. So, our goal was to reduce again this time-exponent. So, now for the quantum computing path. One of the most famous quantum algorithm is Grover's algorithm. The idea is that we have n data on the check function that takes an x in input and returns 0 or 1. And the output of Grover's algorithm is to return an x so that we have f of x at which value 1. So, Grover's does this calculation in a square root of n steps, where in a classic model, we have to take n steps until we find the correct answer. Another very useful algorithm, quantumly, is the quantum model work. So, it takes in its input a graph J on the function f as before. And we can choose f, so just we have f of a vertex value in 1 as we want, and we call it a marked vertex. And the quantum model work returns a marked vertex. So, I will explain further this with an example to be more concrete. So, now our algorithm is basically a sieve step. So, we begin with n lattice vectors at most of them there, and we return a list of the same number of lattice vectors, but they are shorter. The main idea was to take the previous quantum algorithm and to replace the Grover's such step by a quantum model work. So, for this first step, we sample a code on the associated alpha filters. So, there are filters of angle alpha. And then we insert each list vectors in its unique nearest alpha filter. So, basically it separates the sphere into large areas of angle alpha. And we can choose with this parameter C, we can choose the number of vectors there in each alpha area. And we will optimize later the parameter C. So, here we have again our sphere of dimension D. We have a filter of center S, and as we consider that the lattice vectors act as random vectors. In fact, they are lying on the border of the field. So, there are angle alpha with the center S. So, we can consider that these vectors are d-dimensional vectors. So, in fact, if we take the difference between two of these vectors, it is the same I have considering the residual vectors on the d-1 dimensional sphere. And we can have an equivalent between the angle we are searching. So, we want to have reduced pairs on the d-dimensional sphere. So, pairs of vectors which are often called atmosphere of a stream under the corresponding angle between two residual vectors is a certain theta star alpha, which only depends on alpha. So, now for the steps two, we have our areas of angle alpha. And for each of these areas, we check here in the corresponding filter for finding all of the solutions in this area. So, to do this, we start by constructing the vertex. So, we choose randomly N power C1, which is another parameter. We choose N power C1 vectors from this current alpha filter. Then we sample a second layer of filter ring. So, there are the beta filters of angle beta. And we insert each vertex vector in its nearest beta filter. And then we perform quantum random works in order to find all of the reducing pairs into the alpha filter. So, the graph we are using is the Johnson graph. So, Johnson graph here for our parameter N power C1 and N power C1. It is constructing that way. So, we have for the vertex, each vertex is a set of N power C1 vectors which are chosen from the N power C vectors of the current alpha filter. And we consider that there is an edge between two vertexes if they differ by exactly one vector. So, to see for a simpler example, here we have the Johnson graph of parameter 5 and 2. So, we have five possible elements and each vertex is a set of two elements among these fives. And we see that there is an edge between two vectors if there is an edge between two vertexes, if only if they differ by exactly one element. So, for the quantum random work, we have our graph which is well defined. And here we say that a vertex is mapped if only if it contains a pair of angles at most theta star alpha. So, if there are residual vectors which are the residual vectors of the d-dimensional vector which are reducing. Under the quantum random work, we return such math vertex. So, now to explain how this quantum random work works. So, here we have the graph which is way simplified. And here we have the current vertex we are working in. So, at the beginning we have our N power C1 vectors. So, there are residual vectors and we consider that they are lying on the sphere of the d-1 dimension. Then we regenerate the filters, the beta filters. And we add each vector in its nearest filters. And now we begin the work. So, on the graph we are here by adding this vector from the current alpha filter, so venue. We compute its nearest filters and then we check in its nearest filters if there is a vector which reduces with venue. If it is the case, we win and we return the result. And if we don't find a reducing pair, then we pass to the next vertex. So, to do this, we delete one vector randomly and we add another venue from the current alpha filter. And we do this again and again until we find a closed vector to venue. So, by taking the difference of just two vectors, we find a shorter vector. So, here on this scheme I explained for classic random work by choosing a randomly a vector to be deleted and a vector to be added. In fact, for the quantum random work, the difference is that we do not choose randomly because we do a quantum superposition of all the possible neighbor vertices. So, for the complexity of one quantum random work, we need to have these five values. So, for the setup S, it is a cost to construct the first vertex and to compute the beta filters for each vector. Then we have the update costs. So, we construct the quantum superposition of all of the neighbors of the current vertex and we do, during this step, the search of reducing vectors of venue within its beta filters. By doing this step during the update step, in fact, the check step is immediate. It is in constant time because it is already down before. Then we also need epsilon, the probability for a vertex to be mapped. So, for a vertex to contain two vectors which are reducing. And finally, delta, which is the spectral gap of the graph. So, the overall complexity of a quantum random work is this formula. So, the only difference between a quantum random work and the classical random work are the square roots over epsilon and delta. So, to summarize our algorithm, we have a step one which separates the sphere into large areas of angle alpha. And then, during the second step, we are searching for all of the solutions inside of each alpha area. So, in fact, during this, we are missing all of the solutions. For example, where we have a reducing pair V on the value and V is in an alpha area and the value is in another alpha area. So, we have to run the step again and again until we get the n reduced vectors by changing the alpha area by changing the fielders. So, the complexity of this algorithm is in fact how we are doing n quantum random work. So, the overall complexity is one. In fact, the values of s, epsilon, delta and u are only depending on the three parameter we can choose as we want. So, there are c, so that we have n's power c vectors that are alpha fielders. We have n power c1 vectors per vertex in the graph and then n power c2 vectors per beta fielders. So, after a numerical optimization, we get these three optimized parameters that gives a solution or SVP in dimension d in time 2 power 0.2570 d. And we also have computed the space complexities. So, we have these three different types of memory. So, for the quran on quantum memory, it is quite practical because we see that the space exponents are not as high as for the classical at the time. For other saving algorithms, it's much of the same number of orders, but it requires a model that allows quran on quantum memory. So, finally, we have trade-offs. So, in fact, if we have as much quantum memory as we want, we can perform the algorithm with the optimal time. But if we do not have, if we have limited quantum memory, we can still run the algorithm with less quantum memory and by choosing the right parameters, we get a higher time, but we can still get a solution. So, here it is the same for quran limitation. So, we see that it is very close to offering curves. So, to do a synthesis of this for the trade-offs, in fact, if we choose the best parameter for having zero quran on zero quantum memory, we recover the time complexity of the actual best classical algorithms of SVP by saving. Then, if we had some quran, we recover here the complexity of the previous best quantum algorithm, and here we add some quran on quantum memory and we have our optimal time. So, to conclude, in fact, we showed with stage work that the time to break up to crypto system, in fact, it was lower than we think before. And concretely, that means that before, if one claimed about having crypto-stems with 128 bits of security, in fact, there are four bits of security, which are a lot, and it is required fixed with a slight increase of the parameter. So, thank you very much for your attention.