Ladies and gentlemen, let me give you a very warm welcome to this evening's lecture. My name is Adrian Bowman. I am an emeritus professor of statistics in the university here and also as it happens on the Council of the Royal Philosophical Society. And so I've got the pleasure of giving you a double welcome. The first is from the university as tonight's lecture is part of an annual series which was established a few years ago through the generosity of an anonymous donor. And by the way, the name of the lecture series is also at the generous suggestion of the donor. The name of the series is to highlight the crucial importance of statistics and the mathematical sciences, more generally, in addressing issues of major public importance. And tonight's lecture fulfills that brief superbly, as I will explain shortly. That's the first welcome. The second welcome is from the Royal Philosophical Society of Glasgow. So those of you who are not members. This is a body which for more than 200 years now has been organizing lectures and discussions on fascinating subjects, and continues to do so. Please ask at the desk, if you would like to find out more about program for this year, of which this jointly organized lecture is part. Can I check I'm being heard clearly at the back. Thank you. And I'm going to give you a double welcome in a different sense, because while we have a very full lecture theater here. We also have over 200 people registered to participate online. So firstly, welcome to those of you in the building. And now I'm going to make the standard required announcements about if the fire alarm sounds, please make your way to the exit, either at the front or through this door. So please make your exit at the back. And please switch off your mobile phone if you have one. And I think that's all the main things to say you've probably already discovered that the toilets are one floor down. But the second further warm welcome is to those who are joining us online. I'm myself inviting some people to come and enjoy the lecture this evening. One couple said they would love to do so, but they would have to join online, because they would be on holiday in Barbados. So isn't it good to know that here we are on a Glasgow cold dark November evening and some participants are sipping cocktails on a sun soaked veranda. Cheers to you, the online participants, wherever in the world, you may be. Well, without more ado, the lecture tonight is being given by Sir Paul Collier, who is a professor of economics and public policy at the Blavatnik School of Government in the University of Oxford. Paul has a long and very distinguished career studying the plight of countries, and now also communities within countries, which are stuck in persistent poverty. His insights in his very extensive published work are gained in part from careful examination of statistical evidence, evidence that sometimes challenges the simplistic assumptions that many of us might have about what's going on. But his work is not simply about studying the situation. It's about proposing solutions. He was for a while a director of the research department at the World Bank is advice is widely sought at the highest levels of government in many countries around the world. And as one of many indications of his influence, he received a knighthood in 2014 for services to promoting research and policy change in Africa. Poverty and inequality are evident around the world, but there so often isn't there a double whammy. As those at the bottom of the economic scale are more heavily exposed to other challenges, such as the rising cost of living here and in other places, or the effects of climate change, whatever it may be. He was written widely and very excessively about poverty, including several books which I can wholeheartedly recommend to look him up. His passion to address the issues is abundantly apparent. So it was with very great pleasure that I invite Sir Paul to deliver his lecture. Thank you very much indeed to the university to the society for inviting me. And thank you to you for braving a pretty chill evening and coming out to hear me. And of course, you in Barbados. What should we say. I don't remember the 30th today was a gold star day in my diary. When I got invited here. I'm afraid it wasn't because of you. It was because November 30 today was the day that I was due to deliver my next book to my publisher. And I thought, right, I can, I can come here. I can tell them about what's in the book. And it's for me it's a celebration of, yes, I finished this down book right. I should explain I'm trying to write a book which is easy to read, read books that are easy to read are really hard to write. And this book is about left behind places. So that was the idea. And then over the last three months. And only the last three months, something completely infuriating and exciting and invigorating happened. I finally understood what I was trying to say. This is a process that can only describe as sort of a chemistry catalyzed of previously half thought through ideas. And, and it's a fantastic sense of intellectual excitement as these ideas form is why it's why every researcher and there are doubtless mega researchers in this room. That's what you work for. That's why you do the research is so thrilling to get that moment of flow when it all happens. And it also has the infuriating consequence that you've got to change the down book. And, and so I had to let my publishers know, awfully sorry, but it's going to be a better book that's the good news, but it's going to be very late. And my publishers were understanding. And hopefully you will be because instead of being able to stand here and present my book with a clear orderly flow of this is what I've said. I'm still in that state of excitement and flux and flow and crystallizing. And the danger is this is going to be a complete model. Right. And what I hope it can do is share with you this sense of intellectual excitement, which is a thrill. Why would do research. So, how did I get to this three months what was the triggering things, and it was partly triggered by experiences in places that needed to catch up that was stuck that were left behind. So, last week, I was in Zambia. The new president's a very exciting moment for Zambia. I first met the president exactly a year ago here in in Britain. He emailed me to say, I'd like to meet you because I've read your books. And, and I'd like to, I'd like to meet you while I'm here. So that's a good start. He reads my books that's always a good sign, right, in my opinion, right, unbiased. So that was one set of experiences and sure enough, he got a very good question. He said, we are 50 years ago. We're a corporate economy. 50 years ago, we were richer than the other major copper economy, chili. And now we're just about as poor as we were 50 years ago. Now, the OECD is now a member of the OECD. What have they, why they being able to saw pastors when we've just been stuck, what have, what have we done wrong, and more importantly, what now should we do to catch up. This month, I was invited to a place, not that Zambia is a poor country that's stuck. I was invited to a poor region of Columbia, the Atlantic Caribbean region of Columbia, the beautiful region, but it's a very poor region of Columbia that has fallen behind. And they wanted to know, why, why are we stuck when the rest of Columbia has moved on? Why are we falling behind? Now, in parallel with that, I was working on the poorest region in England, which is South Yorkshire and it's called City of Sheffield. I was invited in by the mayor and the chief executives. And so, for the last two and a half years, I've been going there, bringing a team of people who can help, I generally work in teams. And, and it was the same question in South Yorkshire. Why have we fallen so badly behind? Now I grew up in South Yorkshire, I grew up in Sheffield. It was never a fashionable city. But it was modestly prosperous. And yet it crashed in the early 80s. It had been a steel city for 700 years, especially steel, very skilled workforce. It got smashed in about four years in the early 80s. It's still dirt poor. It's still not recovered. And the mayor and the chief executive wanted to know, why, why are we stuck? So all these places were asking the same question in parallel and somewhat bizarrely.  And I've come to have quite a respect for Michael Gove. He's a clever chap who's understood the key point which we'll get to in a moment. And very few other people have. So he, so he appointed me as advisor on leveling up to the government. And, and I'm supposed to report annually to parliament from now until 2030. Fair enough. And then he disappeared off the scene. There is back. Thank goodness. Right. We won't comment on the intervening time. So there's a clear question. Why are these places places stuck. And economics. Before I was at the Vovac School, I was one of the six professors of economics at Oxford at the time. And then I got a chair at Harvard. So, there is an orthodox economic answer to that question. Why are you falling behind. And I'm going to give it to you. There's going to be a slight parody, but I think I think it deserves it right. It's really the, the, the, the orthodox account of why poor places are poor. Don't catch up is the economics of Dr. Panglis. It goes like this. Don't worry. There is a unique equilibrium, which all economies tend to.  And so you don't need any other interventions.   Oh, well, that's because the world's changed, and the place you're living in is now completely geographically unsuited to to growth and so, so you're in the wrong place. We can't get on your bike. It will be a distortion to do a place based intervention to help you. And we know you lobbying for that that's understandable. That's understandable, but it would cost. It would be a wasteful subsidy. It would reduce the growth of the rest of the country. And so we don't want to do that we in the treasury. This is the treasury orthodoxy. We know best a standard approach. No place based interventions, a standard approach because any place based intervention is either unnecessary because you'll catch up anyway, or a waste, because you'll reduce growth elsewhere. So we know best standard approach everywhere is the right thing. No distortions. That's also true globally at the World Bank. I used to direct research center is full of very clever people, but one thing I could not get changed was, there's a boilerplate model. The World Bank staff very clever. They know best boilerplate. You do the same thing everywhere. So, that's where we are. I think that is utterly wrong. And the truth is, I think that there isn't a global equilibrium to which market forces push you. There are multiple spatial equilibrium, both locally stable. That's a mouth for the concept that multiple locally stable equilibrium so let me give you an image. And it's an image of a sailing dinghy. Learn how to sail a dinghy. Yay, some people have right. And you will realize that a dinghy has two locally stable equilibria. Right. One is when it's the right way up. And the other is when it's upside down. And the upside down equilibrium is all too locally stable. Right. And it's not taught how to turn it back up. It's just a set of skills that you have to be taught will come back to that. I'm going to call it a cognitive gadget, which you'll come to. So, there's the reality. And the places that are like the Atlantic Caribbean region of Columbia, Sheffield, Zambia. There are upside down capsized dinghies that are stuck in locally stable equilibria. They're on a different trajectory. Namely, very little growth. A different trajectory from other countries. We're going to turn to some models that validate a purport to validate the that process of natural convergence. They purport to validate the orthodoxy and they're deeply misleading statistics. I'm going to show you some data, which is hopefully just coming on your screen now. This is about divergence amongst the poorest countries in the world. The 64 countries. 60 left behind countries. And the pernicious statistical claims at the moment are that we've got automatic convergence. We don't need to worry about the poorest countries because they're catching up with everybody else. And that seems to be right until you look more closely. We've got three groups here. The 60 left behind the emerging market economy is still awful awful about 6 billion people, and then lucky billion plus the top the OECD. So three groups of countries covers the whole world between them. And there are three time periods now the trick that the key thing to note here is that that middle time so we bought everybody pre 2000 and three from independence to 2003. 2003 to 14 is an middle period. And it's a very unusual period. We're not looking here at a trend that's been going on for 40 years. We're looking at a deviant decade, which I sometimes call the golden decade. It was, it was a series of wonderful things that were very good for the poorest countries in the world. And then that whatever was happening to them, China debt forgiveness, commodity super cycle, all that ended, and they crashed from 2014 on to the end of 2019. COVID is a different story. They're in an even deeper problem with COVID. We'll take these three periods. And we're using some new data. This is all World Bank data on the changing wealth of nations the best estimates of future growth should be the, the increase in your wealth, whether it's investment or savings. And this is what this data is showing is that change the capital in total wealth. And so the left behind the story is tragic. In fact, 2003, the long term trend the annual change in per capita wealth was negative way behind both every, everybody else in the world, they were falling behind. This was the slow death of stagnation, the interview the middle period when everything were right for them. The opportunities fairly well. And so, wealth per capita increased quite rapidly three percent a year. And then if we go back to what's called the new normal after the super cycle ended, they're back to rapid decline. And so they're diverging from everybody else both in the new normal and the pre 2003 period. That's divergence big time. But if you run a statistical regression just through that lot. It's dominated by the six billion countries of the emerging market, which are catching up with everybody else. And a lot of the left behind get missed out, because there isn't enough data to cover them. So that's the myth of automatic convergence. This has been perpetrated, and it's wrong. Thank you. Now we're going to turn to recent advances in science. So the really exciting message here is that policies should vary country by country. It's actually efficient to have different policies in different places. Context matters. There's a need to vary the policy interventions according to the local context, but who knows the local context best. Is it places like the World Bank and the US and the Treasury know the people who know local context best a local people. And so the punchline of this lecture is that the modern advances in research which I'm going to go through in a moment. What they advocate is different policies according to context, and who should do those policies, the local people, if they are to do them, they need to have agency. And so instead of the top knowing best, the British Treasury knowing best, the World Bank knowing best, you've got to do the opposite. The local people who know best, and only if you devolve agency to them, will you get an efficient process of mutual comfort of the of the poor is catching up. So that's the sort of punchline of the lecture. It's true, even if you stick within economics the latest advances in regional economics, so that far from the market forces, happily taking you back to that unique equilibrium. So that's a place as crashed, like Sheffield did. And market forces amplify the divergence. There are many reasons for that it's all published in the literature now. So that I can take as given. What's more exciting, much more exciting. And once the place has crashed become a lot poorer. Poverty produces a load of further problems of once Sheffield became poor. Once any region becomes poor. You get a lot of political problems, social problems, psychological problems, moral problems. And what we need and those then become a syndrome, which interact with each other and reinforce the collapse. The only way of breaking out. From those collapses those traps is if you try and understand and integrate all those different subjects the political, the social, the psychological, the philosophical. And that's hard. We haven't got an integrated social science that has done that we need it, but we haven't got it. So, either you stay in your little academic silo of your subject, in which case you can be precise, but you will be precisely wrong, or you can be roughly right. Because that's the best we can hope for at the moment, have a go at integrating these things. It's better to be roughly right than precisely wrong, in my opinion. I am an intellectual Maverick, who has stuck with a problem of the left behind. And as that problem has needed different disciplines. I've tried to learn about those disciplines. I'm an amateur, but I've been very fortunate to work with professionals. And so I've got a working knowledge of three major new advances that I want to share with you. And the first is evolutionary social psychology. Economics has picked up quite a lot of individualist psychology, they call it biases, but it's not the individual psychology that's the needed here, it's social psychology. And it's not any old social psychology evolutionary social psychology. We are a mammal that is involved in a very peculiar way to become quite remarkably pro social. Why? Because when we came down from the trees to survive, the only communities which survive with the communities that learned how to collaborate.  We behave according to the norms and ideas of a network community, and we learn how to do that through evolutionary pressure. We're still a mammal. And like all mammals, we can be dragged down into greedy lazy selfish if we have find ourselves in an organization, which is very badly behaved and very badly led. For some reason, into my mind comes an image of those London lawyers, heroically defending the oligarchs, so that they can retain their super yachts. You will have followed that in the press, I hope. But it doesn't have to be like that. There are many examples and I'll come across them later tonight of communities which actually managed to behave remarkably well. So the, that's the, that's the first area, evolutionary social psychology. And the, the second area is moral philosophy, not the utilitarianism that tended to dominate for the last 40 years, which is the individualist calculus of, I'm good. If the consequences I intend from my actions add up to a net plus for other people, right. That calculus of the intended consequences produced the extraordinarily named bank free bankman freed, who you may have read about bank and freed, who has just run off with the biggest crypto scam in human history, with devastating consequences for millions of poor people around the world, who've been suckered. The people who are most suckered by these things are the people who are poorest and therefore most desperate. That's what bank and freed has achieved. I'm really sorry, I intended to do well. I was going to make a few billion and give it all away so I'm all right really unjustified. The, the moral philosophy that I buy into was pioneered by Adam Smith in the theory of moral sentiments. And this most recent development is by Michael Sandell, the most eminent moral philosophy in the world, I think at Harvard, and there the idea of morality is not this calculus of intended consequences. It's relationships of mutual trust and kindness between people in a community that to my mind is morality. The, the final survey to do evolutionary social psychology or to do moral philosophy. And finally, we're going to do decisions under uncertainty. And decisions under uncertainty. And if you're in a utilitarian bureaucracy, and you're facing uncertainty. And you're going to be judged by the utilitarian calculus.  If there's a lot of uncertainty. It does nothing. Because nobody gets stacked. If they intend to do nothing. The consequences of nothing, nothing. And so bureaucracies freeze up when there's uncertainty. But what we need when there's uncertainty is action, despite the uncertainty. If the transition out of poverty in a place like Sheffield or Zambia or the Atlantic Caribbean region, that transition will take a generation, and it will be highly uncertain. We need action, despite the uncertainty. And that's been developed the answer to what how do you do that how do you get action is pioneered by the greatest great Scottish economist John Kay, with whom I've just written a book, or greed is dead. And I learned more from partnering with john than any other person in my, in my entire life. And the key message of how do you overcome uncertainty is if you don't know what is going to happen. Find out, learn quickly. Let me give you one image which encapsulates very rapid learning, and it was by the great Chinese leader, then shall pin. Then shall pin came in after the disasters of now. And, and his challenge, as he described it was to try and modernize China. It was he said it's like crossing a wide river. There's no bridge. And so what you have to do is try and forward the bridge, and you feel one stepping stone at a time. And it's that image of feeling for the next stepping stone, which is the right approach in this gargantuan task of getting of breaking the trap of left behind places. And I followed that through with the strategy where he had experiments in parallel. I had a five year programming, five year program. Here's my objective. You're the 40 people who are going to be the young car at the most elite in China, the Communist Party, you'll each become governor of the province. Here's the goal I want to set to you. We want to reduce infant mortality. I don't know how to do it. Modesty. Here's the goal, you try something. Does the bureaucracy freeze up with the message it doesn't know how we don't know how to do it. No, we have to space that he said, we'll be watching you if you've not done anything in the first six months, you're a failure, you're thrown out. We'll be watching you. If you succeed, we'll hover that up and share that information. Places are different. What works for you. Great, it's working. But it may be that sitting there is different from sitting there, but maybe you over there should go and have a look. I think that every five years for 40 years, he touches in the fastest growth, the fastest poverty reduction ever seen in human history. That's rapid learning in action. Okay. Let's turn to something a little sadder, which is Britain's regional problem, our very own regional problem. We have chart one. This is a chart showing life chances. What are life chances. There you're the chance that if you are born in, in the bottom part of society. What's the chance that you will end up in the top half. We're talking about social mobility between one generation and the next. There are four awful Latin American countries with the worst measured chances life chances on earth. There's a dead heat between Italy and the United Kingdom, Italy, famously, two nations sell it eight to into one that desperately backward south Sicily, and the booming vibrant north. Well, Britain is as bad as that. What's driving it. Why are we so completely exception I mean the difference is huge by the time you get to Denmark, you're talking bust orders of magnitude of more equal life chances. So why life chances in Britain so bad as two things riding it. It's very straightforward. What is, do your parents go to university. The answer is, yes. That's good. The next question is, do you live in the southeast of England, or East Scotland. If the answer is yes. You've you've tick both boxes. You're in the best place on earth. Your kids will do well, regardless. If you tick those kids camouflage claws. If you give birth to a camouflage clock, and you've got those two boxes ticked, don't worry, they'll do just fine. If you take the other two boxes. You don't live in one of those that you don't live in the right geography, and your parents didn't go to university. Sorry. Sorry, love. Right.  You can count your lucky stars you're not in Peru. So, that is compounded that inequality of life chances is compounded by inequality in current incomes. So, you bring the two together. And so intergenerational earnings mobility, very, very low. He has Britain up here. Wonderfully high down here. And what we're looking at here is just income inequality. Right. United Kingdom looks really awful. Even less intergenerational immobile than the United States. And by the time we get down to the cluster of Scandinavian countries where massively different. So, Why is Britain so bad. And the answer is, is we've got extreme concentration of power of decision in London and Edinburgh. It's not just government is everything is government is media is finance is the course is the infrastructure. It's all concentrated in the booming region. Doesn't have to be like that, but it is in Britain. The, the course of that, it destroys the chances of local knowledge being used by local people. Look at is a couple of charts on the regional inequality. You see where Britain is the gap between Britain and the next is bigger than the gap between the next and the best. And we're off the map, regionally unequal. And we're also really pretty unequal in terms of local authority autonomy. This one shows local authority autonomy will briefly we skip to the next one, which is the same thing only with fiscal powers. And now let's go to the last one. This is this which is kind of really rather sad. This is the UK compared to the rest of Europe. Life chances and regional inequality. And just look at us. I mean, it's a crushing disgrace that we are so regionally unequal. Compared to anywhere else in Europe. We know what's needed. It's not conflict roughly. This is roughly right the next things I'm going to say, we need devolved powers. We need an automatic revenue transfer mechanism between poor regions and rich ones based on some objective deprivation, rather than political lobbying. We need local control over a chunk of the taxes that are collected nationally. We haven't got any of them. That's what we need all of them. We've known that we've needed all of them for an enormously long time. In particular, the lack of finance for smaller medium firms in a poor region. It became so apparent that it became apparent in the 1920s so much so that in 1931, a committee recommended action. 1931, right. In 1991 years ago that committee was called the Macmillan committee. It was led by adult Macmillan. Who then became Prime Minister, even he as Prime Minister couldn't do anything about it. What on earth is going on. Why have we not done anything about it for all this time. This is a very simple answer. When political parties are out of power. They often promise devolution. Sometimes they put it on tablets of stone, right. But when they get into power. They change their minds, because it would mean giving power away. We know how to use it really well, and so they're anal retentive. There's no incentive to give power away, and that's why for 91 years we've known what to do, and we've never done it. So on that happy note. Let's look at something more cheerful. You can get change. You can do it from the top, you can do it from the bottom. I'm going to look at her passive leadership. I'm going to tell you the story of Zelensky and Zelensky draws on all three things that I will use them bad models that mispredict the good models. So bad models and Zelensky. I used to work on conflict by a conflict. And just as I accepted this, thinking, oh yeah, I can do that. And as part of the celebration. I was invited ages ahead by the Department of War Studies at King's College which is the fanciest conflict department probably in the world. I was invited to give the opening keynote at a conference like this. And I said yes. It was in my diary for the very beginning of March, this year. At the very beginning of March, two weeks earlier, Putin had just invaded. And so I couldn't stand up and say, I'm going to talk about conflict in Guatemala. I have to say, I'm going to talk about conflict in the Ukraine. The first thing I did was I went to the models. Now look, what's the models say, and the models, or very fancy quantitative all coming up with a high degree of precision probability point 9999. Putin will walk over the Ukraine. What were the models doing, they were precise. They were precisely wrong. They were measuring tanks, aeroplanes, number of soldiers, number of Kalashnikovs and that sort of thing. And then there were complicated issues of what's the trade off between a tank and an aeroplane or that rubbish, right. And I learned enough from the social psychology the moral philosophy and the decimals under uncertainty to stand up and to the astonishment of the audience. I put my professional neck out and said, I predict that that Zelensky will defeat Putin. And so far, that prediction was roughly right. Remember the choice roughly right or precisely wrong. Right. So, what, what was the Lensky doing that made him that made him that made me think he would, he would win. You remember what he did. He sacrificed his own self interest, very publicly, I am staying in Kiev. Goodbye, this might well be the last time I can speak to you. That was a very dramatic personal sacrifice. He then had the decency, the modesty to say, I'm not a military man. I'm going to devolve agency to you.  I'll get you the guns. You then have to work out how to how to use them against the Russians. And then the great insight of rapid learning. He said, we have, we will win, because we have one advantage. In your local area, know your context, the context of the terrain, you know, your terrain, a lot better than the Russians. That is why we will win, we will use context as our advantage. And that was the rapid learning. So far, it's worked. I'll give you two examples of places that did rather similar things. Pittsburgh in America. Pittsburgh was a steel city, very like Sheffield, it crashed. Disasterity. It was, it was, it was a half its population left. It's now one of those prosperous cities in America. So how did it revive. It revived, because its mayors and its governors state had a lot of authority, and they use that authority to build mutual responsibility. So the business community in the state and in Pittsburgh and the universities, all worked to a common purpose, encouraged by good leadership. And my final example is East Germany. East Germany in 1990, when unification happened, it was very much poorer than Sheffield and South Yorkshire. Now, it is very much richer. So South Yorkshire is left behind by a place that overtook it dramatically so how what happened. First, West Germans were rose to a sense of duty and obligation to help East Germany. It was a purpose that united them. And secondly, they introduced an institution which delivered it. And that institution was called KFW, it had been founded after the Second World War with the explicit purpose of regenerating Germany. And by it, and as soon as the Tusk became East Germany recovery, KFW was switched to do that. This was big stuff. It was about 70 billion pounds a year for 30 years. KFW has a labor force of 7000 staff with 80 regional offices. It's capitalized at 500 billion pounds. Last year, Britain set up its own version of KFW. It's called the National Infrastructure Bank. And amongst other things, its stated purpose is to help poor regions to catch up within Britain. Great, we've done it. It took us till 2021 to do it. Germany started in 1947. But there is an order of magnitude difference. Remember the number 71 billion for 30 years. The National Infrastructure Bank has 22 billion for 10 years. Spread over the whole country. Remember the 7000 staffing KFW. The National Infrastructure Bank has at the latest count 127 staff. Capitalized in Britain at 22 billion. KFW currently capitalized at 500 billion. These are orders of magnitude different. We're not serious. So that was a top-down process of leadership. And we finally turn to a bottom-up process. And I'll give you one example, and it's the Basque region. And the Basque region was a catastrophe. It was a combination of an industrial collapse, a very bad industrial collapse. It was the rust belt of Spain, compounded by major violence, ETA. And so it was a disaster. It's now got the lowest poverty rate in the whole of Spain. It's a very prosperous region. It was a disaster of the first order. And it's now a spectacular success. How did that happen? And it wasn't top-down leadership. It was bottom-up. The guy who achieved that is called Jose. He's a priest, an old man now. But he started in very unprofitious circumstances. He was in a little town. He was a priest in a little town. 7,000 people, a broken town. And his principles were solidarity and mutuality and participation. Everybody's got to participate. And he built a little institution to do that, which was a cooperative. And it was a cooperative based around training. We've got to get practical. We've got to train, learn how to do recovery. So it was a very unpromising start by this young priest. And where is it now? It employs over 80,000 people. It has over 250 companies within its portfolio. It's the biggest enterprise in the bus country. It's the seventh biggest enterprise in the whole of Spain. It's been a massive success. And it was all a bottom-up process. So if he can do that in very unprofitious circumstances. So can we. I've just got time or hope for one last story, which is from very poor country. And it's, I'm going to use the concept of a cultural gadget and talk about drones. Drones used to deliver blood to clinics. Celia Hayes, the great evolutionary social psychologist would describe that invention of drones to deliver blood as a cognitive gadget. And where was it that invented? Who had that idea to deliver blood by drones to cognitive to to to clinics? Well, who developed drones? Amazon. Amazon. What is Amazon? It's a brilliant website. And very clever people. And logistics. So they developed drones. What did they develop them for? Well, they developed them to deliver packages to people who ordered stuff on a website. So that was the problem they solved. And there's the machine. It takes off. Very clever. Did they go the one step extra and say, not only could we deliver packages, we could deliver blood to clinics. No, they didn't. Let's go across to the other side of America to the Pentagon. They also developed drones. Slightly different person purpose. This was targeted deaths to people they thought were terrorists, right? So, same very fancy technology developed. Oh, brilliant. Did they think all not only could we deliver targeted death, who could deliver targeted life? No, they didn't. Just down the street from the Pentagon is the World Bank. Now that does have a whole big vice presidency on health. And they're very clever people. And so they've got the purpose of delivering health in very poor countries. And they're very clever people. Did they come up with it?  No. Does anybody know who thought of how to use blood? Who came up with this idea? Rwanda. Rwanda. Why did they think of it in Rwanda? Because they knew their context better than anybody else. They knew the terrain in Uganda in Rwanda was very hilly and there was no road network that was adequate and they are broke. They had to come up with something cheap or give up. And so they developed a mindset of innovation. They were the ones who thought about it. And now the happy news that once you've got that cognitive gadget of a drone to deliver blood, it can spread to other places where it will be useful. It's West Scotland delivering blood by drone to clinics. I imagine it would be quite useful. I don't know whether you're doing it. We are well done. You spoiled my punchline. I'll tell you where it spread first in a network community and the network community didn't include Scotland. The network community did include other African countries. That was a network community. And so now Ghana is delivering more blood by drone to clinics than Rwanda. And that is the good news that once poor countries realize that their context is their advantage. Then they can come up with these great ideas and those ideas can spread, even sometimes to us. Let me conclude. There are vast differences in life chances. And those vast differences in life chances are entirely avoidable. I feel this very personally, because my own situation ticked both of the boxes of disadvantage. I was born in Sheffield, a very unfashionable place. And both my parents left school age 12. And so they had no chance in life. They stayed fairly poor, respectable just on the lower edge of clinging on to respectability. They had no chance in life. But thank God, written, got one good, modest leader, just in time for me. He was called Clement Attlee. All the institutions that took me from that beginning, all the way through to a doctorate at Oxford, all financed by the state. And for that, I am eternally grateful. We need more Clement Attlee modest leaders. If you remember, he was famously accused by Churchill of somebody who said to Churchill, he's very modest man Churchill said he's much to be modest about. Well, he's much to be proud about as well. And what we ought to do is fairly obvious. But we're an upside down dinghy. Britain is an upside down dinghy we're stuck. If you're an upside down dinghy, you need to learn from others how to turn that dinghy right. We refuse to learn from others. Why do we refuse to learn from others the British Treasury is arrogant beyond belief just as the World Bank refuses to learn from others is arrogant beyond belief. We need a dose of humility. How much more before we find a modesty to learn. Thank you. Thank you so much, Paul. I think you can hear the way in which your lectures been appreciated. It's been absolutely fascinating description and hugely thought provoking so much so I can guarantee that we plenty of questions coming your way. I would ask when the questions come please be concise so that we can get as many questions in as possible. Anyone who are listening, please use the question and answer facility, not the chat facility, and we will sort out the questions that way. The other thing to say, however, is that we're going to have a very brief pause of two minutes, during which we will set up the roving mics, we will give Sir Paul a chance to catch his breath. We know that sometimes people travel some distances to get here. It may be that you have to slip out, in which case feel free to do that to catch trains and whatever. But we will start again with the questions in two minutes time. Thank you. Okay folks let's begin. Can I just remind you, please. When you ask a question be as concise as you can, and then we'll fit as many in as we can. And please forgive me for stating the obvious but if the microphone comes to you, the trick is to point it at your mouth, not at the ceiling. And that will ensure that we all hear very clearly. Can I just also interject. I was deaf as a post. So please speak up. If I gave you an inadequate answer. And that's because I haven't heard it right. Let's have the first question. Thank you very much. I've got a question about place based initiatives for over many decades I've worked for projects funded by the European Regional Development Fund. And I wondered whether you would think that was genuinely place based initiative, or whether it was there was faith, whether there were, there was a failed place based initiatives the European regional development funds. Oh yes, so we've got lots of little funds. The problem is, they're not big enough, and they're not sustained enough. So of course we need regional funds. We need bigger sustained. So just look at these, look, look at what what it costs in East Germany, right. 10% of German GDP for 30 years was poured in, right, with a big institution that managed it. That's the scale of serious. Even with all that East Germany is still poorer than West Germany. So we, we've got little pots. It's very likely got about, I've just been counting them. I, I, one of my advice, bits of advice to Michael Gove was count how many pots you've got, and then get rid of them. Next question, the gentleman right at the back there. Keep your hand up please. Sorry, is it a lady, it's a lady a bigger part. I say it's not that good. Hold it like this, not like that. Thank you. Thank you very much for the lecture. I work in the humanitarian and development sector and a lot of what you were saying reminds me of a discussion we are having just now on localization. And I think, for me, it's not that we don't know that we have inefficiencies baked into the system because decisions are delocalized. We do know this but many of the decision makers are incentivized to hold on to the decision making power that they have. How do you challenge those power structures. Yeah. That's the right question. That's the right side. Right. And the only answer is, and we've got to create a groundswell of opinion that says enough is enough. Right. If, and I think this is a good moment. Here's the hopeful bit. If not now. For goodness sake. Right. How much more do things have to fall apart before we say enough. So that if not now when. And the next question is, if not me. Who. Give it to somebody else. I've tried to give you here examples, you know, a priest in a little town made a vast difference. Zelensky, a good leader made a vast difference because he had a purpose. He wasn't trying to granize himself for once he got a purpose and so brought people together, made demands on people. So we can do it. I am completely incompetent in social media. I don't even try. I don't tweet or Twitter or whatever it is. But I try and reach young people, because young people have a great skill, which is social media. And the power of youth in social media is what swept the crooked, encrumbled president out of Zambia and brought Hitchhilema, the new president into power. It was youth backing it. They said, you sound as if you're speaking the truth. You've got a strategy. You're being honest. And we're going to support you. We have created a tidal ways of the youth vote, which swept the crooked incumbent out. So use can be an enormous force for good. It can equally be an enormous force for bad. Right, just as we can be dragged up or dragged down. So that's the best I can do. It's a struggle. And old men can be just as impatient as young men in wanting to hurry up. Was there a second question at the back, and then gentlemen here, and then online. You showed some depressing charts comparing the UK with other large countries within Europe. One difference is the electoral system used well in our case for the Westminster government. I think we're unique in having first pass the post, whereas the other countries have some form of proportional representation. Do you think that's significant in helping maintain a long term strategy in government. I think to get a long term strategy in government. You need something that is goes beyond party politics. So you need to actually try and build some common purpose. And that is that is a cross parties and I'll give you an example that's happening now in Bangladesh. It's a young man, remarkable young man from a very humble background. Who's running a network, which is built up to 35,000 young people. He's aged sort of about 20 to 30 educated. And he's built this network. And he gets distinguished old guys like me to speak on it. And they have a protocol. And the protocol is that everybody has got to be courteous, all political views included. But nobody is allowed to be rude, or, or, or not listen to others so you try and get they then the 35,000 breakout in discussion groups to say how can we use this knowledge we've heard in our own context. And they are so influential that politicians are queuing up to try and join it to comment and join it join it. So, it's very influential, but it's protocol is, we're not putting up with ideological opposition, which we're trying to find common purpose across political lesions. That I think is what's needed. And I should also say that there's a very clear relationship between devolving power and participation. So, in Britain, the turnout local elections is in the range about 20 to 25%. Most people just don't bother to vote because local governments have so little power and they know it. In continental Europe, where there's much greater devolution, turnout at elections is in the range 75 to 85%. People hold their local government to account because they know it's got money and powers and it matters. And that forces the parties to be non extreme, because most people are not extreme Britain is governed by the 1% who joined political parties. 1% of the adult population is the most extreme people on the right, the most extreme people on the left. So the 1% choose the menu.  And the rest of us then choose and the none of the above isn't on the menu. Gentlemen halfway up. You mentioned social media a minute ago, and I've got a question related to your examples of the Basque and of Germany, East Germany and not so much social media, but where does the media in general stand in these countries compared to the power of the Netherlands in the UK. Where does the what, where does the media stand, the best etc, compared to the power of the, the mother, the meal, the telegraph etc here. That's a good question. The honest answer for the Basque countries. I don't know. For Germany. The media much more devolved much more devolved you've got a regional media used to have a regional media and Britain, and it collapse. The tragedy now that the, the, the used to be a thing called the Sheffield telegraph and the Manchester guardian, and the Sheffield telegraph is no more. And the, and the Manchester garden guardian, and survived by moving to fetch to London so that we've lost a regional press is terrible. And it's all bound up with the fact that regional press can't report on local issues because there's no local power to do things and so everything is focused on politics in London, and this polarized system. Oh, I see. That is a good question. I really don't know. Is the honest. Is there an online question. Yes, we've got a few. Kristen Morrison asks, what can be done about the prevailing attitude in some parts of Britain, that the state, the council should do it, whatever needs doing. How do we galvanize innovation, imagination, energy from the bottom up. Yeah, and the, and that is that that's a good, that's a good question that there's in most people are not given anything like the, the powers to use their potential. And so most people are performing way under their potential. And there's a lot of survey work, it shows that it's got much, much worse, because businesses, and indeed public organizations, and we've got more and more run from the top down. The work satisfaction has declined consistently. I have always run the organizations I've run, always being run as teams in which we have a common purpose. And I've adopted one principle. Which is, if you in the team feel that you know how to answer this, what to do in this situation, do it. If you don't know, don't feel obliged to do something, you can always ask me or anybody else. If you feel confident, do it. If it doesn't work. And we learn something. We don't expect anybody to get everything right. And so I never criticize things that go wrong. And I always support that principle that if you feel you can do it, do it. And what that reveals in the end is a massive increasing commitment because people recognize they are part of a team they are jointly responsible. I've got two PAs because I'm kind of busy, but one of my PAs has a cup. And on it is written just the words Professor Sir. So I grew up in a household where if you're given something like a knighthood, it will be deeply pretentious to refuse it. And it will be even more pretentious to use it. And so, when I do something really even more than usually idiotic, she gives me a cup of tea with Professor Sir. And that's the spirit that makes a difference. I think, Adrian, you will testify that I've got a staff which is second to none. You're a very lucky man. Question from a lady at the back and then the gentleman at the front. Thank you. Going back to the question from just behind me about the deficiencies of first past the post. You agree that in the Westminster system, we have the leaders of the two main parties who do have a commonality of purpose. And our dingy is really stuck upside down. Yeah, I think that a proportional representation system works much better than the first pass the post because it forces people to work in cooperation. And so stabilizes the range here we here we've got these these these oscillations between extremes and to extremely damaging. So, trying to build a, I'm a, I'm an advocate of what I call the hard center. The hard center is one that says, we're proud of being centerists. The left center which apologizes for not holding the extremist views, we believe in the center. And so that's I believe in pragmatism, because we never know enough to know what utopia is. There is no utopia. We're not in a dynamic, uncertain world. The best we can hope for is Providence, that things on average will up to the best. And I do believe in that. So, there's no utopia. Anybody who says has an ideology which says, this is the way. Whether it's Marxist or capitalist is obviously wrong. Obviously, in my view, you just the basic fundamentals of decisions under uncertainty, say, you can't identify a utopia and stick there. That's not the nature of the life we're in. And so, pragmatism and pragmatism plus strategy. That attempt to learn rapidly. That's the best we can do. But we're not doing it. Anything like one more question. Professor sir. You intrigued us at the beginning of your talk by saying that you'd had this Eureka sort of moment where you've, you'd worked on this book for ages, and then suddenly had to rethink because a different perspective came to you. What was that. Okay, let me spell it out. It was the realization that far from this standard model of, we do the same thing everywhere. Right. It was catastrophically wrong, because the knowledge of local context could be turned to advantage. Once you start to see the differences that a poor region has from a rich one, once you start to see that as that's the advantage. And who knows about it best, we do. That's the key insight that using difference to advantage. I'll give you a little example. When I flew into and out of Heathrow, sorry, when I flew out of Heathrow today, I noticed. Two jets, a finite jet just coming in. And a ice air isolate just going out. And Finland and Iceland have both in the last few years developed a very big, very successful airline. And they've both hit on the same idea, which is, let's use the polar route, let's use our weird locations far up in the north, but it's too bloody cold. Let's use those to advantage. And so the polar route to the, across the Atlantic is Iceland's developed at the polar route to the northeast, Asia. That's what Finland has developed. It will it last, it'll run for the next 20 years. And then, then that will burn out, but with a mindset of innovation, they'll think up with someone else. And that's the, that's what life is like. There are some nations, which just keep turning their local context to Advantage. And some which don't. One final question from gentlemen over here, and then we'll draw to a close. Was Michael go right to dismiss the need for experts. What he has understood. So let's give him some credit where it's due. He's understood that market forces are pernicious in left behind places that you actually have to have active intervention to offset these market forces. What did he mean by exit or the silver mark about excellent and you better ask him. But I'm an expert, but my expertise. I know it's limitations, right. I'm not saying I can give you the precise truth. I've told you, I think I can be roughly right. And so I think modesty in everything, including an expertise would not be a bad thing. And perhaps that's, if we're generous, perhaps that's what he meant. I'll just note, I fear we're going to have to draw the discussion to a close. We could go on all night and I'll remind you that there is a reception outside where you're most welcome to have a drink and keep talking. But for the moment, I really would like to thank Sir Paul very warmly for taking the time out of these busy schedule to come and give us such a fascinating evening and giving us so much to think about we really appreciate it greatly. For the moment, you will have the opportunity to show your own appreciation in the usual way but before we do that. There's a short presentation from the president of the Royal Philosophical Society, Mr Pat Monahan. Thank you. Yes, sir. It's a great pleasure for me to present to Sir Paul Collier, the Royal Philosophical Society of Glasgow's Adam Smith medal. Now the links to Adam Smith in the lecture that we've just heard are clear. Paul has told us about the wealth of nations being linked to the wealth of communities, and that the wealth of communities can translate into the wealth of individuals. To reach that, we need to decentralize, we need to localize, and it's the local understanding that we need to get the decision making to that level, because in the local level, you have in a way that sympathy of sentiment which was central to Adam Smith's other book, the theory of moral sentiment. And I think we've heard all of that captured in this lecture so on behalf of the University of Glasgow, but primarily on behalf of the Royal Philosophical Society of Glasgow. It's a great pleasure to present to Sir Paul, the Adam Smith medal, and please join me in congratulating him on a wonderful lecture. What can I say. The right answer would be as little as possible, please. Thank you enormously. I you cannot. I cannot tell you how much this means to me. Not least because my friend and mentor, John Kay, I will, I will say. Yes, I got this medal. Thank you very much.


Hi, I'm Johan Damen and I want to draw your attention to our paper German on the deck. This is the paper we submitted to Asia-Crypt and it got happily accepted and it will be presented by one of our co-authors, Sjil van Asch, on Wednesday at 8.50 in the ballroom B in the session on symmetric crypto. It's a joint work with old-time collaborator Ronny van Keer, the catch-up team, Seth Hoffert, who also is in our team since a few years and has always great ideas. Bachelor student Norika Bakueti, who was at Radboot and did an internship and whose internship led to this work, and last but not least, Sjil van Asch, who will actually present the paper. Okay, what is it about? It's about refactoring symmetric crypto. Let's take a look at a metaphor. A metaphor for the field of symmetric crypto is this sea landscape. So we have two worlds, actually, and the first world is above the water, and that's a world where everything is nice and clean, and the world base itself on ideal primitives. And these ideal primitives, they're represented by the water surface, so the water surface is nice and smooth. And if that is the case, then we can do nice things about the water, like make provably secure schemes, and these schemes, for their provable security, they base themselves on some assumptions on the water surface, so on the primitives, and the primitives are typically a block cipher. It's like dominantly the block cipher. But under the water, there is another world. And that is the world of cryptanalysis, of people that try to find weaknesses in block ciphers, try to specify attacks, or try to prove properties of block ciphers. And these are two different worlds, and it's a nice interface, and this interface has given us a lot of nice modes, and also nice block ciphers, and it divides the world of symmetric crypto into nice parts. But there are some constructions that do not fit this nice image. And one such construction is something, I go back to my work with Vincent Hyman, as you know we did together the AES, but later we did some other work, and one of these other things was Pelikan Mach. And Pelikan Mach is a Mach function based on AES, Heindalen, that only requires four rounds per additional block of plaintext. So additional block of message to Mach, and so it's about two and a half times faster than AES. So the problem of this construction is it cannot be reduced to the PRP security of AES, but you have to really do cryptanalysis. But the gain is that you get much more efficient Mach function. Another example is the monkey duplex. So monkey duplex. In general the duplex can be proven secure if you assume a random permutation, if you believe that such a thing exists, it's a kind of controversial issue. But monkey duplex is not anymore because you use different number of rounds and there's no way you can model this underlying permutation as being ideal. The monkey duplex is serial, more parallel function is farfalle, so it's a construction to build a function with variable length input and variable length output based on a permutation, in this case symbolized by F. And it has also several instances, cravat and zoof, cravat based on the Kacak F permutation and Kacak P permutation, and zoof based on Zudu are more recent permutations, a bit more lightweight. And all these things they require for their security cryptanalysis. So we thought maybe it's a good idea to kind of put the border elsewhere and put the border at a level where the underlying primitive can handle variable length messages and make one function like that and build modes on top of that. And this interface is a deck function. So a deck function is something that takes as input a sequence of strings of all arbitrary length and generates an output string also of arbitrary length. And using this deck function, we can build very efficient modes and these modes can be proven secure with reasonably simple proofs, assuming that the underlying deck function is hard to distinguish from a random oracle. And that is actually what the paper is about, that's also what the talk is about. I hope we will show up in large numbers, thank you.


The next talk is entitled inverting HFE systems is quasi-pollinomial for all fields by Gene Tiding and Timothy Hodges, and the talk will be made by both of them. Okay, thank you. So we want to present a new result on the complexity of the direct algebraic attack on HFE systems over fields of arbitrary characteristics. So this generalizes a result that was announced crypto 2006 by Grambolin, Juin Stern, and I thank the previous speaker for the introduction to multivariate crypto systems, and I won't discuss too much about that. So I'll present an introduction and then Gene Tiding will step in and talk about the main results in some future work. Okay, so basics of the hidden field public key crypto systems. We have a pair of fields, f and k. A base field has order q and k is of degree n over the base field. The private key is a univariate polynomial defined on the larger field k. And this algebraic structure of that larger field is kept secret. So the other part of the private key has two invertible affine linear maps from k to fn. The public key then is the composition of these three maps, which in terms of the underlying space f to the n is a set of n multivariate polynomials in the base field. So at this point I want to emphasize that we'll always consider these polynomials as functions, so they'll be in the polynomial algebras factored out by the field equations. Okay, so an effective implementation of this was given by Petra 15 years ago. So we required that the polynomial have low total degree d. This enables us to do efficient decryption using standard algorithms for solving univariate polynomials. And we also require that it p should be quadratic over the small field f, so that the public key polynomials p are quadratic, which enables efficient encryption and relatively small key size. So putting all this together, it means that the polynomial has to have this form here, because these x to the qi are functions on k, which are not linear over k, but they're linear over the base field f. And so the quadratic functions are the products of two of those functions, so they look like x to the qi plus q to the j. And our condition here is the condition on the degree of the total degree of the polynomial, that its total degree should be less than or equal to d. So that's the basic setup that we want to analyze. What's the attack? So the attack is just the basic grobner basis solution of the system of equations that we get. From any ciphertext, y1 up to yn, that gives us a set of n quadratic equations, which we would like to solve to get back the plaintext xi. Now in general, if this were a random system of n quadratic polynomials, this would be a very hard problem. But for HFE systems, they're not random systems. So the algorithm terminates significantly quicker on HFE systems than it would on random systems. So the problem for assessing the complexity is to try to understand how the restriction on the degree of the big polynomial p affects the complexity of this grobner basis algorithm. So as I said, this was done in 2006 by GJS. And they showed that it was quasi polynomial when q is equal to 2. Now that techniques didn't adapt very well to the general base field situation. So it's remained open for a little while. And so we want to generalize this result to an arbitrary base field and introduce some new techniques. So how do we even get a grip of the complexity of a grobner basis algorithm? Well, we use something called the degree of regularity. Essentially the grobner basis algorithm is roughly kind of looking through the ideal generated by the PIs for equations of smaller degree, which can help us solve quickly the system. So what we want to do is look for the first point at which we find a non-trivial degree force. So we find a combination of the PIs, which is a smaller degree than we would expect. So some real cancellation going on. And we want to avoid the trivial degree falls where we get a combination equal to 0 or a degree fall caused by the fact that Pi raised to the power q is equal to Pi. So avoiding those trivial degree falls, we're looking for the first point at which we have non-trivial degree falls.  So this is a good marker for how quickly the grobner basis algorithms are going to terminate. Just a little bit of technical stuff that we need. This is really a question about the highest degree part of everything. So we can reduce to the associated graded ring, this truncated polynomial ring, and just look at the highest degree part of the PIs. This translates the concept of degree of regularity into a question about the existence of non-trivial relations in this algebra, which is much easier to deal with algebraically. So the degree of regularity now is the first degree at which non-trivial relations occur between these PiHs. And we have the similar kind of trivial relations that we're trying to avoid in this case. OK, so these are the same thing. So that's what we're trying to find is still, we don't know a whole lot about these Pi functions. So that's not a good place to look for a solution. What we have to do is lift back up to the larger field. And this is actually not such a complicated operation. It's just tensoring with the larger field and using a little Galois theory. It enables us to re-express the degree of regularity of these Pi's in terms of the original function and its translates under the Galois group or the Frobenius maps. In addition, we need to use this kind of intuitive but not completely obvious how to prove a result that the degree of regularity of a set is bounded by the degree of regularity of any subset. So this was a basis of the ideas in GGS's result, and it was recently very neatly detailed by Du Bois and Gamma in their recent paper about this subject. OK, so now we combine that with this extension of the field. And so let's bring back our original polynomial, p of x, and look at p0 of x, which is the quadratic form associated to this part of p of x. OK, so the degree of regularity that we're looking for is actually equal to the degree of regularity of p0, and it translates under the Galois group in this algebra here. So putting all this together, we get the kind of rather unexpected result of the degree of regularity that we're looking for is bounded by the degree of regularity of this single quadratic form here. Now, this doesn't look as if it would give us interesting information, but it turns out to give us very useful information, and I'll now pass it on to Gentile to tell the rest of the story. So what Tim has talked about by now is what's everything done before. So what I will talk about is what we have done after that. I'll present first our main theorem. OK, basically what we did is we give a global upper bound on the degree of regularity in the sense of Du Bois and Gamma for the HFE system, and the mentoring are given as the following. So the degree of regularity of the system defined by p is bounded by the following formula. Rank of p0, so remember the p0 introduced earlier is by linear form, so if you view it as a matrix and it has a rank, and then times q minus 1 over 2 plus 2. So this is the main result I was. So here I would like to really especially point out the importance of q here. In the previous result, this q was never used in any form, and in the result presented by Ju and the 4j on the algebraic attacks on HFE system, where they only discussed a case q equal 2, but what they said seemed to suggest it works for all the q's, which means the degree of regularity is independent of the size of the field, and our formula suggests otherwise. So those are universal bounds that require no additional assumption, which means we prove this formula without any additional mathematical assumption on the degree of regularity. Before I present the basic idea of the proof, I would like to say a little bit more what I was done before. So GGS, what they did basically, they outlined a new way to study or to bound the degree of the case q equal 2, and their approach is very interesting in the sense that what they realized that since HFE design is over the bigger field, therefore you must lift the problem back to the bigger field to look at what's going on. And they sketch a way to connect the degree of regularity of the HFE system to the degree of regularity of the lifted system over the bigger field. So here I would like to emphasize the word I used as sketched. And with this idea, they used the following mathematical assumption, which I will not say one by one due to a time constraint, and the key things, they derived a heuristic and asymptotic bounds for the degree of regularity for the case q equal 2. That's what they did, okay? And to study the case for general q is still a very open problem. And after the work was done, me, with my colleagues, Dieter Schmidt, and Fabio Warder, and a student at TU Dammstadt, we found something very interesting, which means we did some experiments. What we found out is that the prediction of Jue and Fojie didn't work for the case if q is a final field of other characteristics, for example, 13, 31. And why so? What we realized that is what is called the role of the field equation. So in the algebra attacks presented by Fojie and Jue, they implicitly used the field equation. Namely, they're not solving equations with n variables, n equations. They're solving equations with n variables, 2n equations. And if q change, which means that if q is large, you can do the same. But in the case of gf2, your field equation is also degree 2. Therefore, it can be efficiently used. But if q is 31, then you will have 10 additional n degree q equations. And they cannot be efficiently used because of degree constraints. But mathematics being, that means you're not solving the equation of the final field. Instead, you are solving the equation of the extension field of the final field. And in that case, the number of solutions actually is 2 to the n. Therefore, it becomes a much harder problem. So also, in terms of understanding the degree of rarity, there's no and sometimes only for the case of other q. And in terms of my own opinion, the real breakthrough happened in the case of Fojie and Jue is the work done by Dubois and Gamma. What they did in the A-script last year is to present a very rigorous mathematical foundation for the argument of GGS. And they present a new method to compute the degree of rarity. This is an inductive computing method. But it does not give us a closed formula to tell us the behavior of the degree of rarity. And our approach is the following simple observation. What we realize is that because the theorem previously presented is the degree rarity of this set of polynomials is less than the degree of the single polynomial p0. So what we did is that we just tried to find the bound for the degree rarity of the single polynomial, which is a p0. And our proof is also very different from what was done before. The proof done before resides on the continuum dimension of certain spaces. What we did is we just did a construction, which means we construct explicitly nontrivial sausages. And to show that the degree indeed falls at this point. So the constructor means I will find a low degree nontrivial annihilator in the associated greater algebra for p0. And this set of construction relies on the following mathematical structure, which means we're used to the classification of quadratic forms of a finite field. And this is where the rank comes in greater rows. I just give a brief idea of how the proof is done. So given the polynomial, quadratic polynomial, you have the following theorem in the case of q is even that there must be the following canonical form. Let's look at the case when the rank is 4. If the rank is 4, given any quadratic polynomial you can convert in this form, which means x1 times x2 plus x3 times x4. The question is how to construct the nontrivial sausages. And it's pretty simple. Those are the guys. Those are the annihilators, which is x1 to the q minus 1 times x3 to the q minus 1 and the rest are very similar. What you do here is basically you find the crossing terms. You choose one term from the first one and another term from the second one and you raise the power q minus 1. And then here you can observe easily that if you multiply this point by this guy, they will become zero because after you multiply them, you can see here that you have x1 to the q here and the x3 to the q here and there's a degree 4 that occurs. And that's it. So this is the basis of our proof. And this basically implies all the idea we use here. Of course, in terms of the mathematical writtenness, we must prove that a annihilator is nontrivial, which is a little bit hard in general cases. So now what is the implication of our result? If you look at the degree of regularity formula, you realize if you fix q, the degree of regularity is all log q to the d. Let me emphasize again if q is fixed. In this case, you can see that the complexity is indeed a quasi-pornomial. But what we've shown is something very different here in terms of our theory is if you make the q change, as in the case of lattice cryptosystems, let's assume if q itself is of the scale for all n, then suppose the bound is good, then we have a very different conclusion, which means inverse HFV systems will be exponential instead of quasi-pornomial. So we present a very different idea to look at the HFV now, which means when you design HFV, you should not fix the size of the field. Instead, you should change your size of the field q according to the size of the vector space, which is the n. And now I want to point out a few things related to our bound. First, I want to emphasize our bound is not optimal. Why is so? Because in the proof itself, you notice we only use one polynomial P0. There are P0, P1, and the other polynomials. We never use it. So therefore, this is definitely not optimal. And in the work of Dubois and Gamma, they made a very detailed list of the degree of regularity computed. So we did a comparison of their result with our result. Of course, their result should be better than ours because their result is global. We only use one polynomial, and they use all the polynomials. But however, we find something very interesting, which means in the other result, we have seen as n becomes large, and our bounds have become very close to their bound. So we don't know exactly what's happening, but I think it's very important that we should study what has been the connection between these two bounds. Now I was finishing the talk with a little bit mentioned of future work. So after this was done, I did some work in the case of if you are polynomial with px equal to x squared. In this case, I can actually prove not our upper bound, but the lower bound, or exact the bound, which means I can prove in the case of a square where px equal to x squared inverting the HVV system algebraically is actual exponential. And in another joint work with Clio, we now can prove the degree of regularity for the case of HV minus. And Hodges and did some other work related to the extension of our result. What is really important, I think, in the future is that we need to really do a very good comparison with the DG's result, which means we want to know how good our bound is. And it's possible we can find better bounds. And also, we feel there's possibility we can apply our techniques to other systems and the proven security-related problems. And of course, I have to thank the people who prime me with money to do this. And here I would, in particular, thank Vivian Dubois and Nicolas Gammar because they sent me the paper before it was published and for numerous discussions with them. And it was extremely helpful. And thank you very much. So we have time for one question. Three weeks ago, Petale, Fugire and Peret published complete cryptanalysis on FHFE. Do you know that result? What's the result again? Complete cryptanalysis with a practical break. After nine days, they break the most conservative parameters with N256. Which system? HFE. What is the D? What is the D? HFE. Yeah, HFE has a degree D there. What is the D? I don't know what is the D. I think, if I ask her, does the paper attack the D equal to 2? Yeah, yeah, yeah. That's a mean run. Yeah, that's a mean run. That's a mean run attack. My question is how that work relates with your work. So what we say here is, remember, I said it is a complexity of algebraic attack on HFE system. For HFE, there's another major attack, which was developed first by Kibli Shamir, and which I can call it mean run attack. And if you look at the queue, as I said, the rank Q0 I used earlier, if the rank is very low, 1, 2. And there's an attack due to Kibli Shamir, which is that we should use the property of no rank to attack the problem. And there's a work done by myself to show that actually Kibli Shamir attack doesn't work, again, due to the field equations. And then for J and the parade, and they also did some work to show that, in one of the instances of the square system, it was broken. In this case, the rank is equal to 2, or equal to 1, Fx equal to x square. And actually it's very interesting in that if you read the paper very carefully that they showed attack on the system, mean run attack system, and they show the complexity, and realize the complexity actually has exponential growth. That only means, to me, that only means the parameter we choose was too conservative. So if we choose the parameter properly, it should be no problem. This is my opinion. OK, thanks. Let's thank the speaker again. The speaker. Thank you.