Okay, thank you all for coming, let me begin by introducing our speaker. And I appreciate all of those who have been tracking us around campus as we change for our 7-hour series. But this is a very good room and we will make sure that we get enough time to respond to those announcements. And we also always publish contact information for those who need additional guidance on our next series and where we'll hold it. Our website also has all of the seminars that we've hosted this year and luckily we have them recorded. And if you miss any particular seminar, you can go to open courseware through the university extension and everything is captive, including my introductions, I suppose. So we have three more this quarter, exciting seminars, so please look forward to those announcements. It's a particular pleasure for me to introduce Dr. Eric Walsh. It's a distinct pleasure for me to introduce Dr. Eric Walsh. I've heard of him almost two years ago now. And what does that mean? He contacted and said, what's going on with the public health program at UC Irvine? He's collaborated with many colleagues around campus and we had a great meeting and shared a lot of information and mutual interests. He is MD, MPH, he got his MD degree from Florida, but he's accomplished a lot since and he's traveled all over the world doing medical practice. And currently he holds two very challenging positions in the Oriental Health Care Agency. He's the internal director for the correctional medical services and he continues to support the family health services as the medical director for the County of Orange Health Care County family health services. He is nationally, he is on the Presidential Advice Committee for HIV AIDS and this of course involves a lot of international activities and advice to the President. He was also an advisory committee for the Surgeon General, David Seicher, who is currently at the Morehouse School of Medicine. He is currently helping us with NIH-funded global health framework here at Irvine and many of our students are benefiting from his wisdom and we thank you for doing that for us. So today I'm going to talk to us about what keeps you busy the most. I hope stress and health is part of this. Thank you. All right, we'll get right into it. I'm hoping that I don't be able to take the whole talk in some sense, but we're going to talk about stress and health disparities and hopefully give you a framework, a new framework for how it is that America has the best medical system in the world. The most resources of any nation in the world. I still believe a nation of the greatest opportunities in the world and yet we have these staggering health disparities and we'll show you some of that today and how that might be possible. So we're starting a case study. This is how we do brand rounds in medicine. So we'll start a little case study to show you an example of this. This is a 70-year-old African-American boy. You can see his picture in the far left there. He has repetitive visits to the emergency department with asthma exacerbation. He's on Albuterol inhaler, PRM. I mean you know about Albuterol if you ever did summer camp. Some kid was on inhalers and if he didn't have him when he played softball or dodgeball, he'd go into a fit. He's on an aggregate discus twice daily and is needed steroids for treatment many times. This could be pressure zones or going to the hospital. He has to get salu-medrol injections. He's been hospitalized three times secondary to uncontrollable asthma exacerbations. And as a physician, if you have a patient with asthma, it's one of the most important questions to really ask to find out how controlled their asthma actually is. How many times have you been hospitalized? And really I should have put here three times in the last two years over what period of time is pretty important. So we don't want to just look at the child. Let's look at the mother as well. The mother is also very important. The single mother with three children, works for minimum wage, the biological father is absent, neighborhood with high crime rate, high violence, living conditions with high environmental pollutants, poor social support network, feelings of hopelessness and feelings of lack of control. Some of these all of us can probably relate to. But the one that really is the staggering overall arc is being a single mother with three kids without the support of a partner of any kind. So this is a stress life of the mother. Well, just to really make, to really drive a point home about asthma, you can see that asthma actually from a pathophysiological standpoint is quite an interesting disease. It has three components and I always explain this to patients because if they understand the disease it often helps them to take, manage it better. asthma is a perfect example of a very intricately involved medical condition but has strong public health foundation. And the good physician is going to make sure that they blend the public health with the medical treatment because they go together so well. Normal bronchiol is wide open. You can see big open channels here. There's no inflammation along the lining. The muscles around me, the bronchiol is relaxed and there's no mucus plugging the bronchiol. The three components of asthma, of course, are constriction. That's what the Albuterol inhaler is for. You open it up. It's inflammation, which is what happens right here. This gets all inflamed. This damage to the lining of the bronchiol which inhibits gas exchanges. And there's also mucus plugging, which is what this yellow stuff is here. Mucus plugging.  So when we treat it, we treat it with Albuterol or the other. Prandosone, tapering cores, if they can go home. And I always tell them to take mucus next. It breaks the mucus up. One of the things that a lot of people don't think about is how does diet affect this? Diet affects this greatly. We do know that if they eat a lot of, take a lot of dairy cheese, things like that, it actually increases mucus production. It can predispose them further. If they eat foods that are simpler, refined carbohydrates, it will be pro-inflammatory. They increase blood sugar, lower the immune response, and they'll actually have more problems. So how much access does this kid have to fruits? Vegetables? Whole brain foods? How clean is the area they breathe? How stressful is the environment you're going to find? All of these things make a difference in asthma. So it is not just, you can't just treat that patient. If you do that, you'll be throwing a lot of medicine at a little baby or a young child, and you won't necessarily get to the core root of the problem. So what I want to do now is go through a few of the Centers for Disease Control slides from 2002 from their National Health Interview Survey. We're just talking about, I think someone just mentioned it actively. So let's look at the statistics here. They're pretty interesting. If you look at this, more females than males have a prevalence of lifetime asthma. More Puerto Ricans than most other Hispanic groups and most ethnic groups. 196 per thousand population. Total Hispanic is 83. Native Americans, 133. Non-Hispanic blacks, 138. Non-Hispanic whites, 111. Those here, everybody go Puerto Ricans, it actually balances out, looks a bit balanced. Asthma attack prevalence Puerto Ricans still beat, and this goes back to a lot of environmental factors and stressors. We don't often, one of the problems we have when we deal with Hispanics in the United States is we lump Hispanics together. It's almost one of the most, from a statistical, ethnical, sociological standpoint, one of the most wrong things you can possibly do. I'm technically part Hispanic. My stepfather's from the Dominican Republic. So I guess not by blood, but by love. And so I've been to the Dominican Republic. Dominicans are very different than Puerto Ricans. They're very different from Cubans. They're incredibly different from Mexican-Americans or Argentinians. So when you lump them all together, it would be like saying everybody from Alabama is like everybody from Washington State. Except even a bigger difference than that. That's one of the problems. You see it when you break out the data like this. You can see age differences and so forth. Look at asthma outpatient visits. Blacks and whites are almost the same here. Females more than males. A lot of times we really give this a disease of young boys. In fact, you'll see that it's gender. It leans towards young girls. But let's look at what happens to the disparity in health outcomes and health practice once you start looking at specifically bad outcomes or more high energy outcomes, more acute outcomes. As emergency department visits, look at the difference between blacks and whites. Look at the staggering difference between how many visits per 10,000 population you would get in 2002 compared to whites with asthma. Staggering difference. And the female male balances out. The younger you are, 17 to none of that makes sense. But that staggering difference of a disparity in that outcome between blacks and whites. That shouldn't happen. They've been equal. Every other slide, they were just about the same. All of a sudden, bam, blacks jump way up. Well, let's look at another one. Look at hospitalizations. What did I say? That's one of the most important things to ask if you're trying to gauge how severe the asthma is. And when you do that, look what happens. Three times per 10,000. Three times a rate for blacks and how asthma hospitalizations. Very, very serious difference there. And most important in all medical research and public health research is mortality. We forget that. And the pharmaceutical companies do put a lot of people into a lot of fancy expensive drugs that actually never affect mortality. They don't change anybody's death outcomes. They may change your blood pressure. They may change your cholesterol level.  So we spent all that money on drugs. And this is the quintessential most important slide in essence because it shows you that per 100,000 of deaths are more than three times higher for non-Hispanic blacks than for non-Hispanic whites or even for Hispanics. Huge difference. This is a health disparity. This is not diabetes. It's not heart disease. These are children who theoretically should have a better start at life than to have these kind of odds stacked against them if they're asthmatic. So you start looking at the literature and looking at some of the data and prenatal stress and impaired immunity and infant like Rosalyn Wright of Harvard University did a study and she showed that if the mother had stress while pregnant, this is critical, if the mother had stress while pregnant, what they did is they actually took cord blood. Kind of reminded me of the National Children's Study. They took cord blood and they actually looked at how well do the immune cells respond when challenged when the cord blood is drawn. And they found that if the mother reported any of the extensive questionnaires when she was pregnant, if the mother reported higher stress levels during pregnancy, the child's immune system didn't work as well based on cord blood and they're following these children to 18 years of age. There are a lot of people who say that it's not a big deal. I tend to believe that there's something probably there. And Dr. Pate Guaduahere of UCI would probably back that up with some of the great research that he's done. And his team has done here. So when you look at that, that's one thing. So if you're stressed before the baby's even born, it begins to tell. So interesting is the study that they even have made reference that I did and it's generational that the grandmother's stress can actually affect the asthma outcomes of the grandchild. The grandmother's stress during pregnancy and stress in her life. There's a very interesting text in the Bible that says that God would visit the sins of the generation to the third and the fourth generation. My mother would always tell me that when I act bad. So it's interesting that from a public health standpoint, you almost get to see that. The power of one person that affects the generation's lower down. Is that when the grandmother lives in the household? No, that's just in general. Just in general. When they ask questions about the grandmother. Do they think it's genetic? No. It don't think it's genetic because when you look at it, there are other ethnic groups and I'm going to get to that in a second that actually live in just as poor neighborhoods in New York or Chicago and just everything else is pretty much the same. They still have better outcomes. And when you look at it, if it was purely genetic and the kids all have asthma from whatever ethnic group, you would assume that you'd be able to trace genetically back the same way. And you can't. It doesn't genetically trace backwards. It's not genetic. They're genetic predispositions. I know from the research also that if you change certain things the rate of asthma actually goes down as well. Violent neighborhoods and caregiver stress are predictive of asthma severity. Dr. Gupta of the Children's Memorial Hospital in Chicago, Noyes did a study which was pretty profound and showed a strong statistically significant connection between two things. The caregiver stress of the asthmatic child. Who's the caregiver of the child in the case study? The mother, her stress levels, even after the baby's born are also predictive of how much, how severe the child's asthma is going to be. So that single mother with three kids working two jobs trying to make ends meet, doing whatever she has to do, hustling to make a dollar, trying to make a dollar out of 15 cents, they say. Her stress also will predict what that child looks like even after the child is born and they're growing up. The other thing that's interesting is the violence in the neighborhood. The actual violent accident study actually looked at the police records and mapped them and overlaid them with asthma. And when you do that, the more violent the neighborhood, the worse the asthma. There's a lot of ways you can try to explain that. It could be purely stress related, but it can also be that if the neighbor's more violent, you keep the child where? Inside. Inside, so they get less fresh air. It could be that you are less likely to go to doctor's appointments. It could be that you're less likely to go get an inhaler from a drugstore if it's dark and you ran out. But these things are predictive of more severe asthma and those studies will continue as well. So let's look at some of the things that they say about within the first 48 hours of a stressful life event, there's almost five times the likelihood of a new asthma attack. The report effect increases the risk of 4.69. The risk subsidized within three to 10 days, but flares up again five to seven weeks after the event, this time to almost double the risk. And Dr. Jarvenpa, this is a study that was done after exacerbation of children immediately following stressful life events. So we know that acute stressful events will definitely trigger asthma. This is one of the things I saw when I was a resident doing my, or a member of the student actress doing my pediatric rotation at the University of Miami in Florida, that you saw that there would be sometimes a breakup in the family, a divorce, you know, some other stressful event, domestic violence happened in the home and the child would have an asthma attack and we would see the child in the hospital. So we know that stress works this way and can contribute to that big disparity that we saw in the earlier slide, mortality, ER visits, and other things. So stress can be part of what's doing that. But I want to show you that there's stressors that are, that lean more in favor of one group of people over the other. Before we get to probably getting beyond even this kind of data. And this is from, this is a 2005 preliminary data from, I think from the Bureau of Statistics. Percentage of all births born where it is a by race unmarried women.  Look at the percentage of all births that were to unmarried women by race. These are staggering statistics. This is the federal government data. Staggering statistics. How stressful is it? 70% of the births are born to unmarried women.  But when you look at it, 70% is a staggering statistic. And if you add up all that we know about being a single mother, not having a biological father, being in poor neighborhoods, and then we're going to throw in discrimination and other perceived things, the stress levels are probably pretty astronomical in that group of people. So, how do we explain this? And we go to a new concept, well, a relatively new concept. Bruce McEwen is the researcher who was most responsible for this. Sterling and Iage reported this in 1988. Allostasis is a new, a relatively new concept. When I was in a study of biology in college, it was only homeostasis. So, allostasis has come along, and it is the process by which the body maintains stability or homeostasis during adaptation to environmental and physiological events. It is adaptive change. It has changed the maintaining stability. So, it's a bit different than homeostasis, as you'll see. So, allostatic load then, if allostasis has changed to maintain stability, allostatic load is used to explain how the burden of external stressors can become normal allostatic processes and become pathophysiologic processes. This is carrying a burden of stress, the weight of stress on you. And it's technically quite measurable based on the literature as well. So, some of my students have seen this, but this is the actual slide that we used to show how that happens. So, if you look at the top, that is the normal response. When you come down, it happens if you are that single mother and you're getting, you know, normal responses every time you hear a gunshot in the neighborhood, every time you hear a helicopter flying over the neighborhood, every time you, you know, you see the police pull up and run into a house or every time a bill simply cannot be paid, every time you have an argument with the father of your children who happens to be in prison or not in prison or whatever the case may be, every time that happens, and this is for all of us, you have a normal response. If the hits are too repetitive, if they're too constant, then you stay in a state of fight or flight all the time. The human body's not made to be in a state of fight or flight all the time. It's not designed that way. And there's a lecture coming up May 11th here why zebras don't get ulcers. I think you should see it because it'll speak to some of the reasons why some of the same things probably from a little different angle. You get kind of a a wading effect, but without it you get a lack of adaptation and you respond to the stressor because it's the first time you see it every single time. You're going to have a long response of people who just don't turn off their stress response. It just stays on. They just hype all the time. And then there are people who just don't have a response at all. And this is Bruce McEwen's work again as published. So when I was doing the research at Loma Linda on the Adventist Health Study and some of the other studies that they were doing we were working on looking at the difference between white seven-day Adventist and black seven-day Adventist. We found some interesting things in that study although many of the stress indicators for black seven-day Adventist were greater than for white Adventist. If they lived the seven-day Adventist lifestyle they actually were able to remove much of the health disparities. To that respect. When we looked at what are proxy markers and true markers I've designed this myself so this is a don't write anything down. But we did this just for the studies and we'd have an idea of what we're looking at because we couldn't we couldn't afford to draw blood on everyone so we tried to set up a proxy marker. I just put this up here to give you an idea of what we're looking at when you want to measure alastatic load. So diabetes in my life is used as a proxy marker. They were diabetic. Alastatic load we graded these things so we could just do a questionnaire and come up with a number on a scale without drawing blood. Then there was a group that we actually did draw blood and then looked to see how well it correlated. So he would open A1C from Diabetics is one of the things that we looked at and if you have a high hemoglobin A1C it is this side of high alastatic load systolic blood pressure this more specifically. We have glyceride levels BMI and waist tip ratio interleukin 6 we'll talk about in a second CRP C-reactive protein and fibrinogen levels so if they had a history of MI stroke we assumed that they would have high levels of this shortness of breath asthma we would say if you have that history or shortness of breath we said you had higher alastatic load but ideally it would be actually even peak flow measured that would give us that information Today we look at catecholamines thyroid function higher cognitive function and we did a memory test on some of them we run a small group and it was very interesting because the minimum age was like 70 in the study so it was interesting because we have these the older 7-year-old men who have lived in lowland or other life and they're able to put their feet up and do this and they drive to the meetings at 100 years old and you can see what markers were true and what weren't and this is how you can actually quantify it and I'll show you in a second but the way that we do this is that we look at in a cute stressful situation such as being chased by a dog and I always tell a story students are here but we always taught the fence to cut through neighborhoods that was a shortcut and it was a fast way to get where you were going but every now and then you drop into the wrong backyard and you see it's interesting when I see people in Orange County walking around with a dog in a bag you know when I was growing up dogs had one singular purpose security they weren't pets, they weren't well fed nobody bought special food for them they were lived in the yard and they were fed in the yard they bathed in the yard if it rained there wasn't a whole lot of love but those dogs were angry so they worked well for security and so you land in the yard and Brutus, I always say the dog's name was Brutus picked up his head is that all of a sudden even if you're a 12 year old boy like I was many times adrenaline would be rushed out into your system and all of a sudden your pupils are dilated blood would be shunted away from your digestive organs the blood flow to your muscles would increase your heart rate increases respiratory rate increases you're ready to do one of two things fight or fly you fly you learn to walk on water if you have to and this is how you respond and that is a normal stress response you should do that when you're faced with a challenge this doesn't change if the challenge is that you go to work and there's an argument between you and a co-worker it's as if you were in to Brutus this doesn't change if there's certain things that you're trying to do the National Children's Study just isn't working right you're banging your head on the wall your body still releases adrenaline it still goes up your pupils still dilate if it's acutely stressful enough you still respond this way and remember based on the graph this is how you're supposed to respond you're designed to respond this way so that in stressful situations you can better respond to the stress why digest food when you need to be running your body can digest the food later time to run, so you run and this is typical of how we respond to stress that we do the problem is the chronic exposure to stress poor social supports and limited social networks these have been shown to increase disease risk so the Institute of Medicine actually put out this report that somehow if, and so there's two sides with one of course are all those graphs and all that all of that is static load we also know there are some things that are protective which is what we're really looking for in here in this health study what about that lifestyle that's so protective even when people have higher allostatic low risk so if you don't have certain things you're kind of in trouble so that's single mother if she doesn't have, if she has poor social support if she is limited social networks if she's high stress as she probably has it's going to increase disease risk Philips looked at reaffirming a connection between acute stress and acute respiratory infections due to decreased secretory or secretory immunoglobulin A again your body shunts your immune system does not take priority if you're acutely stressed and one of the ways that you know that one of the proxies actually is how often do you get the common cold when I was in college we got a lot of colds I have a question going into that first comment right here I think it's very interesting but is there evidence to show that so say lower SES groups do have African Americans Blacks have poor social supports for love babies and things like that because I think it could be argued that since this is, there's so many babies being born that actually the support system is there and it's sort of an accepted situation two things I was correct in what you just said one, I can't assume African Americans are low socioeconomic but you were using Blacks in the first and that's what you were right no no it's a lot of people who do that you said you identified it as well actually that hasn't happened though the idea, because that's different even if people accept it, it doesn't mean it's supported when the baby needs changing in the middle of the night it's not like you can call a neighbor and it'll come over and change the baby you know what I mean, different than if you have a partner in the house with you if the bills need to be paid, there's no pool of money somewhere sitting you can draw from and help pay the light bill there's no, the social support network just doesn't exist like that the closest you might get is some faith-based organization or maybe some other community-based organization but the kind of support that all of those women simultaneously need really doesn't exist the closest we have in the United States is the government and government programs but again, there's stigma that goes along with that there are challenges, there are a lot of women who refuse to go and do it they don't want the stigma of going again so they don't go and get it and all of that, you know, it's complicated and obviously anybody who's raised children knows that first two years in life is enough of stress if you have to deal with the child by yourself never mind dealing with them for the next 20-something years and naturally what we're speaking to unfortunately, I wish you were right I wish it was communal living, it's not those mothers are left to deal with that child by themselves so going statistics that this multi-generational families and certain ethnic groups I don't know there are multi-generational families they have the same house there's some research on that but even then even if that's the situation it's not ideal these women they don't grow up into a single mother with four kids I know I've worked with the population that's not what they're saying instead this is kind of what happens and some of the bad choices when people say well it's their choice is because their default the default choices are often the worst choices as well in other words, our society hasn't given them the best opportunity to make good choices so we say those kids should have fruits and vegetables in Santa Ana, I do talks on our availability of healthy foods right here in Santa Ana the truth is that many kids come outside these poor Mexican-American families they come outside and there's a truck that supplies them their food they don't walk as far as to the grocery store if they're gangs in the neighborhood there's no real good way for them to get to healthy food all the time there's no good way for them to get to exercise so we come in and we say with our health promotion, health education having a child run more he's getting too fat having a child eat more fruits and vegetables well, he's going to be running in ducking bullets at the same time you should understand or running and seeing things he shouldn't see so a mother who cares for the child would rather they stay inside and go outside and get shot and we assume that somehow it's always the individual as a society we have some responsibility to make sure every child has that same opportunity that the child in Irvine goes outside and get run free that is so that is what we really started looking at it's a little more complicated even in personal choice, genetics it does get to a bigger, stronger connection that's kind of what I'm trying to say stress has also been shown the potential to negative effects of a high fat diet initiate atherosclerotic platformation so I'm going to read early research on this actually came from World War II soldiers on autopsies done when 18, 19, 20, 21 year old American men came back from the battlefield they did autopsies and they found atherosclerotic platinum a lot of people said well let's the American diet what a lot of people now say is it's probably that combination of the American diet with the stress of going to war in the early age and that's how fast it sped up the development of atherosclerotic plaques so adversity this is Kanye West, he really made me upset when he stepped on stage with I wanted to jump to the team here but his lyrics here are interesting he says they're going to have to take this is speaking to adversity, we're going to talk about adversity they're going to have to take my life before they take my drive because when I was barely living that's what kept me alive just the thought that maybe it could be better than where we were at this time make it out of this grind before I'm out of my mind and he's speaking of the challenge, his mother was a single mother trying to get out of poor neighborhood difficult neighborhood and he's saying he's going to keep his drive before he goes out of his mind because at some point you will collapse if you're bucking your head and you go to school the school system doesn't offer you much when I lived in Miami to go to high school we left Connecticut, I went to suburban school system that was just phenomenal there was no question at all the advanced placement classes I wanted all the honors classes I wanted to take we moved to Miami and we lived on the line where I could either go to the predominantly black school or the predominantly white school they bust us from my neighborhood to the predominantly white school and that school had every advanced placement class you could possibly think of every honors class you could possibly think of they had water polo they had every sport you could possibly think of sports I didn't even know existed at the time and I was busted at school and graduated at the top of my class went on to have a good life and I go into the predominantly black school I had two advanced placement classes the difference in what would have happened would have been very different based on where the line fell for me and myself and my family my mother was a single mother of three boys just kind of like the case study none of us luckily had any asthma we had other problems mental problems but Kanye West has another lyric that resonates with me as well he has a lyric where he says drug dealing just to get by we weren't supposed to make it past 25 but the jokes on you were still alive and if you grow up in these neighborhoods a lot of times they think the honest opinion of the average young male in poor neighborhoods is they're not going to live very long so all of our health promotions all of the things that we targeted with doesn't work because if I'm going to be dead in 10 years anyway what do I care what I do now if I smoke, drink, take drugs fight, gang bang at least I'm living how I want to live today because I don't see the hope of tomorrow very few people do I see live black men do I see live long get out of the neighborhood not go to jail or prison not wind up on drugs it's dismal, in fact the only real successful people that come out of the neighborhoods are athletes entertainers and drug dealers if you want to call that success I don't call that success and so what happens is you kill those three babes right and if you go into an inner city school and you say to an average young African American kid what do you want to grow up and be you're probably going to get one of those three answers and it's unfortunate because they don't understand statistics so they don't know that there's only going to be one Michael Jordan every 50 years that of all the kids they play basketball probably not one of the ones that they know is actually going to make it to the NBA they see the one who makes it and it's like a dollar in a dream you know what they say about the lottery right it's tax on people who don't know math because if you actually do math you'd never actually spend your dollar on it I thought it was really fascinating that you talked about this type of thing is it possible that what we're seeing with these disparities is something about coping mechanisms and beliefs powerlessness empowerment and assuming that that's true how would you improve health outcomes it sounds like you have to improve somebody's health coping skills in order to address their asthma or maternal morbidity associated with pre-traumatic which is exactly right it actually begins to speak to the new public health paradigm has to be brought in when we look at it as and this is a very ugly news but this is flame to flame I don't know how they made this show out of this guy it's pretty embarrassing but he has a lyric from one of the old public enemy songs and he says speaking of hostility he says I got a right to be hostile man my people are being persecuted and that sounds crazy all by itself but if you feel like you are the bottom of society the lower run of the socioeconomic status of the socioeconomic total pool and nothing is going right and you've been victimized whether you're Native American whether you're Hispanic, whether you're black whether you're poor white and Appalachia it doesn't matter the reality is if you get this feeling there's a hostility that will develop this is the hostility that has Orange County jails full of Aryan skinhead gang members this hostility that somehow our people have been treated unfairly this is why the Indians we talked about this in our last class where you showed a clip of a video Native Americans that's one of the reasons it parallels the high diving rates of other people around the world who have been disenfranchised, lost their land the aboriginal people of Australia there's a pattern across the world and hostility is one of the things that leads to health disparities if you feel you've been treated unfairly as a people never mind as an individual you're going to carry a burden of stress that other people won't carry so hostility and low perceived control part of what kind of a lesson we're talking about is also related to poor health outcomes low perceived control is a determinant of heightened stress responses and poor adaptation adversity and vulnerability along with psychological markers such as low self-esteem and loneliness are also associated with poor health outcomes so you start looking at this and you can start to see that certain groups of people are going to be more susceptible to this than other groups of people it's not genetic it's a lot of societal norms a lot of societal stereotypes things that people assume about you before you open your mouth and one of my good friends she was a pretty blonde girl and she said what she hates most of the mechanics because the mechanic assumes because she's a blonde female she's dumb and he can steal our money and so she goes with her husband or she goes with her father every single time and I said I feel you and you feel like you're being taken advantage of that it isn't unique to any one group of people we all have it but all of it is the kind of stress that can over time change health outcomes so depression and anxiety have been shown to increase the production of pro-inflammatory cytokines including interleukin-6 this is one of the actual markers you can draw and look at allocytic load high levels of interleukin-6 predict future disability in older adults cardiovascular disease arthritis all-timers certain lymphoma proliferative diseases or cancers my mother died multiple mile on non-oxidous lymphoma chronic lymphocytic lymph leukemia and I looked at this when I started looking at stress after my mother passed and I started to realize how much of a weight of stress she carried ever since the day my father left her when I was two years of age I can't imagine now that I'm an adult what in the world she went through when she was trying to make it she was very successful in life but she was on the hospital board in Florida and on the board there were clansmen no clansmen in homestead Florida I can't imagine what it must have been like to go into the meeting my mother was a strong woman but when it came to work she was quiet she didn't want to stir anything up so she would have just gone and sat in the meeting and left even though she would have been very uncomfortable interleukin-6 is key to promote the production of C-reactive protein C-reactive protein is now recognized as a risk factor for myocardial infarction so we now know that it is truly you can begin to connect the dots the depression and anxiety that can come from stress literally can be quantified into interleukin-6 and we now know interleukin-6 connects to all of these diseases and the major number one killer in the United States of America we actually know how it happens now and if you're from a group that is disproportionately anxious and depressed the discrimination real or perceived because of environmental issues real or perceived you're someone who is going to be more prone to these outcomes it starts to make no better sense another one to look at elevated glycoheal movement levels were observed with increased burden of adversity and vulnerability glycoheal movement levels represented in peer response to glucose tolerance before the diagnosis of diabetes glycoheal movement independent of other factors has been shown to be predictive for cardiovascular as well as all cause mortality again we go straight to the real crux of what we're trying to prevent early mortality and we now know that you can draw the dotted line and we know why you can draw it but we know what is going on that actually is correlated to elevated levels of glycoheal movement and this is something that is important if we're going to change the way we even look at how we practice medicine in the United States and how we do public health depression and anxiety have been shown so so to look at African American more specifically they bear disproportionate disease, mortality disability and injury African American men are 6.2 years less than white men and 8.3 years less than the national average of 77.8 years Martin Luther King one of my favorite quotes he says he was learned to live together as brothers or parents together as fools and so we look at it as reported death rates per 100,000 for people 35 to 54 years of age notice the youngest age there is 35 it's 2.3 times higher for African Americans than whites that age is important because that does away with all of the homicide deaths a lot of HIV deaths in the black community all happen before 35 for white men HIV deaths happen after 35 there's a difference when you look at the data adjusted for six risk factors and everybody says well it's because blacks are high blood pressure cholesterol or fat or drink more alcohol or diabetic when you adjust for those it goes from 2.3 to 1.9 times if you adjust for income everybody says ultimately this is about money blacks are poorer when you adjust for income it decreases to 1.4 times that means about a third of the difference completely unexplained something else is actually going on it's not what everybody thinks it is and I'll try not to mess this up like I did in class Bernie Mac, Steve Harvey, but that's Bernie Mac that's Nate Dogg poverty control for these in excess of 38,000 deaths per year or 1.1 million years of life of life loss among African Americans in the United States let me emphasize that this is not unique to African Americans I use this as because it's an easy way to show this I can show this with Native Americans I can show this with certain groups of Hispanics I can show this with poor if you compare whites poor whites in the south to whites in the north there are a lot of ways you can show this exact same thing and Hawaiians you can show this with a lot of different groups but this is one of the ones where the numbers are pretty big so it's easy to show and again that was 35 to 54 if you go back further and look at infant mortality rates so first you look at the 70% unmarried rate but look at infant mortality rates here's the total, so here's the average here's non-Hispanic whites interesting, all of these groups actually do better than whites that's Asian Americans, Cuban Americans Central South Americans, Mexican Americans infant mortality when you come over here, look at the rates for non-Hispanic blacks for American Indians and for Puerto Ricans higher, especially for African Americans infant mortality is a lot higher and again, a lot of the freedom of stress that is looking at that would your graphs be any different if you were using socioeconomic status instead of ethnicity? they would be different but again, if you correct as we did in that last slide even when you correct the socioeconomic status the differences remain the reason I'm raising it is that we know the blacks have moved into the middle class or a small percentage of them signifying that there is some capacity to correct this under capitalism well, yeah, if capitalism capitalism to me could be part of the solution it would be a great part of the solution if everybody starts off with the same footing if everybody has the exact same opportunity and there's true competition capitalism probably would help level the playing field well but if certain people have advantages out the gate capitalism is not very good at correcting the advantages that certain people get out the gate that's the challenge you have in capitalism and I'm into free markets I do believe well, regularly free markets but I do believe that unless you have fairness I make the analogy all the time what would the Olympics look like if every American girl had a chance to learn gymnastics but if every single young girl regardless of race, ethnicity had a chance to learn gymnastics well, you would increase the pool of people you choose from and all of the talents that go on tap would get tapped the communist system, what they did different every single child is tested young and in order to prove communism was better than our system they try to get every child into the pool to pull from so that they can compete and it worked for the Soviets it worked well and it worked well for the Cubans I didn't learn well for the girls gymnastics is not the most healthy thing oh it's not a good one where do I say basketball there are some factors and social disparities that act in early childhood there are some factors that act throughout the lifespan and people that move from core neighborhoods move up in the social ranks carry the risk we're going to get to that in a second because that's really the crux of this how is it that you don't even when you become wealthy like Bernie Mac or Nate Dogg how is it that you still die early as both of them did how is that still happening and the Australian government actually put these posters out how many of you saw the movie Australia I saw them first as I woke up and crawled out of sleep but I thought it was a brilliant movie the parts I did see and one of the things Australia is coming to grips with now many of the actors they argued that Tanzania is one of the few places in the world where you have actual genocide of an indigenous group of people they talk about the fact that much you could almost parallel what I'm saying about African Americans and Native Americans with the Aboriginal people of Australia the state health department for Australia put out these posters and said racism makes me sick but in fact it's about blood pressure and critical anxiety and depression racism makes me sick and damage is my heart blood pressure and my unborn baby the state of Australia has got to the point where they say look these things actually harm the outcome for groups of people if we don't treat them right white only policy up into the 60s even if you were from the south of Europe and you weren't fair enough you couldn't be allowed in to live in Australia into the 60s they had that policy so they're dealing with that now and I should commend Australia because this is a hard thing for the government to actually put out so Carlson and Chamberlain as well as Sandin both present arguments for outside of the framework to explain health disparities perceived race-based discrimination positively associated raised and poor self-rated health and I think one of the things that's important is the word perceived because it doesn't have to be real people just have to think it's real and that's a problem because we probably should ban Al Sharpton from television for that reason but the reality is if people think they're being treated unfairly it still creates an increase in outside of the world like it was someone said about coping mechanism if you can't learn to cope with it and you just internalize it it's going to damage you perceived that discrimination is the best predictor of smoking in two studies exposure to racial discrimination increases risk for preterm and low birth with babies experience with discrimination associated with delays in seeking medical care how do you answer that when people leave poor neighborhoods and become more wealthy Oprah Winfrey is a billionaire would it be I'm dying for my introduction to her she's a good capitalist if I ever had some of her money but Oprah Winfrey had an experience where she went to a boutique in Paris and wasn't allowed in and she perceived I don't know if this is actually what happened she perceived it was because she was black and probably not dressed up and they probably couldn't recognize her even though I don't know if they watched over her in Paris and so she wasn't allowed in and she made a stink of it and thought of it because she was black she was allowed into key cities in the world New York, London, wherever came on a show and apologized extensively and probably said when are you coming to the store I'll open it for you personally because I don't want this bad press but I think about it with all of her billions she's still a victim of the perception that she was treated unfairly based on her race that means all of the allostatic load of things that I've mentioned before she couldn't even protect billions couldn't protect her from the response the money can't protect from the response if that's what you feel is happening that stress level then doesn't go away it's a similar finding about social class that perceived social status subjective social status predicts more disparities than objective very true and so that's one of the things this is one of the things that I think I don't think the solution is necessarily simply as Australia's to stop racism I think part of it also is for African Americans to be kind of to work with African Americans to cope better and to actually realize it's not always racism it's sometimes the person just isn't nice and you go in there and you assume it's because you're black but it may not be it may just be that this is a bad person it doesn't matter who was walked in there so you gotta learn to actually turn the other cheek to look the other way to go to a deeper, stronger because being angry hostile, pent up as Martin Luther King described in the Civil Rights Movement does you know good if you hate your brother your brother goes on and lives his life and doesn't know all of the hatred actually ends up destroying you all of the anger ends up destroying you you can't live angry in the world especially in the world where you don't know you're angry because it will destroy you and this is one of the messages I think for all of the different groups of people now white males to some extent I mean all Americans everyone fighting for that piece of the pie believes that they're the ones getting the short end to stick a study that had young black children and some white dolls and the black dolls and the children perceived the white dolls as smarter and prettier prettier, more valuable and yeah I saw that a girl like me and he is the male that was redone back in the fifties and it was shocking and it made sense in the fifties everybody was saying well if you look at television if you look at billboards it would make sense if you think that way nobody thought you would get the same exact results in the two thousands but you do and so you're right it goes beyond this being kind of a more palpable way to see it but the fact of the matter is our society presents images and realities that make you think you're inferior that makes you internalize hatred of yourself and that internalizing is also something that will set off out of static load the reason I'm raising socioeconomic status is that the history of this country with its terrible prejudices against blacks people of color led in the forties and fifties the black power and white supremacists and those in power received this effort on part of the blacks as threatening their status whereas if we emphasize socioeconomic status to turn to the labor movement as a means of correcting this terrible injustice that has existed in our society I agree with you I actually think it is about time with certain exclusions, America moved beyond race because the fact of the matter is that my work in Alabama when I was a family medicine resident in Alabama and I used to moonlight down in the town called Widowley now the principal of the school there shut down the prom because a white young man was going to bring a half black, half white girl to the prom he canceled the prom, the clan marched and of course being not known trying to make extra bucks, he was driving into the hospital to work but so you know what I found in those situations is poverty doesn't know color poverty is real, they are twice the when Martin Luther King wrote his last book in 67 one of the things he said is that he will move beyond dealable poverty as it has been produced because of race and discrimination instead he said we will deal with poverty because poverty there are twice as many poor white Americans as there are black Americans so Martin Luther King said we are no longer being incredibly unpopular in the north see in the north we are happy when we deal with Jim Crowism in the south they didn't have Jim Crowism once he started dealing with labor movements and fair pay and poverty regardless of what you look like and the Vietnam War of course he became much less popular in the north among even liberals and you are right, it's right on the mark again if we correct opportunity and make sure everyone has more fair opportunity and we do certain things to protect the most vulnerable aspects of society, some of it can correct on its own, we've seen that in other parts of the world but it's important in America that we recognize why we got where we got but we do need at some point to move on and I think labor and again, fairness, social justice as it pertains to all these different groups of people is the solution because again there are groups that are being left behind inside the current there are many white Americans that need to be socially supported just as much as black Americans that's just the reality especially if you go down south certain parts of California even I went to parts in Alabama where there were trailer parks without electricity and running water and then happens in rural white and I've never seen anything like that in any other ghettos in the north so it's bigger than race, clearly race is probably one of the best ways to show the example but again, Americans have to move beyond that to social justice and fairness for all of our citizens the country is what they show as far as I know is that the more equal the society is I mean the less of the range of social differences the shallower that's gradient but one of the fascinating things about the social greatness of health is that it's not just the difference between the rich and the very poor it's something that acts in every step of the social ladder even when your religion being well-tuned or in Britain or the white-owned studies where they compare civil servants with the British government you have a good job here earn your income you have a national health service but still your health is not as good as the one that's one step above you as a hierarchy I did that talk for the students two weeks ago that you can look at the social determinants of health one of them is where you fall even on the socio-economic well not on a pecking order inside the organization where you work how many Oscar awards an actress or actor wins will determine if they live longer than actors and actresses that don't win them there are a lot of different ways that this plays out but the bottom line being I think going back to really fairness and all of those different things and you're right it isn't this simple I mean this is one good example but it really shows that as a society you have to speak to deeper, harsher issues and when you get beyond this one you're right there will be other obstacles other ways to find ways to try and make things better as well let me get through the last two slides we have about a minute left so public health implications hopefully when we start looking at allostatic load as a cause stress as a cause of health disparities we'll look at a more defined way to deal with it it may change certain policies as stronger connections are made hopefully shift the focus of medicine to be more preventive in nature environment and relational issues facing patients strengthen the role of different intervention models such as group visits social support systems inside medical treatment and we know that that works with drug addiction to some extent we don't use it as much for diabetics we don't use it as much for obesity treatment so it may be that we can do this to gain social support and social networking since those things seem to work some of the future research stuff that can be done search for treatments that block the release of the mediators or diminish their effects I hope this isn't the only way we do that but this is something that I'm sure at some point where these things are stronger pharmaceutical companies will look at if they're not already how does lifestyle changes affect market levels and affects maybe I didn't finish that but lifestyle we know can be protective that's one of the big things what you eat, how much water you drink how much sleep you get all can be protective and you have in this health study we found that we averaged two hours less than white adventists and that is in the study where the black women in the study actually made more money than white women in the study it was an interesting different group of our segment of our American population and sleep is strongly a predictor of how healthy you're going to be so what lifestyle changes need to be how does social support and faith participation affect market levels and functions and how does peer pressure and mediostereotypes affect allostatic blood that goes back to the idea of the dolls and those different types of things so we probably don't have any time for questions but we did sprinkle them inside the talk thank you for coming I appreciate your comments and questions we keep looking at this hopefully we keep making progress in the research and in the literature so that we can actually come up with different practice models for medicine and public health many thanks for the questions there may be time for one or two more questions yeah so are you saying that the stress in the fight or slight creative conditioners to be reacting which one comes first? I can't say I have the definitive answer on that but I would say this, I think once that stress pathway is turned on and allostatic blood is increased you turn down the immune system you increase inflammatory reactions in the body so by default anything you come in contact with that would be a pollutant it's probably going to have much more of an effect on you than it would have and there are studies that show that that literally how you respond to environmental toxins, allergens, whatever can be dampened or exacerbated by what your stress response or stress level is so I can't say that one starts I don't think that stress as a toxic stress really is probably what triggers much of it the more stable environment for children especially the more wholesome environment for children the better long term health outcomes that child's going to have because these patterns then begin to develop from childhood and they begin to affect disease years and years and years later I do Mr. Johnson I do not recognize disparities in health and cancer outcomes but I want to come back to your point about the impact of perceived racism on health I think it's a very real thing and I think it's really important that we look at both of those issues together and separate and I was wondering if you knew anything about some of the implicit association studies that have shown that that racism isn't always something that we consciously perceive which I'm really good work out of Harvard Nancy Krieger's group has done a lot showing that racism is very much still around and it's just not something that we've always consciously perceived that there's some interesting effects and it's not just racism there's lots of different sides gender, body weight discrimination ability discrimination and so in that group there's a lot of that I've done research on longer hours and sleep definitions and coming back to cardiovascular health and that is we can associate with the concept you're talking about and I wonder when you do research on research on the American level of health do you see kind of training that you have to have a group of educators or just pick up a few I think it's a group of educators you have to kind of look at them love them together that's what in the South study I was important I collected them to name it was kind of a stalk of them so you had to say they didn't just say one thing and in fact I think one of the weaknesses of research in the United States is that we always try to find the one thing that one aspect, that one factor, that one thing and it's so much more complicated that's why I'm such a big proponent of that because I think until you do the research where you actually look at everything together kind of at once a lot of the answers just want to become clear because we're going to ping-pong back and forth what's the problem if you're only looking at one step we're only looking at systolic blood pressure cholesterol, how much meat they eat how much dairy, if you're going to look at one thing whether or not they eat goji, goji, junsu, berries whatever we're always looking at one thing as a magic bullet to solve the solution it's so much more complicated than that and that's why stress makes sense for myself that it's mediated by certain things or exacerbated by certain things so I think lumping things together made a strong in the ambulance health study made a much stronger statement of who really was stressed and how much things actually helped or hurt the stress levels and then the disease out thank you


Hi, I'm Lior, and this is a talk about simple and efficient better verification techniques for verifiable delay functions. So let's start by defining delay functions, and then talk about verifiability. Roughly speaking, a delay function is a function which is efficiently computable, but only in a manner which is inherently sequential. One way to capture this is by introducing a delay parameter t. Then the function should be computable on every input in some time polynomial in t, so for example 40 or t squared, but on the other hand, it should not be possible to evaluate the function on a randomly chosen input in time less than t, even with pre-processing and many parallel processors. A verifiable delay function, or a VDF for short, is a delay function which allows for first verification. So when computing the output f of x of the function on input x, it should be possible to produce alongside the output a short proof pi asserting the validity of this output. Then, given x, f of x and pi, one can verify that f of x is indeed the output of the function on input x, and this verification should be much quicker than computing the function anew. Though this is a recent notion, VDFs have proven to be extremely useful for a wide array of applications. So just to name a few, we have time-based proofs of replication, verifiable randomness pickings, computational time stamping, resource-efficient blockchains and much more. The main candidates that we currently have for VDFs are based on the repeated squaring delay function put forth by Rivest, Shamir and Wagner back in 96. This function is defined with respect to a cryptographic group G, and on input x, the output is x raised to the power of 2 to the t. The fact that this is indeed the delay function is based on the assumption that there are groups in which this computation cannot be significantly sped up, even with pre-processing and a polynomial number of parallel processors. It's not hard to see that for this assumption to be plausible in some group, it should be hard to compute the group's order from its representation. We currently have two main family of candidates for such groups. The first is the family of RSA groups, and specific subgroups of RSA groups. For this family of groups, a recent result of Gil Sagev and myself showed an equivalence in the generic ring model between the sequentiality of repeated squaring and the factoring assumption. The second candidate family of groups is the family of class groups of imaginary quadratic number fields. Indeed, several works, starting with the works of Piotr Sakhand-Vesolowski, constructed VDFs based on the repeated squaring delay function. The basic idea in all of them is to augment this function with efficient proofs of correct exponentiation, on which we will focus later in this talk. Now in some scenarios, one might need to verify not just one, but many VDF outputs at the same time. As an example, consider verifying using a VDF-based proof of replication that some storage service maintains many copies of the same file, or verifying the randomness generated by some VDF-based randomness beacon over many epochs. The naive solution is to simply use the per instance verification procedure of the VDF and to verify the outputs one by one. The downside of this approach, of course, is that it incurs a blow-up in both the proof size and the verification time, which is linear in the number of outputs to be verified. The question is, can we do better than that? Before going back to verification of VDF outputs, I want to take a little detour and to talk about the related work from over 20 years ago by Bellary-Garai and Drabin that deals with better verification of exponentiations but in cyclic groups of prime order. So the setting is the following. We have n exponents, x1 to xn, and n group elements, h1 to hn, and we wish to verify that hi is equal to g raised to the power of xi for each index i and for a publicly known generator g of the group. Bellary-Garai and Drabin presented several batching techniques to solve this problem, and some of their ideas are actually implicit in some of the recent works even on single instance VDF verification. We explicitly observed this connection and built upon it for the sake of batch verification of VDFs. But in order to do so, we need to overcome two issues. The first is that they consider the setting with no additional proofs. All you have are the xis and the hi's, and you want to verify that they indeed satisfy a certain relation. In the VDF setting, we are in a setting of an external prover proving that the shared input satisfies some relation, so we also need to account for the proof length or the communication complexity in the interactive setting. The second issue is that the more efficient procedure of BGR relies on the group being of prime order, which is not the case for the candidates that we currently have for groups of unknown order. Going back to VDFs, Veselowski, in an update to his original work, already presented the batch version of his proof of correct exponentiation. So this batch protocol implicitly relies on ideas from BGR, and instead of producing a separate proof for each output, it produces a single, shorter proof for all outputs, which is also quicker to verify. Unfortunately, this batch protocol was presented not as a modular compiler that works with any proof of correct exponentiation, but rather as a direct generalization of Veselowski's single instance protocol. The more serious issue is that this protocol is proven secure based on the adaptive root assumption. This is not an issue when compared to Veselowski's single instance protocol, since it already relies on this assumption. However, the adaptive root assumption is stronger than those needed to prove the security of other proofs of correct exponentiation. The soundness of PSX protocol is based on the low-order assumption, which is seemingly weaker than the adaptive root assumption. And moreover, a very recent work by Block et al modifies PSX protocol and obtains an information theoretically sound proof of correct exponentiation. So this raises the question of whether we can apply the techniques from Veselowski's batch protocol to these protocols as well, and must we introduce additional assumptions in order to do so? So what we do in this work is to present general and modular batch verification techniques for VDFs that are based on a proof of correct exponentiation or a PoCE for short. First of all, we define soundness notions for batch PoCs, and then we present two compilers that take any single instance PoCE and compile it into a batch PoCE. The first compiler doesn't make any group-specific assumptions and can be applied in any group, and the second compiler has better parameters but it relies on the low-order assumption that we will describe later in the talk. Both of these compilers extend the ideas of BGR to the VDF setting and improve on the naive approach for batch verification that we described before. Additionally, we also have two specific protocols in RSA groups where the modulus is the product of two safe primes. First, as we will discuss, the low-order assumption doesn't hold in these groups, so we show how to extend the second compiler to these groups as well. And secondly, to complete the picture, we present a single instance PoCE which is information theoretically sound in these groups. This is a table summarizing the parameters achieved by our compilers. Let's assume that we want to verify any instances and we start with a single instance PoCE with proof size l pi and verification time t pi. In this case, the naive solution gives you a proof of size n times l pi and verification time n times t pi. Our compiler in general groups gives you a proof of size lambda times l pi and verification time lambda times n times tg plus t pi where lambda is the security parameter and tg is the time it takes to compute the group operation in the underlying group. Our improved compiler, which is based on the low-order assumption, doesn't add anything to the proof size and its verification time is n times lambda times tg plus t pi. Note that in both of our compilers, the proof size is completely independent of the number n of instances to be verified. When it comes to verification time, there is still a linear dependence on n, but it is decoupled from the dependence on the verification time t pi of the underlying PoCE. So even if the PoCE is very expensive in terms of verification time, we still only pay for it essentially once and not once per every VDF output. Now, it should be mentioned that VDF proofs for repeated squaring are typically obtained by applying the Fiat-Chamiriuristic to an interactive protocol. If one doesn't want to assume the sound of Sophia Chamir, our compilers can be instantiated as an additional message to the underlying interactive protocol. And in this case, the communication complexity and verification time are essentially those listed on the slide, and we will see this in more detail later on. So the talk-out line from now on is the following, we'll start by defining batch PoCs, then we'll present our two compilers, and we'll move on to talk about our protocols in safe-primes RSA groups, and then we'll conclude. So let's start by defining batch PoCs. First, we'll define single-instance PoCEs and the setting is this. We have some underlying group G, two group elements, X and Y, and an exponent E. The prover wishes to convince the verifier that Y is equal to X raised to the power of E. So a PoCE is a possibly interactive protocol between the two parties, and the completeness requirement is that if indeed Y is equal to X to the E, then the verifier accepts with probability one. Security is captured by the delta soundness property, which states that if Y is not equal to X to the E, then the probability of acceptance is bounded by delta plus some negligible function of the security parameter lambda. In the paper, we can actually consider an adaptive notion of soundness, allowing the malicious prover to choose X, Y and E, but for ease of presentation, we'll forget about adaptivity in this talk. Now, obviously, this completeness and soundness properties are trivial to satisfy on their own by simply having the verifier compute X to the E. So the non-triviality of PoCEs is that the running time of the verifier needs to be much shorter than the time required for this trivial verification. As mentioned before, a non-interactive PoCE can be obtained from an interactive PoCE using the Fiat-Chamer transform, and this is of course assuming that this PoCE is indeed compatible with Fiat-Chamer, as is the case for existing PoCEs. In a batch PoCE, we have amperes of group elements, and the prover tries to convince the verifier that YI is equal to XI raised to the power of E for every I. As before, if this is indeed the case, the verifier should accept with probability one, and the delta soundness requirement is that if this is not the case, then the verifier accepts with probability at most delta plus some negligible function of the security parameter lambda. Now, in the batch setting, we want to achieve verification time, which is non-trivial, not only with respect to verifying the statement by direct computation, but also with respect to the naive approach that simply applies a separate PoCE to each pair XI, YI. We also want the overall communication to be non-trivial in the same respect. As before, a non-interactive batch PoCE can be obtained from an interactive one using the Fiat-Chamer transform, and as we will see, all of our compilers preserve compatibility with Fiat-Chamer. We can now move on to consider our compilers, and as a warm-up, consider the following simple compiler for transforming a PoCE pi with delta soundness into a batch PoCE. First, the verifier sends to the prover a uniformly random subset I of the indices from one to n. Both parties then locally compute X prime, which is the product of all the XIs for little i in the subset capital I, and Y prime, which is defined similarly. Then, the parties simply execute the PoCE pi on the joint input X prime, Y prime, and E. This is the entire compiler. The main observation underlying the soundness guarantee of this compiler is that if Y i is not equal to X i to the E for some i, then the probability that Y prime is equal to X prime to the E is at most one half. This immediately implies that the compiler yields a batch PoCE, which is one half plus delta sound. The communication complexity is n bits needed to represent the subset i, plus the communication required for a single execution of pi. And the verification time is roughly n times tg plus tpi, where tg is the time required for a single multiplication in the group, and tpi is the verification time of pi. Obviously, we're not happy with soundness error of one half, and we wish to reduce it. Naturally, this is done by parallel repetition. So now, the verifier chooses m-independent random subsets of indices i1 to im, where m is the parameter of our compiler, and sends these subsets to the prover. The two parties compute the corresponding m pairs of group elements, X prime j and Y prime j for each j from one to m, and then run m parallel executions of pi, one for each computed pair of elements. By the independence of the subsets, we can show that if Y i is not equal to X i to the E for some i, then the probability that Y prime j is equal to X prime j to the E for every j is at most one half raised to the power of m. This implies that the resulted batch protocol is two to the minus m plus delta sound. And for example, setting m to be equal to the security parameter lambda, or even anything super logarithmic in lambda, we get a protocol which is delta sound which is the best we can hope for. The problem that remains is that the communication added by the compiler is linear in n. This is not a problem if the Fiat-Chameleuristic is applied since all of this added communication is from the verifier to the prover, so it will be locally computed by the parties. If one wishes not to rely on the Fiat-Chameleuristic and to retain an interactive protocol, then this first message from the verifier to the prover can be de-randomized and made much shorter. For example, this can be done by having the verifier send the seed to a pseudo-random generator. This results in communication complexity, which is m times the communication complexity of pi, since we run m executions of pi plus the seed length of the PRG. The verification time is now m times n times tg plus tpi, plus whatever time it takes to evaluate the PRG. It should be mentioned that one can also de-randomize the verifier's message using combinatorial non-cryptographic tools like epsilon-biased sets, but this would incur a slightly larger communication overhead. Okay, so let's move to consider our second compiler, and to do that, we first need to recall the low-order assumption. This assumption is parameterized by some integer s and is captured by the following experiment. First, we sample a group G according to some underlying distribution and give the description of G to the adversary A. The adversary then needs to output a group element x and a integer omega, such that x is not the identity element, omega is smaller than the parameter s, and omega is a multiple of the order of x in G. We say that the s-low-order assumption holds if the probability that a succeeds is negligible in the security parameter. Candidates in which this assumption might hold for super-polynomial values of s are the group qrn of quadratic residue's model when and its isomorphic group qrn plus of sine quadratic residue's, the quotient group z and star over plus minus one, and class groups of imaginary quadratic number fields for certain parameter choices. In some of these cases, the s-low-order assumption even holds unconditionally for s which is exponential in lambda, and you can see the paper for a more exhaustive discussion. The second compiler is defined as follows. The verifier first samples n independent integers, a1 to an from the set 1 to s, whereas it's a parameter of the compiler. You can already understand that it's not a coincidence that we use the same letter that we use to define the parameter of the lower-order assumption. The verifier then sends these ai's to the prover and the two parties compute x' as the product of xi raised to the power of ai and y' which is defined similarly. The parties then execute pi on the input x' y' and e. The soundness of the resulted batch protocol is based on the following lemma that states, at least informally, that if yi is not equal to xi to the e for some ai and the probability that y' is equal to x' to the e is at least one over s plus epsilon, then we can break the s-low-order assumption in the group with probability which is at least epsilon squared. At a high level, the proof of the lemma is by a rewinding reduction. Observe that if we have integers a1 to an such that the induced y' is equal to the induced x' raised to the power of e and the same holds when we change ai to some other ai' then we can divide the two equalities and conclude that yi over xi to the e is a group element whose order divides ai minus ai'. Since yi is not equal to xi to the e, this group element is not the identity element and since ai and ai' are between 1 and s, their difference is less than s and so we break the s-low-order assumption. So this lemma immediately implies that the resulting batch protocol is one over s plus delta sound. Note that the reduction is non-tight as we move from epsilon to epsilon squared and so it's worth mentioning that we do have tight reductions for specific groups and you can see the paper for more details on that. Also recall that as we mentioned we do have candidates for groups in which we believe that the s-low-order assumption holds for super polynomials values of s. In this case, when instantiated in these groups, our compilers yield the delta sound batch protocol which is the best we can hope for. The communication complexity of the resulted protocol is n times log s for the first message of the verifier plus the communication complexity of pi and the verification time is roughly n times log s times tg since each exponentiation takes roughly log s group operations plus the verification time of pi. As before, we can get rid of the added message of the verifier using via Chameer or we can de-randomize it for example using PRG. Now let's move on to discuss our protocols in SafePrimes RSA groups. Just to be on the same page, we're now considering the RSA group z and star of integers model when where the modulus n is the product of two primes p and q. Note that the s-low-order assumption cannot hold in this group for any non-trivial value of s since minus one model when is always an element of order two in this group. This is not just a problem in the proofs but indeed the protocols of Pietzak and Wieselowski can only make sure that y is equal to plus minus x to the e and the same problem arises in the random exponents compiler that we just saw. A possible solution that has been suggested is to quotient out plus minus one from the group. But in some cases, one might want to stick with the group z and star for example, due to implementation issues or compatibility with other cryptographic schemes. In this case, one can consider settling for the above mentioned weaker security guarantee as it might be sufficient for some applications. Another possibility that we will now see is to have the prover prove that we are not settling for this weaker security or in other words, that yi is not equal to minus xi to the e for every i. And we do that for the special case in which p and q are safe primes. As a first step, let's see how to prove that y is not equal to minus x to the e for a single pair of elements x and y and we'll do this by generalizing an idea by Degreshen Zoetal. So the prover computes e plus one over two, rounds it up, raises x to the power of the result and sends the result group element u to the verifier. The verifier then computes z as y times x raised to the power of one plus e plus one model or two and accepts if and only if z is equal to u squared. The main observation is that if y is equal to minus x to the e, then z must be a quadratic non-residue model n. This is true since in this case we can write z as minus one times x raised to the power of e plus one plus e plus one model or two. When p and q are safe primes, minus one is always a quadratic non-residue. On the other hand, e plus one plus e plus one model or two is always an even integer. So z is the product of a quadratic non-residue and a quadratic residue, which means that z is indeed a quadratic non-residue. Hence it cannot be equal to u squared regardless of what element u the prover sends. Now we want to generalize the same approach to prove that yi is not equal to minus xi to the e for n pairs xi and yi. The way the Kreshenzo et al did this is by repeating the protocol from before n times over, which results in a proof size which is linear in n and this is exactly what we're trying to avoid. So the solution will be to apply the same ideas as in the random subsets compiler. For each i, the prover computes ui from xi and the verifier computes zi from xi and yi as before. But instead of having the prover send all of these ui's to the verifier, the verifier now samples m subsets i1 to im and sends them to the prover. For each j, the prover computes wj as the product of all of the ui's for little i in ij and sends the wj's to the verifier. Finally, the verifier computes for every j an element tj as the product of all of the zi's for little i in ij and accepts if and only if tj is equal to wj squared for every j. Incorporating the ideas from before with the ideas of the random subsets compiler, one can show that the soundness error of this protocol is at most 2 to the minus m. As before, we can get rid of the verifier's first message using Fiat-Chameer or the randomize it to make it shorter. The last protocol that we will see in this talk is an information theoretically sound POCE in RSA groups that are defined by two safe primes. So the only POCE that we know of that is secure in z and star is the recent protocol of block et al extending the protocol of Piedzak. The upside of their protocol is that it works in any group but the downside is that it incurs a blow up of factor lambda in communication when compared to the protocol of Piedzak. What we will see now is a protocol that incurs a blow up of factor only two. It can be proven to be information theoretically sound in RSA groups that are defined by two safe primes but it can also be assumed sound for other reasonable choices of moduli. We start by describing the protocol of Piedzak and for this presentation we focus on the case where the exponent is 2 to the t and the prover wishes to prove that y is equal to x raised to the power of 2 to the t modulo n. Piedzak's protocol proceeds in iterations where in each iteration the prover computes z as x raised to the power of 2 to the t over 2 and sends z to the verifier and the verifier replies with a random integer r between 1 and 2 to the lambda. The input to the next iteration is then x prime which is x raised to the power of r times z, y prime which is z raised to the power of r times y and t prime which is t over 2. After log t iterations we get to t equals 1 and then the verifier can verify that y is equal to x squared on their own. As we mentioned before this protocol is insecure in RSA groups since in each iteration it might be the case that y is equal to minus x raised to the power of 2 to the t. To make sure that this is not the case we ask the prover to additionally compute in each iteration the element u as x raised to the power of 2 to the t minus 1 plus 1 and send u to the verifier and the verifier then rejects if x squared times z is not equal to u squared. We will not see the proof for the soundness of this protocol in this talk but it relies on similar ideas to those we saw before and the fact that all elements in z and star when n is the product of two safe primes are either of order two or of order at least two to the lambda. Okay, so let's conclude. What we saw in this talk are simple and deficient batch verification techniques for verification of VDFs while focusing on proofs of correct exponentiation. Concretely, we saw two compilers that take any POCE and turn it into a batch POCE that improve upon the naive solution of simply repeating the POCE and times over. We saw the random subset compiler which works in any group and we saw the random exponents compiler that assumes the lower the resumption in the group. We also specifically saw how to import the random exponents compiler to RSA groups where the modulus n is the product of two safe primes and we also saw an information theoretically sound POCE in these groups as well. An interesting open question is to devise batch verification techniques for other VDFs that do not rely on repeated squaring and batch proofs of correct exponentiation like isogenic based constructions or constructions in prime fields. Okay, so that's the end of the talk and thank you for listening.


Good afternoon, everyone. This is Melissa with thestockswish.com and welcome. Welcome to O-W-W. This is Orbis World Wine. This is the Stock Swish Show Play of the Day. Interestingly enough, this wasn't what I thought I was going to do last night. And trading always live in the real-life time, in the real-life moment. And then I rated this gap this morning and this turned out to be the best gap of any of the gaps that I saw, even the ones from last night. So I decided to do this one today and it paid me twice. I'm all out of this now, had a great exit on this actually, the two times I did it. And I said, don't go back in this today. It's flip-flopping around here now. I still like this lower and the bigger timeframe here. But I'm out of this as a day trade and I wouldn't re-short this today. Here's the gap. Nice little gap here, had the move. Same target was $7.00, $6.75-ish, really, $6.50 even. It's not going to get there today. I would not re-short this today and I'm out. But really two nice trades in this today, so here's what I did. Really like this today too. Really happy here. This was really nice to do. Very aggressive. Just so happens I decided to do this and then I was up really good in here and I just got out. I mean, really, this was the first target and it didn't break $60.00, so then I took the whole first trade off. You can take a portion off, but I saw what I was up. I saw the area. I saw the area on the daily chart where it came into. I had all the numbers figured down. I got out of the whole thing, rallied back up, decided to retake it. Nice stop here then over the base, dropped on down. I actually got out of this here in this bar here, but you could have held it all the way down into here and was a really, really, really nice trade. Great exit. And again, $7.25, if you don't get this, you can't stay in a train when it rides back and give half the money back. So you have to be out. And here, the next number was $7.40, and that's the reason I got out of this guy here, but if you stayed in it here, you could have actually made a little bit more. But do you see what happened here then? Actually, went over the high of the day, showed now, hands off this now, the rest of the day, but a really nice gap and paid me very, very well this morning in two nice trades. And that's your day. I mean, you can do one trade to be done. You can do two trades and be done if they're both positive and you've got your day in. There's no reason to do anything else. You can leave and go to the gym. Really, really nice gap here and O-W-W orbits worldwide. Really nice way to get going here again. I mean, really solidify the week here with a solid, solid, really nice day to get going. And it's only Tuesday, Wednesday, Thursday, Friday, have left for the week. Nice, beautiful, fabulous earning season when there were a lot of good gaps today. There were several gaps that rated more than 20 points. You could have done any one of them per my rating system. Orbis did pay the most, the best, and was a really nice gap. I'm so glad I did it. And guess what? It was the highest rated gap. I love the fact that my system tells me what's really good and what's going to work and have the best and cleanest entries besides the directional bias in the follow through. This is Melissa with the stockswish.com. If you'd like more information on the upcoming gap course on November 9th and 10th, it's this weekend. Then email me at melissa at the stockswish.com to sign up. Thanks everyone and have a fantastic day.