Good morning and welcome to the Green Mountain Care Board. My name is Kevin Mullin, chair of the board and we are going to start this morning meeting which will be recessed to an afternoon meeting as well. So the first item on the agenda are the minutes of Wednesday, November 25th. Do I have a motion? Some moved. Second. It's been moved and seconded to approve the minutes of Wednesday, November 25th without any additions deletions or corrections. Is there any discussion? Hearing none. All those in favor of the motion signify by saying aye. Aye. Those opposed signify by saying nay. Let the record show the motion carried unanimously. The next item on this morning's agenda is the executive director's report. Susan Barrett. Good morning everyone. Happy Wednesday. I just have a couple of comments. A reminder that our ACO FY21 one care budget period that public comment period is open until December 21st. But as a reminder that we're asking that public comments be submitted by December 2nd 2020 which is today to be considered for the December 9th presentation. We will be accepting public comments up until the 21st. In fact we accept public comments 365 days a year but wanted to make sure that if folks wanted to have those considered within this presentation for December 9th to get those in to our public comment portal. And all of the public comments posted to date are or received to date are posted on our website. And then I also just wanted to mention that yesterday we had our first meeting of the Green Mountain Care Board Prescription Technical Advisory Group. I want to thank Christina McLaughlin who is leading the effort from our team as well as Board Member Lunge for her expertise in that group. And we met yesterday for a couple of hours. It was a really informative discussion. I'm hopeful that this this group of experts in pharmaceuticals can help the board and the state address the high cost of prescription drugs. And I don't have anything else to report. Chair Mullin I'll just send it back to you. Thank you Susan. So the next item on the agenda is a further discussion on the hospital budget lessons learned and I'm going to turn it over to Patrick Aruni. Thank you Mr. Chair. Good morning board members hospital budget stakeholders and members of the public to build on what Kevin had said. We are here to discuss the continuance of the hospital budget debrief and let me know when you can see my screen. We can. Okay and I apologize for the barking dogs. Those are mine that may go on for a couple of minutes just to warn you. So we're here to continue this work about a month after our initial meeting in which the stakeholders that being the board the Green Mountain Hair Board staff the HCA and VOS got together in a public meeting to discuss the hospital budget processes opportunities and challenges etc. And then following that we were asked by the board to kind of digest all that was downloaded from those various parties. So we got five board members the staff the HCA and VOS representing 14 community hospitals. It's a lot of perspectives. There was a lot put forth that day so we spent a couple of weeks building this into a structure that we hope can serve the board to make some decisions on how best to move forward. So what we are looking at here is a structure that from this we hope that the board will provide the staff with some guidance on where you want us to begin to spend our energies and our our resources to improve this process. And that's the approach that we were going for. And what we arrived at was this list here and we'll go through this as we move through. So what we did was we we bucketed what we heard from everyone into some common themes. We figured the best approach here because we're all stakeholders in this process is to try to find some shared interests common ground etc. So we bucketed pretty broadly some common themes. We then took those and moved them into short term and long term considerations as in what can the board act on now and what might take some time third party involvement research etc. to achieve to return a value to this process. So we've got some items in here that we've tagged in certain areas where things like for example the hospital budget guidance if we want to shorten that. That's something the board can pretty much take unilateral action on whenever they so choose. And then there's other items as we'll go through what that could take some time to get at. We then decided that we'd try to peg these items on an implementation analysis. What's of importance. What really isn't. What is easy to implement. What really isn't. And so on. And we wrap up with some other comments of items that weren't explicitly stated as a common theme across parties but that we felt should be should be built into the process acknowledged or even continued throughout. So saying that I'll move into some of the common themes. And the three common three themes on the screen on slide three here are discussions around change and charge. We heard several parties discuss the potential to to arrive at some opportunities there or acknowledge challenges. What's the best measurement of growth currently. It's MPR. Are there alternatives that we want to explore. And then transparency in the decision making process. So those are kind of the big three and moving through that there were more detailed matters that were brought up that kind of build into the change in charge discussion. And on slide four here we've kind of we bucketed what we thought were some of those items. So more specific guidance around the components of change in charge. For example does the board want to acknowledge the inflationary factor and have the hospitals show that explicitly when discussing their charge if you ask for 4 percent. How much of that is is inflation is built into that. Does the board want to allow an allotment for cost shift. Does the board want to allow an allotment for a margin. Like what what do we want to go into that. And how explicit do we want to get. That's something that the staff felt we could probably get at sooner rather than later should the board want to move forward with it. The next one up that we had was the COVID component. Originally there were some temporary nature to that. It was then made permanent upon reconsideration. So what is it we need to do with that. And I believe the HCA had brought up concerns about that becoming permanent. So how do we want to get at that. That's something we will have to address in the short term going into the next guidance process or budget process in general. So therefore what do we how do we want to approach that that piece that we built in this year to deal with the COVID pandemic. Standardizing the measurement the measurement of change in charge. We came across an issue this year where there's been kind of an adoption of effective commercial rate for the UVM health network hospitals. And yet we've been doing change in overall charges for the the other hospitals. And we've found that we've been intermingling some of those stats really do have to arrive at one measurement for change in charge in general. And we've got to stick to that. The next one was capturing the impact of Medicare and Medicaid payment policies and changes. Someone had brought up well maybe we do this retroactively looking back at what like say Medicare had given for an increase and having that backed out. That could be a component of the change in charge. You back out payer increases from the prior year to mitigate some of that growth just an idea those are some of the things that we could probably get at sooner rather than later. And the price transparency matter. This one's probably long term. We'll get to that but that was another one that could impact how the board looks at change in charge amongst some of its other regulatory responsibilities. The next measurement of growth with some detail to it would be or the next sorry common theme would be the best measurement of growth. There was some ideas thrown out there about using the total cost of care per member per month in conjunction with NPR. The staff had thrown out using growth and operating expenses in conjunction with NPR as those expenses are what need to be covered by NPR and therefore the growth etc. And also we do need to work on improving comparison to other hospitals because that will help the board members see compared to their peers both in state regionally or nationally what type of growth are we looking at what is acceptable. So building that out improving that and investing in some of those were another item that was brought up. And the last of the common themes with the details would be grouping the hospitals around decision making grouping the hospitals into critical access perspective payment academic understanding the cost structures of those hospitals based on their designations there is certainly some pretty distinct differences there in regard to those designations and to better understand some of that stuff and how it impacts those hospitals perhaps could help guide the board better in their decision making and understanding how fixed some of those hospitals are in regard to their expense structure. And any way that we can try to get a better handle on that perhaps that would allow the board to pinpoint the dollars that they allocate through commercial change in charge in a way that's more valuable to the system and specifically hospitals in those designations. Reducing the administrative burden by streamlining the guidance requirements and delineating need versus want. I think that came from VOS at our last meeting and that is an important point. We don't want to dilute our process by adding and adding and adding and adding things to it. So is there a way we can reduce the burden both for the Green Mountain Care Board staff and the hospitals. We did a streamlined guidance this year. The hospitals exhibited appreciation for that. We felt as staff though that some board members needed some a little bit more. So we thought we had a pretty good pre-COVID guidance going into March of last year we then scaled that back so perhaps within those those confines there is the hyperscale back version and then the pre-COVID version is there a happy point in between that we can arrive at that reduces the burden but also gives the board members what they need to make a decision on MPR growth and change in charge growth. And then there was the topic of the non-financial reporting that was brought up that is usually built into the overall budget process and the deliverable is around mid-May. It was thrown out there that maybe this is not the right place for it. It seems it has kind of organically grown into that process. Is there a better spot where that can fit into the board's regulatory oversight that may not be hospital budgets. All things to be discussed and finally clarity into why the why behind the board's decision on hospitals and ease of understanding for subject matter experts as well as the public. We deal with some very complex matters in health care and in this process there's probably a limit to how dialed back it can get but there's always room for improvement and there's always room for us to explore how we can improve. So those are the three common themes and those are the three common themes with some of the feedback shared by the stakeholders that were put under those buckets. Now we'll move into each one of those for both a short term and long term consideration. So I won't repeat everything I've just gone over but you can see up on the screen here on slide 7 that under the short term considerations for the change in charge bucket more specific guidance around the components that's something we feel we can get at pretty quickly and the board can impact directly the COVID component and standardizing the met the measurement of change in charge whether gross or commercial effective rate or whatever and then capturing those Medicare and Medicaid payment policies. That seems like something that's within the grasp of the Green Mountain Care Board and board members and staff directly. There wouldn't have to be too much outside involvement there to get that done besides maybe some some back and forth with some of the hospitals to make sure that we are capturing exactly what we want to capture. Change in charge long term. The price transparency discussion it's due to come around on or take effect I should say on January 1st of 2021 that is less than a month away. We feel this is long term because this is going to be something that has never been done in health care before. There's going to be a lot of ripple effects following this a lot of uncertainty following this. There's also the impact of there's a new administration taking office on the 20th of January. You may see things differently. So to buy at our time follow some of the the news coming out as this thing perhaps drops on January 1st and kind of studying it as it goes along. And then maybe a year from now or so if it seems like it's going to stay then we can begin to dig into that because price transparency could impact not just this process but also your regulatory oversight on insurance rates. So there would be a couple of teams on the Green Mountain Care Board side that would have to be looking into it and even maybe some outside parties. But we feel that that is a long term item that warrants some diligence but also let's see what happens as far as the impact on the industry as a whole. Short term best measurement of growth improving hospital benchmarks that's something we can begin to put research into now. We are statutory obligated to have some quality by quality I mean good financial benchmarks for peers and then exploring the use of total cost of care per member per month and exploring the growth of operating expenses in conjunction with NPR as options for bolstering that measurement of growth that we currently have as only NPR. It would probably take some time for us to work that through. So the long term considerations have that built in as well using total cost of care as opposed to short term exploration and using growth of operating expenses as opposed to exploring that item at first. So that kind of crosses both of those long term and short term considerations from our perspectives. The transparency and decision making short term we feel that we could group the hospitals into these prospective buckets based on designations and begin to work with those hospitals to understand what are the constraints you're under because of those designations and how much of your cost is fixed and where do you have the ability to make sure you're as efficient and efficient as possible and where do you do not. That's a very real thing in health care is efficiency is a very tricky thing to put your thumb on but we want to make sure if we're saying now you look like your cost structure is drawing a little too much that we actually have something to to back that up with and reducing the administrative burden by streamlining guidance. That's a pretty quick thing to do. We did it very quickly this past year and turning that around. We have a precedent for it now. We also have a work product that we can say okay if that was really dialed back let's build a little bit more into it by getting feedback on the board from the board members of what you absolutely need to see in this to make your decision and going from there and that's something we could turn around pretty quickly. Long term considerations on transparency. The clarity into why behind the board's budget decisions. Really everything we've talked about above should trickle down into this if the board decides to take action on some or all of those. It should help improve the why behind that. That's the idea. So this is long term because depending on what the board decides to adopt when and how it should help better inform as we make those adjustments to the process. So this isn't so much a work product as it is a culmination of the other work products that we would take under our wings in the coming months or years or however long it takes us to make some of these alterations. So as discussed earlier we then took all of that and we tried to peg it on a scale of importance and difficulty. What do we feel is higher importance and lower difficulty all the way all the way around the wheel to lower importance and lower difficulty. So trying to provide the board members with some insight around what do we think we can tackle now. And we'd like feedback from the board on whether or not you agree with some of this stuff or whether or not some of this may have to be moved. But trying to provide some sort of roadmap for making some of these adjustments should the board choose to adopt them because as the arbiters of what does and what does not occur in the guidance in the hospital budget process we really do need board feedback on where to spend our resources. And we'd also advise that maybe the board could also not we could have board members nominate themselves or other board members to help work on some of these products and be that proxy for their fellow board members as kind of the subject matter experts as we work through this and also be engaged in helping make these changes and potential opportunities come to fruition. Lastly as I discussed there are some other comments that were made that we feel are very important to this process. It may take some time to get some of these done. Others may happen. There wasn't explicitly a common ground amongst this. That doesn't mean it doesn't exist. But one of those was reconciling the hospital rates the rate review process. There's a lot that goes that would go in behind that. I think to some extent it's been explored before from what I understand but there's been some legal hurdles and that may change in the future. But it's something we feel we should keep on the front of our mind moving forward especially if price transparency does stick. Another one I think was brought by the HCA was addressing racial disparity in the process. This is certainly something that's probably long overdue to be honest and even though we're not the most diverse state it still warrants understanding what our health care organizations are doing to make sure that health care is being delivered in a way that promotes equality and that all persons regardless of any identifiers are are certainly being cared for in the way that any of us would hope to be cared for. So we think that certainly warrants continuation through this process. And then kind of a broader thing was we we all get dialed into our our perspectives here and our certain trenches sometimes. But I think it was Kevin to take a step back and look at the bigger picture here. And we're all working in this thing to make sure that from honors have access to high quality health care at the most affordable rate possible. So kind of keeping that in mind as we go through this and we you know we all share our different perspectives and everything that the that's the big picture here. We're all you know all these stakeholders are care about that right there on either side any side of this equation. So that we felt was something that deserves some reinforcing as we even work through this process. So that's why we put that in there. And with that that concludes our presentation. It's quick. It's pretty high level. But we hope we captured the thoughts of all the different parties involved and help provide the board with a little bit of guidance here for the discussion that's in front of us now. So Mr. Chair we'll turn it over to you. Thanks Patrick. I'll kick it off on behalf of the board and just say that for me there are two things that really jump out to the front of the list on what I think we should be focusing our initial time and resources on and that is having a common measurement for charges. And it should be across all hospitals. And so that's number one in my view. And number two is to expand the guidance so that we give specific guidance on for example change in charges. And I say that because what we've seen is a repeated effort by a number of the regulated entities to back into that based on putting together a budget and then figuring out what increase is needed to meet that budget. And I think more emphasis is placed on backing into that number than being placed on what is affordable for Vermonters and how do we adjust expenses to make it affordable for Vermonters. And so I really think those are my two highest priorities and with that I'll open it up to any board members for their thoughts. Who would like to go first. Well I have a couple that rise rise to mind readily. You know Patrick said that maybe in the budget process we should make an allowance for the cost shift. And I that's not something I would agree to. It would be that would be like enabling the cost shift. And to me the cost shift is a structural problem valued at hundreds of millions of dollars. And it's possibly a kind of a parasite on health care reform. Assuming that our health care reform efforts are successful and we are finding efficiencies and proving population health etc through the back door the cost shift kind of siphons money out of the system and sends it elsewhere in government. And so you know for me it would be a better course to admit that the cost shift is not a good thing. It is not a good thing for a certain population not to pay not some cost shift is fine. But it just keeps growing and growing and growing. And so and there are places that we could intervene or maybe BOS could intervene and one suggested I would have would be at the emergency board every year at the beginning of the legislative session the emergency board which is comprised of the governor and the heads of House Appropriations and Senate Appropriations and House Ways and Means and Senate Finance they go into a very detailed presentation with the JFO on the Medicaid budget. And I think you know if we could find some kind of access into that system to say you know let's be specific and clear and straightforward about the cost shift so that we know how that is affecting you know the systems that that we deal with as we learned in rate review from the Blue Cross Blue Shield actuary if there was no cost shift insurance premiums could be lowered by 35 percent. So that's that's one area I would want to make more transparent and to be more aggressive on because it is such a large force in our hospital budget system as we saw during the hearings every single hospital complains about the cost shift but the can keeps get getting kicked down the road. We keep whistling past past the graveyard in that regard. And I think that at some point we've got to raise it to a high priority. The other area for me is fixed prospective payments. If you look at the 2019 hospital budget actual fixed prospective payments as revenue it was about 10.2 percent of total NPR FFP. For the 2020 budget which is kind of by the board is given given the COVID problem it was at 14.5 percent and for 2021 budget it came in at 13.9 percent. And I'm not sure how those percentages equate to the leveraging of the reforms that we want to occur is a 13.9 percent FPP across hospitals. A metric that is going to leverage the capitation that we're looking for that will generate innovation and efficiencies and allow us to reinvest in population health. So that's one metric that I would look to see whether or not not just to kind of follow the number but to work to establish a target that we know that we're working for. Maybe that target is 30 percent maybe it's 45 percent. I don't know but I think that we need to spend some time to figure out what the target needs to be for FPP across hospitals such that we can leverage. It has the the capitation and leveraging effect of getting our health care reform efforts where we'd like them to be in the next two or three years. So those are two that jump out at me. Other board members. I'll go. Patrick and team first of all thank you for for that presentation and pulling together all these thoughts and all these conversations that we've had. I feel like some of these components of the presentation were also part of conversations we've had even last year. So you've really pulled in a lot. And I agree with all of the short term initiatives that you've put forth to improve our decision-making process and provide us with better data to be able to be better informed as we're making those decisions. I agree with Kevin in the sense that we really need to standardize the effective commercial rate so that really we're looking at apples to apples across hospitals. And that's really a top priority for me. And also the second component and really understanding the changes in those effective commercial rates. So your point about inflation is important. I want to really be able to unpack what is underneath that commercial rate change. So is it inflation driving it. Is it is it cost shift. I guess I'm going to guess it's both and margins. Right. So how do we start to unpack what's under the hood there and understand what is driving those commercial rate increases. What are the components. I think that's really important. If we are going to put guardrails around commercial rate or effective commercial rate was what I hope that we're really looking at as an effective commercial rate versus just changes in the charge master which we know are not really a true you know showing the true impact of those commercial rate changes. We really want to look at effective commercial rate. How is that changing at the hospital level. I think we need an understanding of the base price. And so where hospitals are now in their pricing and so then we can really understand what are we building on top of that. So one of my questions to you Patrick was the price transparency. You had bucketed that in low importance high difficulty and I'm just wondering I I would have thought it would be high importance lower difficulty given that the hospitals are going to be required to report their prices in January. So the data is is is going to be available. It's just a question of unpacking that data and analyzing that data but we've never had access to that data before. So that's where to me it moves from you know high difficulty to low difficulty simply because of the reporting requirements. So maybe I'll finish up and then maybe you can just answer that question if you have an answer for that. The benchmarks I think are really important. I think we need to factor in when we're looking at each hospital factoring in the size and the type of the hospital and comparing our hospitals and how they're performing outside the state. Right. It's similarly sized and similarly designated hospitals. I think it's really important and like the idea of looking at per member per month growth rates per member per month total cost of care growth rates is a measure of hospital performance. It factors in migrations factors in the patient flows that we're seeing across HSA boundaries and it fundamentally is looking at the total cost of care which is what we are held accountable for with the federal government. So it's it's another look at that really important component. But it also does it's important because it's per capita. So it is recognizing that some hospital service areas are seeing out migration and some are seeing in migration. So as soon as you make it per capita you're accounting for that which I think is really important. And again we're reducing the burden wherever we can I think is is key ensuring that we have the data that we need. But where we can pull in data that's already being reported in other venues and using that data I think would be really helpful. So those are some of my thoughts. I thank you for the presentation. I thank you for thinking about this and I'm excited about moving forward and improving our hospital budget process. But again I would question I want to ask you a little bit about that price transparency difficulty and importance piece. Yeah so the reason that we put it down there was there's still even though it is set for January 1st at least on our end because we've never seen it before we don't know what we're looking at. And it's going to take a lot of time to digest and understand what we're looking at and develop a strategy as to how we're going to use that. And we did not see that dropping on January 1st and being a reality for the upcoming budget cycle. And there's also the fact that because it hasn't been viewed before there's going to be a lot of upheaval that goes into the wake of that coming out. And to to make sure we're knowledgeable and understanding of what we're looking at to incorporate it into your decision making and make a well informed decision it's on the lower importance higher difficulty piece because of that. It doesn't seem like something that we would be able to achieve with confidence and competence going into the next hospital budget cycle. So that's why it's on the higher difficulty lower importance scale right now. That could change several months from now once we understand what we're looking at and and what this means and what it could mean for other hospitals in our region as well. I mean we're certainly going to want to compare UVM with probably Albany and Dartmouth and things like that. So once we see what they're charging we're going to have to dig into that and develop a strategy. Do we want to focus on all of these different charges that they're putting out there or are there are is there a markup that we're looking at like a grouping that we'd want to look at and say OK well this is where they make their biggest markup. How much do we want to really allow for them. So there's a lot out there that we've never seen and don't know yet. So that's why it's down where it is right now. Doesn't mean it's not of importance but it's it's just down on that scale from the staff's perspective. Okay let me ask a quick question that I realized about the non-financial reporting. You had mentioned moving that around some thinking differently about the non-financial reporting. Can you just elaborate a little bit about what you mean by is there a better time. Is there a better way to do it. What were you thinking there. I really don't have any thoughts. I've never heard anyone on the hospital side say that is a burden. It was brought up by one of the board members in our last meeting. So that seemed to fit into that more detailed bucket of is there any way we can through the budget process eliminate some of the administration straight of burden on them developing and reporting a budget to us. So I'm not sure from what I understand as I said it's kind of it kind of ended up there and so it probably warrants us looking at well is that the right place for it. Does does it really inform the budget process around rate and NPR. If it doesn't perhaps there's a different time during the year which we can request that. But again I've never heard any of the hospitals mention that that's a that's an issue for them. Okay. Thank you. Certainly. Thanks Jess. Robin. Thank you. I agree with what folks have said around spending some time improving the change in charge data information and guidance. I do think that that's an area where we can add transparency to both the process and our decision making. And and obvious. So Robin we may be having a problem receiving your signal. Perhaps you could turn off your video and then we might be able to hear you on audio. Can you hear me now. We can. Thank you. Okay. Sorry about that. I'm having all sorts of technical difficulties. My laptop died so I'm trying to do this on the phone. So sorry about that. So what I was saying was that I agree with what folks have been talking about in terms of change in charge and the importance of that part of the process and improving the data and information that we have available given that it is a lever connected to rate review and affordability. And I I think that it makes sense to continue to look at areas in the process where data and information that we're perhaps not using. For me the non-financial reporting is important. It is I don't know how to look at the financial aspects without some concept of the totality of what the hospital is doing including around quality. And so that is something which I routinely have used and missed this past year. We did move that reporting to the spring and I think a lot of it quite frankly is compiled by our staff which is why it may not be perceived as a burden. So all for looking at that but do think we need to in some way continue to try to incorporate quality as well as access measures which I think are sort of the point of those. Yeah and I think otherwise the short-term initiatives did make sense to me as a place to start. I would just make note of a couple things in terms of the total cost of care per member per month. That's something which Sarah Lindberg has looked at a couple of different times I think and there are challenges with doing that which we have been exploring in the regulatory integration. So I would encourage our staff to connect with each other on that piece and also specifically on the rate review and hospital budget component there is a section of that in the regulatory integration paper that I would encourage people to read. So that's that's what I have to say. Thank you Robin. Next we'll move to Maureen. Thanks and thanks for the presentation. I had I want to go on the same line as Jess was going on on the price transparency and you know looking at that chart I also thought that should be higher importance even now I mean we may not have the requirements that they have to file by January but the hospitals themselves know what their prices are. We just haven't always had the transparency of getting the information on prices for services. So I do think that's important and where that kind of piggybacks on is to the change in charge because one of the things we we know is that all the hospitals aren't starting at the same starting place and you know we when we treat everyone the same and say we're going to have a uniform change in charge that that's where I have a little bit of a hesitation. I do think we should give guidance on change in charge. The concern is that those that may be already at higher cost are going to continue to grow at that higher cost and those that have been lower cost and more efficient you know may have more challenges living within those means. So there's just an issue there on you know how do we work that and part of it is we don't really know the starting place and we try to treat everyone all the same which which is the challenge all the 14 hospitals are not the same. So if we were to come out with a change in charge you know as a uniform one rate that might be a challenge but but there may be ways we can come up with some guidance there. You know a couple of the couple of other things that maybe are more in for the long term which we didn't really talk about would be the sustainability plan and how that impacts the hospital budget process and in particular when we talk about talk about services because hospitals may be making a small margin or no margin and part of that may be related to the mix of services that are being provided and are they the right mix of services and all the hospitals. And that brings me to another thing on the chart you had where where you had positioned the ability for I think can you flip to that chart because there are a few things on that chart I think that was good good way to look at it. But when we talk about higher importance lower difficulty understanding the cost structures of the hospitals a challenge that that's lower difficulty and and the reason why is when we look at it on a on a total perspective yes we can understand kind of you know what the cost structures are of the hospitals but really being able to dig in and understand if we were to look at where they make margin where they don't make margin by payer type by services and things like that I mean that's the way you would look at a business right to determine maybe where some changes could be made obviously we can't just look at hospitals and say OK this is a business like that and we cut those things out but but there may be some learnings from that to be able to make hospitals have the ability to be more efficient. So I think that you know it's at what level of understanding cost structures of hospitals so I think that's higher importance higher difficulty because because from what I've seen we we don't really have an understanding of the cost structure of hospitals and when we try to dig into it we don't get clear answers about that you know when we talk about you know cost savings and things like how do we gain efficiencies and cost savings you know that that's really one of the key drivers here to ultimately what the top line will be needs to be in order to create a margin. So so I think we need to do I would move that to a different spot and you know I think the other thing which we didn't completely touch on Tom talked about a little bit and fixed perspective payment but you know just ACO participation and as we move more into that and that becomes a larger piece of the pie how does that then relate to change in charge and things like that. So you know I think I think this has been helpful and it'll be interesting to hear you know some of the public comments you know that we get at this point. Thanks. Okay anything else from the board. Any questions from staff to the board before I open it up to public comment. No not on my end and I'll open that up to Kate and Laurie if they have anything. Hearing none we're good. I'll open it up to public comment now. Does any member of the public wish to comment. Hi Kevin this is Mark Stanislaus from the University of for my Health Network.  So you know just a couple things. I had shared this with Patrick but you know the University of Vermont Health Network has been fairly silent through the last few discussions and I just wanted to share that we're focusing our priority in other areas right now you know given what we're dealing with. So I just wanted to share that out there and then I was taking some notes as I was listening to the conversation. I think these are more items just to be aware of well from my perspective that I just wanted to share. I mean Patrick's summary was a very good summary. I should say Patrick and the staff summary was a very good summary but and so I will just punch down through this list. It's in no particular order. I was kind of making notes as they came to me but I think I think when we focus on growth rates we really need to focus on industry standards and comparisons. They need to be fair and they need to be specific to our industry you know. I think in the past what we've heard we know we should try to keep it health care growth will be low GDP you know that's not a comparable industry standard because you show me how many other states have been able to do that. So I think we need to be very clear on you know what we would like to get closer to and what's are reasonable expectations and you know the focus needs to be on industry standards and fair compare groups. I think as we think about the cost shift the cost shift is real. It is impacting the hospitals considerably and the burden is growing more and more where it has a material impact on the hospital's financial results each year. So you know we can talk about the individual components of that but I just don't know how the cost shift can't be part of the conversation given the significant impact on the hospitals. As we think about affordability I think that we just need to remind ourselves that the hospital process is just one part of the cost structure that all of the Vermonters are engaging in. So you know the more we can transition to total cost of care and those relationships I think that's a better place to be. And you know this kind of gets back to the cost shift component but you know we need to remember that when a patient comes to any healthcare provider they don't think about the cost shift they don't think about the problem. What the what the profitability of that service may or may not be. They focus on what is the best best care that that patient needs to get them healthy again. And so the providers are bearing the cost of that care up front even before any payment is processed. So you know I think that we just need to remember that of you know just saying that and you know this gets back to the cost shift conversation is you know just saying that that you know that needs to be a focus here because you know with the providers that are providing the care they don't think about it that way. And you know if the providers start to think about that way I worry about the downstream impacts that that it could have on our healthcare system. There was no conversation about understanding other revenue. I think we've had some conversations in the past and I think it I think that it you know was said the hospitals wouldn't have a margin if it wasn't for 340B. So we know I think a better understanding of other revenue and the relationship of everything else needs to be there just needs to be more emphasis on that than there has been in the past. I think it makes sense to do the crosswalk on the commercial charge you know we'll talk to all of the areas that are driving that so that makes sense. You know what we didn't talk about at all or you know what I didn't hear and understanding where the components of the math might lead into this. But you know what is an appropriate margin. You know hospitals need to have a margin to continue to invest to meet the needs of the patients. And you know as you just think about the hospitals and the margin and the deterioration of those margins and the number of hospitals that are growing that are in the red I do think there needs to be some aspect of that injected into the process. Let me see. I'm trying to understand this. No Kevin so so yeah. So as it relates to inpatient and many outpatient services we need to remind ourselves that the health care system is complicated and it is complicated. But the hospitals and other providers for inpatient services and many many outpatient services are not paid at the line item level. So that complicates things as we I mean they're simply not paid that way. The inpatient is DRG outpatient many of the services are on episodes of care now. So you know I think that we need to find ways to do a better job than we're doing today candidly.  And you know as we think about the impacts of the decisions that we make and when I say the decisions that we make is it could be the Green Mountain Care Board decisions. It could be decisions that individual hospitals choose to make. But we really need to break that down into what that does to access what that does to cost what that does to commercial rates because you know if say a hospital stops doing a critical service but another provider is going to continue that critical service that isn't the isn't under the regulatory oversight of the Green Mountain Care Board you know while it might appear that the hospital has lower cost it really hasn't lowered the cost of care. And you know at what cost any decisions impact on access. So you know I think you know there's a lot of difficult decisions to come. This is not an easy process. Well the board's role is not an easy role in the process. But you know I believe that we're coming to a breaking point where decisions are going to be made on cutting costs which is going to have a direct correlation on access and we just need to keep that conversation open so everyone fully understands the impacts of those decisions. And I thank you for this time and opportunity to share those thoughts. Thank you Mark. It was really good comments and I sympathize with you on the not being able to read your notes. I have the same problem. I don't know where my penmanship went south but now it's like deciphering whatever I wrote. So with that I'm going to go to Mike Del Treco and the next on deck will be Mike Fisher. Thanks Chairman Mullen. Thank you very much. I don't have as many words as Mark. I never do. So just to be brief I think Patrick the outline that you put together and the efficiency of the conversation that just took place is really important in this time. So I want to comment on a couple of things that I think the change in charge is critically important. I think the board our members really need to be careful not to portray that we have multiple charge structures. Often when we talk about change in charge and we have a commercial rate that's really not true. We have one rate and they have different effects on how payments work. I know you're having a reimbursement discussion next week and there'll be a lot of information shared there. So we just need to be cognizant of potential odd compliance issues where public hears this and they think they might have a different charge than some other individual with a different with a different commercial with a different insurance carrier. Secondly I think transparency I've heard a couple or times not during not just this meeting but the prior meeting and I think from my perspective things are very transparent and it's maybe things that are missing elements and I would like to sort of move into exacting what those missing elements are. And if they're available what can we produce them. And if they're available that's one thing. And if they're if it's thought to be available and there's difficulty and there's reasons why they can't produce we need to recognize those those as well. And then finally I think a streamlined budget guidance or with that always in mind whether it's during this time of pandemic or not I think is important making sure that all parties and entities get what they need to make the decisions must must be part of that equation too. So those are the three areas of comment that I have and certainly happy to talk to anybody in Patrick more in detail but but but thanks for the efficiency of the conversation and the clarity. Mike can I just ask you a follow up question to what you said. Sure can. So you said that people shouldn't think that there's different charges on commercial rates but if one insurer is reimbursing a hospital at 80 percent of charges and another one is reimbursing a hospital at 75 percent of charges isn't that really a difference in charge. Actually you you answered your the question it's reimbursement the payment is different the charge to charge to the patient and payer payers the same. And then what impacts that charge is the insurance program that you might be enrolled in as an individual and then the contractual relationship that that insurance carrier has with any one provider. So the charge is the same those two elements make either out of pocket change or the payment to the provider change. So whether you're Medicare Medicaid commercial self pay if you and I had the identical service at the identical location and I was Medicaid and you were self pay we would get or commercial we would get the same identical charge and the payment for that service and the out of pocket for that service would change depending on the product that you're enrolled in and the contractual arrangement that the provider has with the insurer. Thanks Mike. Next Mike Fisher. Good morning. Thank you Mr. Chair and members of the committee. And thank you board staff. I will echo what's been said. I think that was a great presentation with a lot of important questions. And I also want to just echo I think well this last conversation that was just going on the the the question for me is a common measurement of charge across hospitals. You know is the methodology of determining charge done similarly across hospitals is the way I understood the chair's original comment. And I also want to appreciate the chair's original comment around just understanding what the affordability impacts are about what happens when rates go up. About cost shift I just want to bring it home for a second. The administration is developing a budget at this moment. I would be tremendously surprised if there was any kind of proposal to have Medicaid reimbursement rates keep pace with inflation let alone make up some of the lost ground and also recognized the constraints that they're under they probably can't given the global commitment caps that we live under. But it's a decision happening right now right in front of us and and it's real. And then under the category of other data available I we've spent a little bit of time looking at the Medicare cost report and and attempting and it may be that there is some information in the Medicare cost report or in the IRS 990 that is is close enough to some of the data that the board asks for or at least on a surface level should be that there may be some improved efficiency that the board could ask for you know Medicare cost report at you know S10 line 23 column 3 you know in place of how much do you spend on free care. And I'm going into the weeds for a second for just to make the point I can't recommend such a move because when we compare what the hospitals report on what should be very similar measures to what they report to the Green Mountain Care Board we can't make a lot of sense about the variation that we see. So my real comment is that it would take some work to understand why the numbers show up so differently. But there may be some efficiencies available in those reports to make reporting easier for the hospitals. And that's my comment. Thank you. Thank you very much Mike. Is there any other member of the public that wishes to offer comment. Hearing none Patrick is there anything else that you need to guide you in your efforts to keep this process moving to make the necessary changes. I don't believe so at this time. We will get together as a staff here and digest the discussion today and provide the board with some updates on what we've heard and then probably reach out to some board members to start moving some of these initiatives forward. Super. Thank you. And thank you everyone for the feedback this morning and we are going to go into recess until 1 o'clock this afternoon. Thank you everyone.


Hi, everyone. So yeah, I'm going to talk about worst case hardness for LPN via cod smoothing and some applications such as cryptographic hashing. And this is joint work with Vadim Lubashevsky, Vinod Vaikunathan, and Daniel Wicks. So let's sort of all remember what's the LPN problem. So essentially, it's a problem of solving a random system of linear equations over the binary field. So we have a system of m equations with n variables. So you can just represent it as a matrix A. And this is just going to be a random matrix because we're thinking about a set of random linear equations. And the variables is this secret vector s, which is the variables that we actually want to recover. And we are thinking about these variables also as chosen at random because this is actually the hardest case. So I'm going to give you the coefficients of the equation. So this is the random matrix A. And I'm going to give you the vector b, which is A times s. And the goal is to find the variables s. Of course, this is not an intractable problem. And well, there's no noise here. So you can think about this learning parity without noise. But if you want to think about learning parity with noise, then we're thinking about adding a little bit of noise to each one of these equations. So flipping the output of the equation with some small probability. And again, this can be thought of as adding some IID Bernoulli noise. So this is the learning parity with noise problem, very well studied problem. And let's think about it for a second and think in which parameter regimes this problem is easy and which parameter regimes it's hard. So it's not so hard to see that as the weight of the noise, the hem rate of noise gets higher, gets closer to 1.5. So I'm only going to think about noise with weight less than 1.5. Otherwise, it's symmetric. Then the problem actually becomes harder. So we already saw that if the weight of the noise vector is 0, then the problem is easy because you can just solve it as a system of linear equations. So this is what I said before. So I'm thinking about delta as being the relative weight of this vector, which is also related to the parameter of the Bernoulli noise. So for delta equals 0, the problem is easy. And actually, also for slightly larger values than 0, it's not hard to see that 1 over 5 times n noise is also going to be easy to solve. And actually, you can take this a little further and show that even if the relative noise is log n over n, then you can still solve this problem in polynomial time. And the idea is to just sort of pick a random set of n out of these m equations. And with probability 1 over polynomial, all of these equations are actually going to be noise-free. And you can use these equations to recover the secret s. And then you can test it using the other equations. So I should say that people think of variants where the number of equations m is fixed ahead of time. Like, it's going to be some polynomial in n. So either we're going to take m equals, say, n squared, or you can think about a variant where the adversary can specify how many equations he wants and he can get as many polynomial number of equations as they want. So this is the case of sort of easy to solve LPN. But if you go a little higher, even if you think about noise weight of log square n over n, then the problem, as far as I know, stops being tractable in polynomial time. And in fact, the algorithm that I just described before is going to take quasi-pollinomial time. So it's going to take n to the log n time. And while this is perhaps not the worst running time in the world, it's still not polynomial. So we're going to still think about it as a hard instance of LPN, but it's sort of only barely hard. And I should say that you can also think about any little omega of log n over n and not necessarily log square, but somehow less than n to the log n hardness seems, I don't know, to give me the chills, so I'm not going to do it. So this is on one end, so we're going to think about this barely hard regime of parameters where LPN is hard, but it only starts being hard. And on the other hand, we saw that if the noise rate is equal to 1 half, then this means that the noise vector might be random, and this means that the vector b actually does not contain any information about s, and therefore the problem is not solvable even information theoretically. And you can relax a little bit and say that if the weight is something like 1 half minus negligible, then this property still remains. And the problem is not even information theoretically solved. So we want to consider sort of the highest noise level where the problem is still at least information theoretically solvable. And this is the case where the relative noise is 1 half minus 1 over polynomial. So in this case, at least if we set m to be high enough, a large enough polynomial, then the problem becomes at least information theoretically solvable. And we think of this as sort of the hardest instance of the problem where we want to achieve computational advantage. And I should say that for cryptographic applications, this parameter regime might be useful for at least in some cases. So it's not a completely contrived parameter regime. So this is what I sort of want to set up about LPN, when it's easy, when it's hard, and we're going to think about these two parameter regimes later on. But right now, let me talk about a completely different problem, maybe not completely different. So I want to talk about the learning with errors problem. And as you can see, it's giving me a very easy time preparing the slides, because the syntax of the problem is almost identical. So again, we want to solve a set of random linear equations with some additional IID noise. However, the difference is that now the system of equations is not over the binary field. It's actually some modulus q, and this q is going to be large. It's going to be asymptotically large. And for the purpose of this talk, just think about q being some polynomial larger than n. And usually, people think about the IID noise as being Gaussian, but the exact distribution doesn't matter. The important thing is that the L2 norm of the noise vector, in this case, needs to be small. So notice that here we can talk about L2 norm, because, well, these elements are modular q, which is bigger than the noise regime, whereas talking about L2 norm in the LPN setting, well, it's possible, but it doesn't really carry much meaning. So this LW problem has been pretty useful for cryptography, and we actually know quite a lot about its properties and about its uses. So for example, we have a worst case to average case reduction for the LWE problem. So this is an average case problem, because, well, everything here is sampled from a distribution. However, it was shown that by regive that if you can solve this average case problem, then you can also solve worst case problems on lattices. So you can actually solve these short vector problems on lattices. You don't need to know what they are. Even for the hardest lattice in the world, if you can solve this average case problem, and I guess it's your choice whether to think that this means that this average case problem is actually hard, because it's harder than the worst case problem, or that the worst case problem is actually not that hard, because it's not harder than some average case problem. But at least we know that we have this connection. We also know that this problem is contained in the complexity class statistical zero knowledge. Again, you don't need to know for the purpose of this talk what SDK is. However, we know that or we conjecture that problems in SDK are unlikely to be NP-hard, for example. So we know that this problem is not going to be sort of, we have some evidence that this problem is not super hard. So these are some properties that we know about LWE. And we also have a lot of applications, a lot of cryptographic applications. So starting from sort of the basic symmetric and public encryption, collision-resistant hash function, homomorphic encryption, attribute-based encryption, recently non-interactive zero knowledge. So we know how to do a lot of things. And sort of given the sort of minimal edit distance between this slide and the previous one, you would think that maybe the structure can also carry over to the LPN setting. So whatever we can do with this LWE, well, can't we just sort of translate Q to 2? And maybe, as I said, the L2 norm maybe doesn't make sense in the LPN setting. So maybe we need to replace it with Hemingway or something. And we would hope that things will still sort of work out. Or at least a lot of these things will be able to carry over. But it's not the case. So we don't know of worst case to average case reduction or SDK result. And in terms of applications, we can get symmetric and with some parameter regimes also public encryption. But a lot of these other applications are still not known yet. And I should say that recently, there's a lot of progress in constructing primitives from cryptographic primitives from LPN. So I should probably check on ePrint whether I should update the slide. And I'm hoping that there's going to be a lot of progress in filling up these blanks in the sort of near future. However, at this point, we could still ask, why is it so different? Why is LPN, what we can do and what we can say about LPN is so different from what we can say and what we can do about LWE. And there are a number of attempts to try to explain this difference. But we want to try to close this gap as much as we can. And what we show in this work is a first step in this direction and trying to equate the status of these two problems. So the first thing that we show is new properties. So we show worst case to average case reduction for LPN. So we would like to show that this LPN, this average case problem, is harder than some worst case problem. And the worst case problem that we're going to think about is the nearest codeword problem, which is a problem that comes from the problem of decoding linear codes. So for our purposes, you can think about this nearest codeword problem just as a worst case version of LPN. So rather than the matrix A, these coefficients being random elements and the noise being sampled from some distribution, you should just think of these A and E as chosen adversarial with some parameters. So this is going to be sparse codes. This is going to be the nearest codeword problem. And actually, for our reduction, we require nearest codeword problem with balanced matrix A, which means that if you think about the matrix A as a generator matrix for a linear code, then all code words in this code are going to have Hemingway very close to 1 half. How close? Something like 1 half minus 1 over poly. So this is perhaps a bit aggressive parameter regime. This is what we know how to do. And as an excuse, you can say that, well, since a random code has this property, it means that most codes have this property. I don't know how convincing it is, but at least at this point, this is what we can say. This is still a worst case problem. So any A and E that have these properties are going to be considered in our reduction. And this is not all the bad news. So what we show is a worst case to average case reduction with the worst possible performance. So what we show is that the hardest instance of the average case problem. So you take the LPN, the hardest LPN that you can consider. So the noise is going to be 1 half minus 1 over poly. And what we're going to show is that, well, it's harder than a worst case problem, but it's harder than this nearest codeword problem in this barely hard parameter regime. So if the weight of the noise is something like log square n over n. So this is still better than what was known before. However, you could hope to not lose so much in the reduction, but this is what we get in this work. The other thing that we show is containment in SDK. So again, this could be interpreted as evidence of easiness, like the problem is not going to be NP-hard. And as you would predict, we have this proof of easiness for the easiest version of these problems. So we show that these barely hard LPN or nearest codeword problem are actually contained in SDK. So the easiest parameter regime we can think of is unlikely to be NP-hard. Again, this was not known before, so now it is. We can also get new applications based on these techniques. One thing that we can show is collision-resistant hashing based on the barely hard LPN problem. And I should say that concurrently, you et al were able to present the construction that's almost identical, the construction itself. So in follow-up works, we're actually able to use these techniques to introduce other applications, such as IBE and other things. And again, there's more things that are known now. So this is what we show in this work. And let me tell you a little bit about our techniques. So the technique that we use is sort of, we think of it as smoothing. So if you've heard this term in the lattice regime, hopefully it will connect. And if not, then let me tell you what I mean. So I'm going to start with a work by Luboszewski from 2005. And Luboszewski actually considered an LPN to LPN reduction. So he was considering the following thing. You want to solve an LPN instance with n squared many equations. However, what you have is a solver for LPN, but the solver actually needs a lot more equations. Let's say n to the 100. Actually, Vadim needed even more than that. But for our purposes, this is the parameters that we're going to think about. So we have a solver that needs many, many LPN equations. And we only got much fewer equations. And what this reduction shows is that so long as your n to the 100 solver can manage with much, much, much higher noise than the n squared instance that you started from, then this is actually doable. So you can think about it as a reduction, where if you have, again, if you have a solver which requires many equations, but high noise, you can actually use it to solve LPN with much fewer equations, but much smaller noise. And let's see how it is done. So this is done using sort of re-rendomization. And the observation is that the matrix A, this random LPN matrix, you can actually use it as an entropy extractor. So we know that for a random matrix, a random vector multiplication is going to sort of extract randomness. So we have this now n by n squared matrix, which sort of corresponds to the A part of the n squared LPN instance that we got. And what we know is that if we multiply it by a vector R, which comes from a distribution of sufficient entropy, then what we're going to get is, in the end, is a vector A prime, where the joint distribution of capital A and A prime is mutually uniform or statistically close to uniform. So in order for this reduction to work, we're going to need to find such distributions on R that, on one hand, has sufficient entropy. So the required entropy is, of course, at least n bits, because we're generating this A prime, which has roughly n bits of entropy. So we need this R distribution to have at least entropy n. And in addition, we want, for the purposes of the reduction, as we're going to see in a second, we want this R to have as low as possible hamming weight. So quickly, if we think about it, then obviously we can get such a distribution with hamming weight n. But if we think a little bit more, I can actually see that you can generate a distribution with hamming weight something like n over log n, which still has entropy n. And actually, this gap between n and n over log n is going to buy us a lot in this setting. So this is actually what we capitalize on, what we didn't capitalize on and what we're going to capitalize on. So once you have this distribution, what you're going to do is the following. The reduction is going to generate like n to the 100 vectors R. So each one of these vectors R is going to be used to generate a new sample for the n to the 100 solver. So we're going to sample n to the 100 such R's. And for each one of these R's, we're going to compute a prime as I showed here. So a prime is going to be R times a. And b prime, which is just going to be R times b. And we claim that this is going to be close to an LPN instance with the same secret but with a somewhat higher noise. And since we can generate as many of those as we want, in particular, we can generate n to the 100 of those, then we can feed this into the 100 solver and hopefully get our s back. So let's try to see by how much the noise blows up with this operation.  So what we get is R times a times s, which is just a prime times s. This is good because this is what we want. This is going to correspond the equation that we're getting for the LPN instance plus some e prime. And this e prime is going to be equal to the inner product of this R that we sampled from our distribution and the noise of the original LPN instance e. And again, if you do the arithmetic, you're going to see that e prime actually grows kind of by a lot. And again, you need to do the calculation exactly and not just do the first order approximation, which is going to give you something that is useless. But if you do the calculation carefully, what you're going to get is that delta prime, 1 minus 2 times delta prime, is going to be equal to 1 minus 2 times delta to the power n over log n. n over log n is the weight of R that we picked. So we see that delta prime is going to converge to 1 half really quickly. However, if we plug in this barely hard parameter regime, so if we start with delta, which is log square n over n, then delta prime is actually not going to escape into the regime, which is information theoretically hard. So it's still going to be computationally tractable. So delta prime is just still going to be 1 half minus 1 over polynomial. And this is what happens in our reduction. So this is an average case to average case reduction, which just changes the number of samples. And we'd want to apply the same method also for a worst case problem. So rather than starting with an LPN instance with m equals n squared, now we're going to start with, again, a comparable LPN instance. But now the matrix A and the vector E are going to be chosen adversarily rather than uniformly. So we would like to see what happens in this case. But before that, let me say that the application for collision-resistant hashing actually follows already from this setting of average case to average case reduction. And the reason, I guess, the right way of thinking about it, then thanks to Leo Ducat for expressing it in this way, is that we already know the standard way of constructing collision-resistant hashing is this setting is to use the binary short integer solution problem. So if you thought about it, then you probably know what I mean. If not, it doesn't matter that much. And what this reduction actually shows is how to actually convert the binary short integer solution problem into a solution for the barely hard LPN problem. And this is how the reduction works. But once you have this, then we could just plug it in into stuff that we know, and you get the collision-resistant hashing. So let's get back to the worst-case-to-average-case setting. So now we have this worst-case problem NCP, and we have this matrix A. And we know that A is balanced. But other than that, we don't know anything or close to being balanced, not necessarily perfectly balanced. So an adversarial matrix is not going to be an entropy extractor. So we cannot just use verbatim the same thing as we did before. However, we don't actually need an entropy extractor, because we can choose the distribution of R to be a distribution of R choosing. We don't have to work with any distribution that has been entropy. And what we need to show and what we actually show is that for a specific distribution of R that has the properties that we want, any close to balanced matrix is actually going to be a deterministic extractor from this particular entropy distributions. And the analysis uses Fourier transform, and is actually similar to analysis that's done in coding theory, in particular in work by Kuparty and Saroff. And one has to think a little bit, what is the right way to define the distribution R in such a way as to make the analysis go through? So there's a few sort of obvious guesses on how to choose R with these parameters. But it turns out that only one of them leads to sort of a clean analysis, or at least to a clear analysis that we can perform. So this is sort of how the worst case to average case reduction works. And just sort of end up with some open problems. So I guess I didn't say anything about the statistical zero knowledge result, but again, it follows from the same sort of intuition of smoothing. So again, if you know about this statistical distance problem, which is like a problem that is usually used when we talk about SDK, then you can think how to sort of convert these ideas into a reduction. But again, I think this is the first step, and part of it is to sort of lay out some open problems for people, including ourselves, to think about. So one is, of course, to extend the parameters of the reduction to sort of get sort of less pathetic connection between the parameters of the worst case problem, the parameters of the average case problem. And again, you can also think about sort of whether the balancedness of the code can be relaxed and some other sort of parameters that can be improved. So there is this question of even like for the specific technique of smoothing, are we doing the best that's possible? Can you think about sort of different distributions that are going to have better properties? Maybe you can sort of try to sort of play with a distribution that does not have entropy, but only has like computational entropy or some things of this sort in order to either improve the result or show that at least the use of this technique is tight in some way. Smoothing for unbalanced codes, actually, we can get some smoothing results, even for codes that are unbalanced, but have good minimum weight. But this smoothing property or this extraction property is not going to be strong enough in order to get a meaningful worst case to average case reduction. So more can be sort of investigated in that regime. Another sort of thing that sort of always bothers me when I think about these results is that we don't actually know whether our results actually follow from a trivial property. So it could be the case that even though currently we only know how to solve the log n over n regime, even the log square in over n regime is so vulnerable in polynomial time. And this would explain all of our results, right? I mean, being in SDK, having a worst case to average case reduction, and so forth. So if there is actually a polynomial time algorithm for log square and over n, then this would be sort of one explanation as to why we can do what we do. And we'd be good to know whether this is the case. I'm almost done. Yeah, more cryptography from LPN. People are already working on it. That's great. Last bullet I want to talk about is sort of one of Vinod's obsessions. Can you construct the candidates for collision-resistant hashing that is provably not in statistical zero knowledge? So one has to think a little bit in order to formally define it in a meaningful way. But I think what Vinod wants is some Oracle separation, some Oracle world where SDK is easy, and yet collision-resistant hashing exists, I think. Hopefully, I'm not misinterpreting. Thank you. Thanks a lot for the talk. Hey, Zvik. So what is this distribution on R for which you can do the analysis? Can you tell us? Yeah, so OK, let me first ask you. What do you think the distribution R is? Bernoulli, independent. So unfortunately, we don't know how to do the analysis for this distribution. Notice that this distribution actually does not have high mean entropy. It's only statistically close to having high mean entropy. So the second guess would be to just sample it from a hamming ball. And this, I think, is doable, but the analysis is really hard. And what we end up using is just a sum of independent indicator vectors. So we think about vectors of weight 1, and you just sample n over log n of those vectors around them and take their sum mod 2. So this turns out to be because they're independent, then the analysis becomes tame and doable. OK, another question. Can you do something similar also for the binary version of SIS, a reduction from a minimum distance? So this is the problem that you said is information theoretically unsolvable, because you cannot uniquely recover the secret. But you can still define a problem which is a find a short vector even when it is not unique. So the analogous of SIS, and instead of reducing from closest vector problem, you would be reducing from a minimum distance. So I guess one way to think about what we do here is that you actually have a reduction from the binary SIS to this sort of barely hard LPN, but you're thinking about the worst case to average case binary SIS? Yes. So other than sort of going through this sort of, yeah. No, we don't actually. One direction would be quite. You're going to get stuck, right, because you have the. Yeah, we don't know how to do this at this point. OK, any more questions? Or maybe I have one. So as you said, we always, whenever we do something in LW, we want to do the same in LPN. So the worst case problem in LW is obviously the lattice problems. Can you see these worst case problems for LPN as some kind of shortest code word, right? But is this some kind of a lattice problem, too, or? So yeah, so usually we think of coding problems as different from lattice problems. Actually, never mind. I have a slide about it, but let's not go there. Actually, you could think even about coding problems as lattice problems. So if you think about the lattices that naturally come from LWE, they're going to be periodic over Q times the unit cube, and the lattices that come from binary codes are going to be periodic over two times the unit cube. So these lattices, they still exist, and they still have interesting short code word problems, but a lot of the connections that we have kind of break. So for example, finding short vectors in these lattices is easy, because there's always a vector of length 2, because 2, 0, 0, 0 is going to be in the lattice. However, decoding still translates even in the Euclidean regime to a closest vector problem. So closest vector problems in these types of lattices are still going to be hard, and perhaps I should also mention that Daniela's works on showing NP-hardness of these decoding problems. OK, thanks. Thanks, the speaker. I think you're out of time. OK, you're out of time. So you could consider a variant which is between LWE and LPN, where the modulus is large, but the noise is kind of all-or-nothing noise, either in p-fraction of the coordinates or nosy. And as far as I know, the previous worst case to average case reductions for lattices don't work for this variant of LWE. So my question is, can you do the same tricks and in this domain and whether the parameters are better in this when the modulus is large, when the field is large? So you could do similar things. I didn't write it down. I mean, I wrote down only a little bit. I think the parameters get a little bit worse. You need to, like, your worst case problem actually becomes more restricted. Rather than sort of going with sort of close to being balanced, you need to be close to being sort of balanced modular, like every, you need to be balanced over every sort of QRE coset. So it seems that things do not play as nicely. However, it's definitely something that one should investigate. OK, so let's thank the speaker. And welcome.