Next, we have Oral Questions. I recognize the leader of Her Majesty's Loyal Opposition. Thanks very much, Speaker. My first question this morning is for the Premier. Yesterday, the Premier blamed 10,000 cancelled appointments in Scarborough on a late Moderna shipment or a cancellation of the Moderna shipment. Now we hear from Scarborough Health that in fact that's not the reason for those 10,000 appointments to be cancelled. So can the Premier actually tell us why it was that 10,000 people in Scarborough had their appointments cancelled and are now waiting for another appointment to get a vaccination? Apply for you, Mr. Speaker, to the leader of the opposition. The leader of the opposition has to understand the process, what we're going through. 300,000 Modernas arrived yesterday. 500,000 Pfizer, sorry, 400,000 Pfizer arrived Monday. The shipment that we expected from Moderna, an additional shipment this week, has been delayed again, I got noticed, May the 3rd. So how can you deliver the vaccinations, the areas, when we don't have the supply? It's very simple, Mr. Speaker. If we had the supply, we give it to the public health units, they distribute it, and if they don't have it, they can't distribute it. It's not Scarborough's fault, it's not Toronto's fault. We need the supply of vaccines. Simple as that. That's not what Scarborough Health says. Scarborough Health says it had nothing to do with the Moderna shipment delay. However, last week the Premier promised that there was going to be a program in hotspots for vaccinating people over the age of 18. We find out, of course, that public health had no idea that this was coming. There were no extra vaccines provided, there were no extra resources provided to public health units, and then Scarborough had 10,000 appointments pulled right out from under them. Here's what one source tells the Toronto Star, and I quote, they made an announcement without a plan or a supply to implement it. A, there was no supply. B, people couldn't register for appointments. C, there was no plan. What the heck is going on with the government? Why can't they get their act together and protect the people of this province from COVID-19? Because that's their job. Thank you, Mr. Speaker. The Leader of the Opposition can get up and show up and down and scream and do cartwheels. That's fine. The bottom line is, the Leader of the Opposition doesn't understand the process. It doesn't have a clue about the process, how it's been working. Again, God bless the people of Scarborough. We're going to get them vaccines. There's 3 million, 3 million appointments been booked. We don't have the vaccines for 3 million people. It is as simple as that. As soon as we get the vaccines, we'll be able to distribute it. We'll be able to get it out to the pharmacies with the AstraZeneca and the primary care. We'll be able to get the Moderna and the Pfizer out to the public health units. That will distribute it to the hospitals. It's not their fault because they have 10,000 additional appointments, didn't have the vaccines. There's only one government that's responsible for the supply of the vaccines. It's not the province, it's not the municipality, it's the federal government. We need the supply of the vaccines. Simple as that. Well, I have news for the Premier. There's a distribution issue here in the province of Ontario, and that's his responsibility. But look, the Premier was warned back in February. It is really clear. The warnings came from the experts back in February that we were going to end up exactly where we are now. We have over 650 patients now in the ICU speaker, and these aren't just numbers. These are people that are literally fighting for their lives. Fighting to breathe. Fighting this virus in ICUs. And of course, places like Scarborough are ground zero, where they're literally airlifting people to Ottawa to try to give them the care that they need. People were failed by this Premier. He failed the people of Scarborough. So my question is, when is this government, when is this Premier going to stop making excuses, stop blaming everybody else and start protecting those frontline essential workers, those frontline workers in Scarborough? For you, Mr. Speaker, when the Leader of the Opposition is talking this way, she does a disservice to the public. She does a disservice to our health partners, to the public health units that have been working their back off day in and day out. As the Leader of the Opposition sits there and throws barbs at everyone, when she hasn't even been involved from day one, has done zero, nothing, nothing at all to support the system, nothing to help out. As people up in Hamilton are struggling, what has the Leader of the Opposition done? Nothing. We're going to continue to focus on making sure that we get the vaccines. Part one of our plan is to limit mobility to get the ICUs down with the people of this province. Part two is we are going into high priority neighborhoods. We are going to high priority companies within those neighborhoods. As we speak, right now it's happening. We saw it happen over the last four or five days. We're getting the job done. The next question, the Leader of the Opposition. Thank you, Speaker. My next question is also to the Premier. Well, I can tell you for sure that I would have been listening to the scientists. I would have been following the instructions of the folks who were the experts who were giving this Premier advice, but instead he didn't. He actually ignored the advice of experts and walked us right into this third wave, which is now completely out of control with his eyes wide open. There are a number of things that he could have and should have been doing, and I assure him I would have been doing them. Now, apparently, the Cabinet is meeting today. And so I'm asking the Premier, yet again, as the experts have, as his own Chief Medical Officer of Health has, to start providing paid sick days to essential frontline workers, to all workers in Ontario, start providing paid time off for vaccinations for all Ontario workers so that they can have the tools to do the right thing. I don't want to hear the malarkey about the federal program.  It's a benefit that you might or might not get. The opposition is doing it a service every time she stands up and speaks, every single time. She's telling the people that there's no paid sick days. Imagine the people at home listening to this that won't even apply to the federal government sick day program that we fought hard for, that we fought for $1.1 billion, Mr. Speaker. Order. There's $700 million. But guess what, Mr. Speaker? We're fortunate that 300,000 people in this province are smarter than the leader of the opposition because they did apply and they did get funding for sick pay. So I encourage every single Ontarian not to be double dipping. It doesn't matter if it says the Government of Canada or the Government of Ontario. There's one taxpayer, one taxpayer. There's $700 million sitting there for the people of Ontario to apply. Supplementary. The disservice comes from a Premier who doesn't want to do his job and acknowledge that people need paid sick days. Not a program that you have to qualify for, that you have to jump through hoops for, that you may or may not get access to. Paid sick days occur in the moment. You don't have to wait for them. You don't have to worry that your pay is going to be docked and then wait for even a week and a half. You get them right away. And that's why every single expert, not just me, not just the leader of the opposition, every single expert has been telling this Premier that those frontline heroes, those essential workers, the people he pretends to care about, the little guy, the little guy needs paid sick days. When will this Premier do his job and protect those essential frontline workers who need paid sick days and paid time off for vaccinations? Premier, thank you, Mr. Speaker. Talk about doing a job. Our team, the frontline healthcare workers, the docs, the nurses, paramedics, everyone have been working around the clock for well over a year, literally 24-7 every single day trying to support the people of Ontario. And the negative talk that comes out of the leader of the opposition, again, does a disservice to all of the frontline healthcare heroes, all the people of Ontario. And it's ironic he's coming from a person that has done Italy squat, nothing, zero, sat in their seat. And since there are criticizes, the hard work of the healthcare workers and the doctors that give me advice, no matter if it's Dr. Williams or Dr. Brown and 100 doctors underneath them or if it's Dr. De Villa or Dr. Lowe that all are giving advice. All working their back off. Why does the leader of the opposition do something? Do something positive once in a year and a half because it's not even in her mindset. Thank you. It's going to be the final supplement. Speaker, the people of Ontario deserve so much better than this. Folks are losing their lives. People are getting sick at unprecedented numbers. 650 people, 659 actually in the ICU today, struggling to breathe. The virus continues to grow. Over 4,700 people in Ontario now have the virus. We've given this premier all kinds of advice. We've asked him, we've begged him to listen to the experts, to follow their lead, to do what they're telling him to do. And instead, he walked us right into this third wave, into this rampant spread of variants of concern. And now, you know, he seems to think that it's not his responsibility, that it had nothing to do with what he did or didn't do, the actions that he refused to take, take the actions necessary.  Will the premier do that? Premier? Mr. Speaker, it is so frustrating sitting here, listening to the Leader of the Opposition, disrespect Dr. Williams, disrespect Dr. Brown, Dr. Hire. I could keep rattling all the doctors, all the CEOs that I talk to, at least half a dozen every single day, giving advice. And the Leader of the Opposition wants to disrespect them. We have followed medical advice from day one. We have followed science from day one. And that is the reason we're doing more vaccinations than it... I'm going to ask the Leader of the Opposition to withdraw. That is the reason we're leading the country in vaccinations. Bardonade, no one even comes close to the amount of vaccinations. We're getting an excess of 100,000 vaccines out a day. And guess what, Mr. Speaker? We have 3,200 pharmacies. We're only at 1,400 pharmacies. We need more supply. We can ramp up well in excess of 300,000. I want to ask the Opposition Leader a question. What would happen if we would have... Thank you. Thank you. Then you will take a seat. Bardonade, the next question, the member for Brampton East. Thank you, Speaker. My question is to the Minister of Health. There's no other way to say this right now. We are in the middle of a full-blown crisis. We're in the midst of the third wave. And vulnerable people are going to be paying the price for the concert of government in action. More than just in action. The concert of government actually ignored critical information, advice, and pleas to act that could have avoided this third wave. They ignored calls to bring in greater support to COVID-19 hotspots. They ignored our hospitals who are warning about this third wave and overcrowding in our hospitals. They ignored experts who are calling for paid sick days. They ignored our teachers who are demanding for safer schools. They even ignored our doctors who are warning about this third wave for weeks and months now. Why? Did the concert of government, despite all these warnings, still decide to not act? To bring in the measures and urgency with the urgency that we needed to fight the third wave and stop this third wave? Thank you very much. Thank you, Speaker. We have taken steps every step along the way since this pandemic began, realizing that we would need to enhance our hospitals' capacity. Since this pandemic began, we have brought forward 3,100 new beds, enhanced our ICU capacity by 14%, made significant investments in our hospital, over $15 billion so far, including $1.8 billion in the most recent budget to deal with the extra beds that have been brought on, to deal with the surgeries that, again, we unfortunately have had to delay because of this pandemic. We anticipated, as we saw the numbers rising and listened to the experts, listened to the doctors, Dr. Williams, Dr. Brown, and the science advisory table, the public health measures table. We brought in the emergency break shutdown, and then realized we needed to have the stay-at-home order. I'll speak more to the preparations that we've taken. It was my supplementary speaker. Thank you, Speaker. Again, to the minister, in communities like Brampton and Peel that were the hardest hit by COVID-19, we're in desperate need for help.  Now, Brampton was left behind earlier in this pandemic, and we had to fight tooth and nail to get the testing capacity that our city needed. Now we're being left behind once again by this Conservative government as we fight to get the vaccine to those who are most vulnerable in our community. Now, we knew this third wave was coming for weeks. Every single health expert in Canada was warning that Ontario is facing a third wave. Yet, despite these alarms being raised, the Conservative government decided to not act. And in the end, Brampton is suffering. So my question is this. When will the Conservative government finally decide to stop leaving Brampton behind and give Brampton access to the life-saving vaccine so we can fight and beat the COVID-19 pandemic? Thank you. And you, government, I see that. We know that Brampton is going to get a brand new hospital thanks to the hard work of this Premier and this Minister of Health. But I have some advice to the member opposite. If he is really concerned that the federal sick day program that his brother, the leader of the NDP, helped to negotiate along with this Premier, then he should pick up the phone, call his brother, and suggest to him that when the federal Liberal government delivers a budget, if it doesn't include enhancements that he is talking about, then he does not need to vote for that budget. If he thinks that the distribution of vaccines is not sufficient enough that we haven't got a big enough supply, then I suggest the member opposite. Call his brother, the leader of the NDP in Ottawa, and suggest that he not just give him a blank check on a budget. Don't settle for a stretch goal again. Your brother has the opportunity in Ottawa to ensure that Ontario gets the vaccines that he needs. If there needs to be an enhancement of sick pay, he has the ability to do it. Pick up the phone and help him, Terry. Next question, the member for Northumberland, Peter Burrow-Seth. Thank you, Mr. Speaker. Mr. Speaker, as our government works to protect the health and well-being of Ontarians during this third wave, it remains my top priority to ensure that my constituents remain up-to-date on the latest news and advice and guidance on how to navigate this pandemic. Mr. Speaker, locally I've compiled a website, vaccineupdate.ca, and held many Teletown halls, bringing together our health units, local municipal leaders to provide current information on vaccine availability, health guidelines to my local constituents. Imagine how frustrated I was, Mr. Speaker, when I received an email from a constituent in Grafton, and I quote, she writes, David, I'm writing to you today to inform you that I wasn't able to join your Teletown hall, nor go online to see its recording because our internet in Grafton is so bad that I was not able to participate effectively. We have had so many technicians, new modems, ISPs, and we are on our third dish. Mr. Speaker, my community needs better broadband. They deserve better broadband. Mr. Speaker, would the minister please rise and inform the House what steps are going on? Thank you very much. I recognize the minister of infrastructure. Thank you, Mr. Speaker, and thanks to the member from Northumberland, Peterborough South for his tireless advocacy on this issue for his constituents in his writing. And right now it is so imperative that we work quickly to get more households connected to high-speed internet. How can anyone refute the fact that the lack of broadband is detrimental to the daily lives and livelihoods of too many Ontarians when stories like the members shared clearly indicate that people are being left behind? There's no question that the lack of internet is detrimental to daily lives and livelihoods of Ontarians, especially during this stay-at-home order. And having unreliable internet or even no service at all is simply unacceptable, Mr. Speaker. That's exactly why I introduced the Supporting Broadband and Infrastructure Expansion Act 2021 that will reduce barriers faced by the telecommunications sector when it comes to building broadband faster. We're taking an innovative approach so that everyone in Ontario can get reliable internet no matter where they live. Thank you, Mr. Speaker. You know, Mr. Speaker, to meaningfully address broadband, it's more than just money. It's about measures that that minister just alluded to to reduce barriers in areas of rural Ontario like mine. Mr. Speaker, also it helps when you invest money, and I'm proud of this government's historic $4 billion investment to broadband, the largest in Canadian history. Mr. Speaker, I recently joined PHO and the Port Hope Chamber and other chambers in my writing to discuss what was being done about poor broadband in our area, and its impact on small business. We were pleased to share the $2.8 billion commitment in this budget and steps the minister alluded to to reduce barriers. Mr. Speaker, I think it was put best, perhaps, by the CEO of the Port Hope Chamber of Commerce. She said vital infrastructure such as broadband will help bridge gaps that are happening in these challenging times and improve life for our small businesses. Mr. Speaker, this is welcome news by the Port Hope Chamber of Commerce and Chambers throughout my writing. Mr. Speaker, would the minister please share with the House what more we can expect from this historic investment? Thank you. Well, thank you Mr. Speaker and to the member for the question. Without healthy people, we can't have a healthy economy and that's why we're focused on protecting every life and every job we possibly can during COVID. I too share the member's excitement because for almost 20 years I've advocated for the expansion of broadband across Ontario especially in rural and northern communities like ones we represent. With our legislation and commitment of an additional $2.8 billion for a near total investment of almost $4 billion we can help accelerate broadband expansion across all regions of this province. Mr. Speaker, I'm thrilled to say that finally this groundbreaking legislation has received royal assent and now shovels can get moving, people can get connected and Ontario can recover from COVID-19. Thank you. The next question, the member for Parkdale High Park. Thank you, Speaker. My question is to the Premier. Cases of COVID-19 in childcare centres are rising fast and parents are worried that their children are no longer safe. There have been more than 1,000 cases reported in the last two weeks including 134 cases yesterday alone. 25% of all childcare centre closures due to COVID-19 in the last 10 months have occurred in just the last two weeks. Experts like Dr. Jeanine McCready and infectious disease specialist at McElgaran Hospital are advising parents to pull their kids from childcare. What is the Premier doing to address this growing crisis? Thank you. Mr. Speaker, we've put a plan in place with $234 million of investment for childcare recognising how critical it is to keep kids safe, the staff themselves and our communities at large, $234 million more dollars to help strengthen the infection prevention measures in place. That includes the cohorting of children in groups of 10 or less every day. The establishment of COVID-19 response plans, the screening of all staff and all students active screening before they enter these centres, daily attendance records, enhanced cleaning of the centres, mandatory PPE for the staff and a no visitor policy beyond essential visitors. We have followed all the advice of the Medical Office which is why in this province over 91% of centres have no confirmed cases of COVID at all. And we're going to continue to follow the best medical advice working closely with the Chief Medical Officer because like the Member Officer, we appreciate how critical childcare is right now as we work through this pandemic. Is that the next question? Speaker, childcare workers are working through the shutdown. They perform close care work with unmasked children who are too young to understand social distancing. Children who need help going to the bathroom or changing their diaper. While education workers in hotspots are rightly receiving their vaccines, childcare workers are being left behind. Without childcare workers, essential workers can't go to work. We rely on childcare workers to keep our kids safe. Why won't the Premier immediately prioritise childcare workers for vaccinations? We made a commitment to make sure that our childcare staff can get a vaccine in phase two, which we are in, as the Premier has rightly noted. I think as every objective mind has acknowledged, the first step in defeating the pandemic is this province getting vaccine in the first place. And that responsibility rests to procure it with the federal government. When we get it in Ontario, I assure the Member opposite, in every childcare worker in this province that they will get access to the vaccine.  Those 60 years plus are eligible as well for Pfizer and Moderna. In addition, speaker, anyone who lives in Ontario is eligible for the vaccine, particularly childcare workers. And any child ECE that works within our schools, especially those that work with special education teachers and students can get access to the vaccine. We are making steps in the right direction. We realise there's more to do. And as vaccine comes this province, we will get it out to the people of Ontario. Thank you. The next question, the Member for Ottawa. A question for the Premier. Good morning, Premier. There are 653 people in intensive care units today. 4,736 new COVID cases. And over a million doses of vaccines in freezers. And if we were administering the 150,000 doses daily, which were not, that's about a week's supply. We're more around 100,000 doses a day. And that's about 10 days of supply. Speaker, I don't know about you, but that's a pretty large buffer to hold back in a crisis. So the government says they're spoken for, but there is no transparency as to where the government delivers vaccines here in Ontario. So none of this, none of this makes any sense to Ontarians. So Speaker, for you, can the Premier explain why the government is keeping an almost 10 day stockpile of vaccines in freezers? To reply, Minister of Health. Well, I can assure the member opposite that no amount is being held in freezers. It's not already allocated to people. We have already booked over 2.5 million appointments for people. That's using our booking tool. That doesn't even include the appointments that have been booked in pharmacies, in personal care offices, in primary care offices, in hospital units as well. So those allocations are already spoken for. Most that is in the freezer now has been booked already for an appointment for a person. We are deploying them as quickly as possible. Yesterday we vaccinated 105,500 people and we're able to do more. We can triple quadruple the number of vaccinations we can do every day if we have the vaccine supply. But as has been already indicated, the Moderna supply has been put off yet again. We're receiving the Pfizer vaccines, but we don't know when we're receiving AstraZeneca and we're also delayed. So as soon as we get them, we are putting them into people's arms as quickly as possible. The supplementary question. A million doses in freezers and we're cancelling appointments. That's all I'm going to say. And the problem here is, for the Premier, it's been too much business as usual during this pandemic. He's been too focused on other things like Highway 413, paving over wetlands, or a couple of weeks ago, campaigning in Brampton. Ontarians need a Premier that's focused on keeping them safe from COVID-19. Last Friday, the Premier gave the impression that mobile units were out as he spoke vaccinating people in hotspot communities. And he said, if you're over 18 in those communities, you can get it. He did both of these things before public health units and the vaccine task force was ready. And then he has the temerity to say, it's not complicated. Well, he's making it complicated. Question.  So, Speaker, through you, can the Premier explain why he's announcing things before the mechanisms to get it done are even close to being ready? And the Minister of Health. Thank you, Speaker, and I would say to the member through you, Mr. Speaker, that what you're suggesting is simply not the case. There is a plan that was developed by working with Dr. Williams with the public health measures table and by the members of the vaccine distribution task force as well as with the chiefs of all the hospitals in Ontario and the local medical officers of health in all 34 public health unit regions. The plan was developed with them. They have known about it since the beginning. The distribution for each amount of vaccine that is distributed to the public health units is then given to the units they're going to be providing them. That is what happens. That is what was planned for. That is what we are doing now. And the fact that we've already distributed 3.5 million vaccines indicates the plan is actually working. Thank you, Mr. Speaker. Mr. Speaker, yesterday the Premier joined his counterparts from New Brunswick, Saskatchewan and Alberta to welcome Alberta as a signatory to the small modular reactors memorandum of understanding. Mr. Speaker, I gather that this news generated, pun intended a lot of excitement in the nuclear energy sector and beyond. Mr. Speaker, this matters to the many hardworking men and women in the writing of Northumberland Peterborough South who get up every day to power our province, this nation. Mr. Speaker, will the Associate Minister of Energy please tell the House what yesterday's announcement means for the province, the people of Ontario who are working, men and women of Northumberland Peterborough South? Thank you, Mr. Speaker. Mr. Speaker, to the member from Northumberland Peterborough South for that great question and it did generate some great excitement here in Ontario. Small modular reactors or SMRs are a real game changer that has the potential to power Ontario's future job creation and export opportunities. We're thrilled to welcome our friends from Alberta to the table to be part of the next generation of nuclear technology. The study was also released confirming that SMRs represent an important solution for our unique energy challenges such as power in remote and rural communities that currently rely on expensive diesel power. I thank a Terro power generation, Bruce Power, New Brunswick Power and Saskatchewan Power for their work in preparing the study which will help us plan for development employment of SMR technology in coming years. Mr. Speaker, Ontario is leading the way when it comes to SMR development just like we did with the development of SMR technology but how SMRs can contribute to a clean and reliable energy and environmental future for our province and our country. Thank you, Speaker. Thank you. Thank you, Mr. Speaker. Mr. Speaker, we welcome that news constituents of Northumberland Peterborough South. I know a number of which were very scared three years ago when they heard members opposite talk about shutting down this sector so this is welcome news. Mr. Speaker, I'd like to reference a note of mine, Mike, in Newcastle who said, Dave, this groundbreaking technology has so much potential and I applaud this government for its leadership in this area. Mr. Speaker, it's for hardworking men and women, people like Mike that we get up every day to make this province a better place to invest in groundbreaking technology like this. So, Mr. Speaker, my question back to the Associate Minister, can you please tell us more about ways that SMR can be utilized to benefit this economy in Ontario and the hardworking men and women of Northumberland Peterborough South. Thank you, Speaker. Thank you again, Speaker, and thank you to Mike and the member for Northumberland Peterborough for another great question. SMR Development represents an immense opportunity for Ontario to become a leading exporter of technology and expertise that can address global issues such as climate change and energy reliability and further strengthen Ontario's position as the global leader in the supply of life-saving medical isotopes. SMR could offer energy-intensive industries such as mining and manufacturing a safe, lower-cost source of clean, safe energy and enhance their competitiveness. SMR has also had the potential for innovations beyond electricity generation, such as supplying heat or steam for industrial processes or producing hydrogen, which is another clean resource that our government is very interested in developing. Mr. Speaker, the possibilities are truly endless. For a sustainable, made-in-interior supply chain and jobs, and I share the member's enthusiasm for the interior's future as a world leader in nuclear energy. Thank you, Speaker. Thank you. The next question, the member for Brampton North. Thank you, Mr. Speaker. My question is to the Premier. This stay-at-home order and the school shutdown could have been avoided if this government invested in the safety of Ontarians. There were over 8,000 cases this weekend and over 65% of the cases were between the ages of 20 and 59. This age group represents a majority of Brampton's workforce and they mostly work in frontline occupations such as transportation and manufacturing. They are being heavily impacted by this government's inaction. They need paid sick days. I'll say this once again. They need paid sick days and it is critical to stopping workplace outbreaks to keep our frontline workers safe and stop the spread of COVID-19. My question to the Premier, when will this government help them by mandating paid sick days? Mr. Labour training of skills development. Well, thank you very much and I'm pleased to respond to the member's question. Mr. Speaker, there is now four weeks of paid sick days for every worker in Ontario. I would remind every worker in Ontario to go to canada.ca forward slash COVID-19 and they can apply for those paid sick days. Mr. Speaker, furthermore the members opposite should let their constituents know that there's 20 days or four weeks of paid sick days available to each and every one of their workers and their constituents. In fact, Mr. Speaker, more than 300,000 people in Ontario have either received the benefit or are receiving the benefit as we speak and will continue to advocate to the federal government to always be there for Ontario workers. Thank you, supplementary. Thank you, Mr. Speaker. Well, let me tell you how it really works. We just heard the member opposite. I'm going to educate him as to the way it really works. Workers cannot rely on the CRB as a replacement for paid sick days. They cannot apply for the CRB if they take a day off to go get tested. There's a reason why health officials such as Dr. Lawrence Lowe have been advocating for paid sick days because they know the CRB is not enough to stop the spread of COVID-19. And the Premier earlier said he was listening to health experts, but obviously he's not listening to Dr. Lowe. Our frontline workers that are being impacted heavily by the virus and all the new variants need relief and they need paid sick days. The Premier says, Mr. Speaker, he doesn't make any decisions by himself and that he listens to health officials. So instead of accusing the NDP of playing politics, why won't he listen to health officials like Dr. Lowe when they're asking for paid sick days? Mr. Speaker, the very first piece of action that our government took when COVID-19 hit Ontario was to bring in job-protected leave. I'm proud to say that we led North America. In fact, Mr. Speaker, if any worker out there is in self-isolation, if they're in quarantine after our mom or dad, for example, that has to stay home and look after a son or a daughter because of the disruptions to the school system. You can't be fired for that. Furthermore, Mr. Speaker, we were the very first jurisdiction to bring forward job-protected leave for those getting vaccinations. And I have to say it was just last week when Columbia reached out to my office, we helped them. They're drafting legislation now to bring in job-protected leave for vaccinations, but we were the first ones to do that, supported by all members in this House. But, Mr. Speaker, every member is doing a disservice to their constituents when they don't tell workers in their own local communities that there's 20 paid sick days available to each and every one of them. The next question, the member for Cambridge. Nearly after the Premier issued yet another stay-at-home order, my constituency office started to receive an increase in calls asking for clarity and reasoning behind these new rules. In one instance, a gentleman was denied the opportunity to purchase batteries for his smoke alarm from a store because the clerk said it was non-essential. Another individual said that the local Dalarama would not sell them school and office supplies as it was deemed non-essential. A constituent was even barred from purchasing sandwich bags at Sobe's, because they were deemed non-essential. My question to the Premier is, after saying from months on end that restricting stores from selling quote non-essential items would be detrimental and impractical, what science did he follow that persuaded him to flip-flop on this messaging? And how did he determine what makes an item essential or non-essential? Mr. General. Well, thank you, Speaker. If the member opposite is not willing to educate and inform her constituents, I'm happy to do that. The reality is, from the beginning, businesses across Ontario have been allowed to provide curbside service. It's safer, it protects the customers, it protects their employees, and it also allows individuals who need to purchase things for their family to get that safely. Thank you. And supplementary. Thank you, Mr. Speaker. Aside from her childish jab, what this government has done is pushed to do just that. Once again, favouring the big-box doors over our local small businesses. Not everyone can afford a lobbyist, especially ones who used to work or volunteer with any of those who serve on the government benches. What we are seeing is a lack of science behind decisions that are having detrimental effects on the small business owners and their families in this province. This new state-of-the-art home order is wrong and the restrictions that come with it are confusing, heavy-handed and ineffective. It is insulting to Ontarians to know that pot and booze are essential, but car seats for children are not. So I ask, again, why did the Premier and this government change their stance on placing restrictions on businesses from selling certain goods? So, Mr. General. Speaker, the short answer is because lives were at stake. We have instituted a stay-at-home order to protect the most number of Ontario citizens. It truly is the difference between ensuring that we can protect the vast majority of people. If people understand that allowing the movement of individuals is actually leading to more transmission rates, then we need to send a clear message that says stay at home, order online, pick up by curbside, do your delivery models because at the end of the day it will protect your family, your neighbours, you will protect your community and ensure that we have the necessary medical resources to make sure that if someone unfortunately catches a cold, then we can protect them in our hospitals. Thank you, Speaker. Next question, the member for Northumberland, Peter Brilson. Thank you, Mr. Speaker. Mr. Speaker, my question is for the Attorney General. Mr. Speaker, I'm proud to serve in a government that is committed to standing up for victims of crime and supporting the growth of safer communities in every corner of the province of Ontario. Mr. Speaker, recently the Attorney General announced new sexual violence support services for historically under-serviced regions of the province of Ontario and the province-wide expansion of free legal advice for survivors of sexual assault no matter where they live. Mr. Speaker, this matters for rural and small-town Ontario. Yesterday, the Attorney General recognized the exceptional achievements in the service of victims of crime through the Victim Services Awards of Distinction. Could the Attorney General please share the importance of celebrating these heroes and their vital work for communities? Thank you. Thank you, Mr. Speaker. I want to thank the member from Northumberland, Peter Brilson and my colleague and friend for the chance to honor with him the remarkable contributions of 50 individuals and organizations from across the province who have been recognized through the Victim Services Awards of Distinction. In the face of unprecedented challenges, these dedicated professionals, generous volunteers and outstanding organizations have demonstrated an impressive drive to raise awareness of victims' issues, increase access to crisis intervention services, and provide compassionate support in times of need. This recognition highlights the dedication and creativity of professionals and volunteers who serve victims in the courageous efforts of individuals who have been personally impacted by crime and are now working to raise the profile of victims' issues in Ontario, including in rural, northern and Indigenous communities. I want to congratulate and celebrate each and every remarkable recipient on the important impacts their service to victims of crime are having in their communities. Thank you, Mr. Speaker. Thank you, Mr. Speaker. Thank you, Mr. Speaker. And thank you to the Attorney General for recognizing these heroes who go above and beyond to support victims of crime and survivors across the province of Ontario. In my region, we are proud of the work that is done on a daily basis by dedicated professionals, volunteers, organizations and partners. Mr. Speaker, I'd like to particularly highlight the great work being done by Peterborough Police Services. Mr. Speaker, I know there's been groundbreaking work done there with the Peterborough Police Victim Services Unit. We are proud of the work of Alice, Zytram and Facility Dog Pixie. They've been accomplishing remarkable work at the unit. And I applaud the Attorney General for shining the light on these important efforts. Mr. Speaker, can the Attorney General tell us about this remarkable pair of recipients? Thank you. Thank you again for the question and the chance to speak about this deserving team of recipients. Alice Zytram is a social worker and civilian coordinator with the Peterborough Police Victim Services Unit who developed its first facility dog program. She is the primary handler of Pixie, five-year-old accredited facility dog. And you can follow Pixie on Instagram if you wish. Pixie helps provide people experiencing trauma with positive physical and neurological impacts. Since the program began just over a year ago, Pixie has provided critical support to victims of crime at court, police scenes, interviews, meetings, stress debriefings, and community presentations. Alice's creativity champions the use of canine assisted intervention. Speaker, the story of Alice and Pixie is one of 15 recognized by the Victim Services Awards of Distinction. And I encourage all the members of the House to share stories from their regions. Thank you, Mr. Speaker. Question, the member for London North Centre. My question is to the Premier. AgriFoods is an important pillar in London's economy and in business is only as strong as the people who work there. Front-line workers are responsible for the high-quality food on our table. This week, the member from London Fanshawe, London West, and I learned that over 80 essential workers at Cargill, were physically distancing in the workplace contracted COVID-19. Right now, we're thinking of all the workers and their families. Without provincial paid sick days, our food supply chain is under attack. Thankfully, Cargill stepped up in support of workers with paid sick leave while this government stepped aside.  Some of this government listened to experts, listened to doctors, listened to nurses, listened to the legion of people calling on them to step up, show some responsibility, and provide provincial paid sick days. Mr. Labour. Well, thank you very much, Mr. Speaker. I do want to begin by thanking all of those farmers, all of those farm workers, all of those AgriFood workers who have ensured that every single day in the province of material all of us have had food on our plates at the dinner table. Mr. Speaker, I think about all those cargo workers and I do want to say thank you Cargill for stepping up for paying those workers who are not going to be on the job for the next number of days, but Mr. Speaker, in the province of Ontario 2.3 million workers actually have paid sick days through their employers. For everyone else, I plead with the NDP, with the Provincial Liberals, with all elected officials please tell these workers to go to Canada.ca forward slash COVID-19 Mr. Speaker, 300,000 workers in the province are receiving this benefit. Its responsibility for all of us to let them know that these supports are in place. The opposition will come to orbit. Supplementary question. Back to the Premier. This is a serious hit to London's economy and our food supply chain, but first and foremost, the government didn't listen to scientific advice to vaccinate frontline workers who want to get their shot. It's even more disturbing that this government is now shirking its responsibility by having employers in hotspots set up their own vaccination clinics for workers in the community and then sticking them with the bill. The Premier's mouth tells workers and businesses he stands shoulder to shoulder with them, but his actions say something completely different.  Paid sick days protect our food chain.  Does this government truly want to protect Ontario workers? Or would they rather save a buck? Mr. Speaker, I am proud that more than 3.4 million people in the province of Ontario have received a vaccination as of yesterday, Mr. Speaker. With millions more ready to be vaccinated, they booked those appointments, but Mr. Speaker the member opposite has to and his party they need to work with us to call on the federal government to get us more vaccines. The supply issue is a real challenge in London in every other community across this province, but Mr. Speaker as a ministry we are sparing no expense to protect the health and safety of workers. I'm proud to say that as of today Mr. Speaker we've done about 47,000 workplace inspections. We've hired 100 more ministry of labour training and skills development inspectors something that that member opposite voted against. We will stand with workers every single day to get through COVID-19. The next question is for Ottawa Vanier. Thank you Mr. Speaker. My question is for the minister of colleges and universities. Mr. Speaker Monday was a devastating day for people in Sudbury. More than 150 members of their community were told that they were without a job in the middle of the pandemic because the university had to cut nearly 70 programs. I know the government has been saying that it can't get involved while the CCAA process is ongoing but the government knew these program cuts and job losses were coming months ago before the process began. So I'd like to ask the minister why didn't the government act before February 1st to collaborate on a made in Sudbury solution and protect all those affected by Monday's cuts. The parliamentary assistant and member for Northumberland Peterborough South. Thank you Mr. Speaker. Mr. Speaker let me be clear that I understand the very difficult and personal situation affecting students, families and workers, Laurentian University. The courses of 90% of students Mr. Speaker have not been affected and for the 10% of those who have are working directly with the institution who are working in turn with each student to ensure a pathway for graduation. Mr. Speaker the member asserts information prior to knowing the CCAA protection proceedings. Mr. Speaker what I can tell you is that the gravity of Laurentian's financial situation only was very recently brought to the government's attention. Mr. Speaker it's been widely reported that Laurentian University has over 300 million in disabilities. Mr. Speaker we've appointed Dr. Alan Harrison to have a look at this and to provide independent and thoughtful analysis to ensure that we make meaningful decisions going forward. Thank you Mr. Speaker. And again to the minister for colleges and University of Laurentian is a northern institution that serves indigenous and francophone communities that are largely underserved by provincial services. 35% of French language programming is being cut and the indigenous studies program has been cut entirely. The institution does not only support these communities but it also supports the vitality of Sudbury as a whole. Once students leave the region to complete their studies most of them will come back. For the francophone community the impact is on the survival of our culture in the north. The government has taken symbolic steps to ensure that the francophone community and the francophone community play in our society. So my question is what does the government intend to do concretely to support the right to study in French for our francophone community in northern Ontario? Thank you Mr. Speaker. Mr. Speaker I'd like to address that. The member opposite said symbolic. Well I can assure the member opposite there's nothing symbolic about 17.6 opportunities for francophone students. Nothing symbolic of the 74 million to support over 30,000 Ontarian students who enroll in French language programming across Ontario. That member is from the national capital region. I would encourage her to work with us, work with the federal government who contribute one fifth of what this government contributes to French language programming in the province of Ontario. One fifth we know the Official Languages and the importance of bilingualism in this country and the important role that francophones play in the province of Ontario. So I would encourage that member opposite to work with us, work with us to grow on the first ever Franco University governed by and for francophones. And in addition Mr. Speaker to work with us. Thank you. The next question. Thank you very much Speaker. My question is for the Premier Speaker. The Minister of Colleges and Universities allowed the CCA process to fire over 100 people and slash nearly 70 programs at Laurentian University. One of those programs was midwifery. I want to remind you Speaker Laurentian has the only French called the profession de sache femme outside of Quebec. It is the only bilingual midwifery program in the entire country. I spoke with Lisa Morgan the director of the program. She said other midwifery schools are only six of them in Canada. Lisa was told the program was cut due to low enrollment which is confusing because Laurentian's program is the largest school of midwifery in Canada. Speaker this program is managed by the Ministry of Health which caps the enrollment at 30 students a year even though they turn away hundreds of students every year. My question Speaker is for you. Will the government finally realize how ridiculous the CCA process has been being? I do acknowledge and understand the rare and necessary programming of midwifery. That is why this government provided an additional million dollars to Laurentian University dedicated specifically for the midwifery program. The real question here and the member alluded to it, is it the position of the NDP for government to now get involved in specific programming at every university across the province of Canada? Is it the position of the NDP to interfere in court proceedings? If so, be honest with Ontarians and just tell them that. Thank you, Speaker. Thank you, Speaker. Speaker, the CCA process is not meant for public institutions. It's a brutal process that's made to satisfied bankers. As long as they get paid they don't care what cuts are being made and there's a community and we care about all the cuts that are being made, especially when they don't make sense. 100% of midwifery graduates have been hired. Laurentian Woodwifes make up one-third of all midwifes in Ontario and in Canada. Alison Crows is a midwifery student at Laurentian. She said, I've exposed myself to COVID for the last year in order to serve the Ontario population. I've moved more than ten times her placements. I've completed unpaid placements. I've acquired significant student debt. I've extended separation from my support systems. And I now have no clear path to graduation or registration to the profession. This cut is unconscionable. He can pivot and dance and sidestep and hide, but I want the premier to answer, will the premier do the right thing for Northern students like Alison and final Laurentian to save programs like midwifery? Thank you, Mr. Speaker. Mr. Speaker, again we understand the important role midwives play in this country and in the province of Ontario. That's why this government provided a million additional dollars to Laurentian University to support that programming. But again, the underlying issue here that that member refuses to address is that he believes that politicians know better than our autonomous institutions on what programming to offer, Mr. Speaker, that politicians know better than independent court cases. We know that when it comes to the independent processes, when it comes to politicians making all these decisions, Mr. Speaker, we understand the important role that the government does play. That's why we're working with the institution to ensure pathway to graduation for the 10% of students affected at Laurentian University, individualized pathways for each. We're going to continue doing just that. Thank you, Mr. Speaker. Thank you. The next question, the member for Scarborough-Gildwood. Thank you, Mr. Speaker. My question is to the premier. So it's a question of the way across the province, while many parts of the province have low case numbers and live in circumstances that help facilitate successful safety measures such as staying home and maintaining distance from others. My riding of Scarborough-Gildwood does not have the same options. Scarborough-Gildwood has been a COVID hotspot since the beginning of the pandemic. A disproportionate number of residents cannot work from home. They are essential and community transmission is also a continuing problem, with a 24% positivity rate more than twice the provincial average. This reflects the numbers of cases in Scarborough. The vaccine rollout has been unnecessarily complicated and confusing for Ontarians, especially newcomers and seniors. They've faced many barriers booking their vaccine. What is the provincial government doing to make vaccines more accessible instead of chaotic by closing hospital run vaccination clinics in hotspots like Scarborough? Thank you and the Minister of Health to respond. And we have been clear that phase two of our vaccine rollout will focus on age and risk while also focusing on hotspots across the province. There have been 114 hotspots identified through postal codes where we understand that there are barriers to people receiving vaccines. There's vaccine hesitancy. There may be language problems. There may be other issues involved with it. We are doing vaccine people through the vaccine clinics. We also are doing mobile clinics and pop-up testing, going to apartment buildings, going to other locations, using faith-based organizations as well, because these are trusted organizations that people depend upon and rely upon. And we're finding that that's really dealing with the vaccine hesitancy. But with respect to the issue about the shortage in the vaccination clinics, it's important, very important to remind the member that local public health units are responsible for the managing and overseeing the distribution and administration of the vaccines across their entire region. Similarly, clinics are expected to administer the vaccine. Thank you. Thank you. Speaker, back to the minister. You know, 10,000 people in my riding and across Scarborough are now out of luck. They are having to rebook their vaccinations. I was there yesterday at Centennial College. I met Lesita.  She has had an appointment booked for weeks. She came an hour early for her appointment. Had to be turned away. 69-year-old Ramjeet, he rode his bike to get his vaccine only to be turned away. So I understand that we are all in this together. We need to roll this vaccination program out across the province. However, we cannot keep passing the buck on others. It's not the local public health's responsibility to coordinate the distribution. Well, the distribution is decided by the province. If you're telling me that that's not the responsibility, then we've got more to do. But, Mr. Speaker, I'm asking this minister, will they send Scarborough an equitable share of vaccines so that they can vaccinate the thousands of people who lost their appointment? Yes. Thank you. Minister Kal. And through you, Speaker, I can assure the member that Scarborough is receiving an equitable distribution of vaccines, as is every other part of Ontario. It's based on age and based on risk. And taking into account the numerous hotspots that we understand Scarborough has within its geography. But we have been working hand in glove with local public health units to ensure that there are clear expectations about what allocations public health units and vaccine sites will be receiving. And to be clear, Toronto Public Health has their own Toronto vaccine table that determines their allocation is distributed within the city. So we know that delayed vaccines are extremely disruptive, but we are working with those local public health units so that they know what allocation they will be receiving and then they distribute that allocation to all of the vaccine sites. So that is something that we are going to continue to work on with them. But be sure that Scarborough is receiving their equitable share. Next question, the member for St. Catherine's. Thank you, Mr. Speaker. My questions to the Premier. St. Catherine's City Council just passed a motion about commercial insurance gouging. They want action. In October, you acted surprised at commercial insurance gouging that you described as astronomical. And wait for the next budget. It was more of the same tough talk that stops after you leave the podium. What's the cost of no action? In St. Catherine's, the Mistopolis family owns three hotels. And in December, their insurance rate increased by 300%. Almost $200,000 over the pandemic. That's more than all federal and provincial pandemic supports combined. Question. Will this government step in to do something meaningful to protect our small businesses affected by insurance profiteering? And finally, will this government finally take action on commercial insurance? To apply the government. Thank you very much, Mr. Speaker. I know that the Minister of Finance has been working very closely with the industry and more importantly has been working with small, medium and large health creators to ensure that the economy continues to grow post-pandemic as it really did before the pandemic, Mr. Speaker. As I said a couple of days ago in this House, back in 2018, the people of the province of Ontario voted for a government that could focus on their priorities. And their priorities, of course, were job creation. The number one priority was job creation. We saw thousands of jobs coming back to the province of Ontario following the disastrous 15-year government of the liberal regime, Mr. Speaker. I'll let the member rest assured that this government will continue to focus on small, medium and large job creators, continue to focus on the tourism industry like she just mentioned in her question. I know she's now hollering and doesn't apparently want to hear the answer, Mr. Speaker, but I guess that's typical of the NDP. Lots of holler, lots of bluster, no action. And so question period comes to an end. Next we have a deferred vote on a motion for closure, on the motion for third reading of Bill 254, an act to amend various acts with respect to elections and members of the Assembly. On April 13, 2021, Mr. Downey moved third reading of Bill 254. On April 14, 2021, Mr. Nichols moved that the question be now put. Bells will now ring for 30 minutes, during which time members may cast their votes on Mr. Nichols' motion that the question be now put. I will ask the clerks to prepare the lobbies. Thank you.


This is circuit memorization-friendly encodings and their application to statistically secure multi-party computation. The setting in this talk is that we want to support computation over arithmetic and Boolean circuits, so we want parties to be able to efficiently convert between the two. And we allow parties access to a pre-processing phase in which they can pre-compute some correlated randomness independent of their inputs, which they can then use in the online phase for more efficient computation. And the adversary that we consider is an active adversary which may deviate arbitrarily from the protocol. And we assume this adversary corrupts less than a third of the parties, t is going to be the corruption threshold, and n is the total number of parties. And we also allow the adversary to abort at any point in the protocol. This is security with abort. And there are standard techniques that there are standard techniques for getting guaranteed output delivery, but that's not going to be a focus of this work for the sake of simplicity and efficiency. So much of what we're going to talk about is going to be based on sheer secret sharing. So let's do a quick recap. To share a secret, we sample a random polynomial where the y intercept is going to be the secret value that we want to share. And each party is going to have a distinct xi that is associated with them, and their share is going to be the valuation of the polynomial at their xi. And to reconstruct the secret, parties announce their shares, and then with all of the points, they can do the grand interpolation to get the polynomial that goes through these points. Parties just need to check that the polynomial that they reconstruct is of the correct degree. And if you look at this equation, the only real thing that might cause issue is that they do have to be able to compute this inverse of between every xj and xi the difference. But since we're working over a field, that basic sheer secret sharing is over a field, this inverse is always going to exist. And so this all works out. If we have sheer secret sharing, we can actually, we can do a general on PC with it. And so we're going to use this notation to denote a sharing of value a with polynomial of this particular degree. And so some properties of sheer secret sharing is that if you add together shares, you get a share of the sum. And if you locally multiply shares, you get shares of the product. The thing to notice, though, about doing this local multiplication is that the degree of the resulting share is the sum of the original degrees of the things that were multiplied together. And so in order to reconstruct this resulting share, you need the degree plus one distinct points to interpolate it, which means that we would need 2d plus one parties to reconstruct. And so even if we have these very small, eventually, if we do enough multiplications, we run out of parties to to reconstruct. And so typically to get more general computation, you have to reduce this degree in some way. And because we allow a pre process, if we we can make use of the pre processing phase to create what we call double shares, which are degree t and degree two t sharing of a random value r. And for each pair of these double shares, we can reduce the degree as follows, which first parties locally compute this larger degree product. Then what they do is they can take this product, use the degree two t double share r to product to their product, and then we can publicly reconstruct the the difference between the two. And so they they only need to two t plus one parties to reconstruct the points to reconstruct this. And once they have this public this value z publicly known, they can use the other degree t sharing to to unmask it and get shares of this product. Cool. So that was Shamir for fields. But what if we want to do a Shamir over a ring? A ring might be something more natural to consider. But the the issue arises with this inverse that we have to compute. It's so computing, because remember, we have to compute the inverse of the difference between every single xi xj. And this doesn't work for an arbitrary number of parties. And what do we mean? Well, it turns out that a ring like z2k doesn't have any subset s x1 through xn, where when we take the difference between every single every single element in the set, that these differences are going to be infertible. It doesn't hold when n is greater than two. And as a side note, we're going to call a set where all of these, the difference of each pair is infertible. We're going to call this an exceptional set. And basically, if you have a larger enough exceptional set, then you can interpolate. And there's a quick proof for why this doesn't hold. But how would we overcome this if we do want to do Shamir over a ring? And similar to how you may use an extension field, in the field case, if your original field isn't large enough, we can do a similar idea for z2k. Specifically, we can do a degree d Gaoua extension of z2k, which is a Gaoua ring. So what are Gaoua rings? So Gaoua ring gRp to the kd is basically going to be the ring of polynomials with coefficients in zp to the k modulo, some irreducible polynomial h. And p is going to be prime and then k is greater than equal to one. And Gaoua rings have, there's some basic properties. Gaoua rings, one of them being if you set k equal to one, then gRp to the d is gfp to the d. Another property is that all zero divisors of this ring gRp to the kd constitute the ring's only maximal ideal. And the last property that we're going to mention is the one that enables us to do Shamir's secret sharing. It's that when you have a Gaoua ring, p to the kd has an exceptional set of size p to the d. And so we rarely have a large enough exceptional set, we can interpolate. And so this just turns into we can set d large enough to give us a large enough set. And this is the, this is sort of the basic idea behind a recent work of ACDEUI, which adapted the multi-party, multi-party protocol of Birlio van Herd, which is a Shamir's secret sharing-based protocol that uses the double-share, double-share is from before to do their degree reduction. The ACDEUI adopts the protocol of this paper to work over the work over rings like z2k using Gaoua rings. What they do is remember if you, since they're working over, they want to work over 2 to the k, you can set your ring to be gr2 to the kd. And so the exceptional set for this is going to be of size 2 to the d. And so they can set their, set this parameter d to be log n plus 1 and have a large enough set to interpolate. And z2k has a natural embedding in R. Basically, if you, if you want basically any, any element like an input in z2k, you just look at it as an element of R. And so all this you have Shamir's secret sharing works over this ring. And ACDEUI is able to, was able to perfectly translate this protocol to the ring setting to work over Gaoua rings. However, remember that this ring is an extension ring of z2k. And so you are working over a larger ring and working over this larger ring, you do have some overhead. And in particular, this overhead does mean that your communication complexity is going to be a factor d larger. Every time that you would normally send an element, when you're communicating an element instead of just sending a z2k element, you are sending a Gaoua ring element, which is going to be a factor d larger. And your computational complexity, when you're, when you're multiplying two ring elements, is going to be quadratic in d. So every time you want to multiply these two z2k elements, they're represented as ring elements. So now you have to multiply these two ring elements together. And I say essentially quadratic because in practice, it's going to basically be quadratic. You could, you could use things like fast Fourier transform to try to do a little better. But the range of parameters is not going to really, you're not going to see a big difference using that. So the main contribution of this work is that we give better encodings from z2k into Gaoua rings. So first, let's look at how the multiplication and ACDEY works. This is going to follow some like similar structure to the multiplication that we saw before, because it's just an adaptation of the yearly over your heart paper. And so first, when you, if you have some elements that you want to multiply, they're encoded into the ring, just using the natural inclusion. And, and from there, and so this iota is just going to be that is just going to be taking your z2k elements into our, this is the exact same protocol as protocols before. But now all of our all of these elements are mapped to our these Gaoua ring elements. And yeah, and so this is how they do multiplication. And you can think of this as basically, you know, this is the the sub protocol for evaluating the multiplication gate, specifically a single multiplication in single multiplication of z2k elements. But if you look at the operations that you have to perform, you are, you are working over this extension ring. And so you're doing, you're doing this, this Gaoua ring multiplication, and you're getting one z2k multiplication. And basically, you have this larger ring that you're working over. And it's sort of wasteful that you're not taking advantage of the fact that you're working over this larger ring. Because even though you want to do this small multiplication, you are paying this overhead for working in this larger ring. And so a question sort of is, can you, can you use the fact that you are working over this larger ring to do more than just a multiplication? Can you compute something more expressive? Can you replace the fact that you're computing a multiplication gate with maybe some sort of circuit? And that's something that we, and we do that in this paper. In particular, instead of having, we take this iota, and instead of mapping just a single z2k element into r, we now encode multiple into r. We, we can encode some parameter delta of them. And so let's talk about this. If we, basically what we want to do is we want to, we want to take this protocol from before, and we can, we can generalize it. So instead of just a multiplication gate, maybe it's just some subcircuit that we want to compute. And the subcircuit could be, you know, could be a simple multiplication, but we want to say it could be something else. And what we want are two encodings to replace our iota, which we're going to call an end encoding and out encoding. And we want that the encodings have this particular relationship. And I'll explain soon how this relationship ties in. But essentially, if we, if we have these encodings, and we plug them, and we replace iota and plug, plug these encodings into the protocol that we saw before, notice that if we have, if we have end encodings of an input x, possibly a vector, and end encodings of an input y, and encoded double shares, then we can compute an encoding of the circuit applied to these inputs. If this, if this relationship holds. And so, and so this turns this protocol from before that we were computing into for the same cost of what you would do before plus the cost of these encodings, then you can compute possibly a more general subcircuit. You can compute, you can compute some subcircuit c. And so the the task then just becomes coming up with these end encodings and out encodings. Coming up with how to encode these values and how to generate double, like encoded double shares of this form. And if you're able to do so, then following this outline, you can compute an encoding of the circuit applied to these inputs. And in this paper, we give three. So in this paper, we give three specific encodings that we come up with. These encodings are actually, I'm not going to go into the specifics of what they look like, but they're actually very, very simple to construct. So the three encodings are inner product, SIMD, and flex. And compared to ACD UI, so when, so for, consider, there's ACD UI, when it takes in two inputs, it can compute one multiplication, one output. And that's, and the two encodings, so two of the encodings that we give also take in two inputs. And they're able to compute the inner product and compute inner products of length, roughly D over two. And SIMD can compute roughly D to the 0.6 parallel circuits with one multiplication and one output each. And these are going to, and so this is assuming a single opening in R. When we say single opening, it's publicly revealing at Z. So it's essentially the protocol, just running one instance of that protocol from before. And for, and if you have M inputs, using the protocol of ACD UI, you can compute a depth one circuit with M multiplications and a single output. And we give an encoding, a flex encoding, which can do the same except it can now output D, it can now have D outputs instead. Cool. So, so we give explicit encodings, these three codeings. And we also give protocols for generating double shares in, for these particular encodings. We also give a way of converting between our different encodings. So there's, there's many, you know, so the, these dotted lines represent encodings that, sorry, represent conversions and protocols that we don't explicitly give, but we give an outline for how to do this. We also note that this framework, you can, you can create your own encodings to that fit into this as long as they, as long as they have the particular relationship from before. And as long as you can, as long as you have some way of encoding and some way of generating double shares, this plugs right in. So you can possibly compute, you can possibly do use this for other sub circuits. This work, we also switch between, give away a switching between encodings. So before we're talking about these ring elements, we give away a switch between an encoded value in a ring and encoded value in GF2D. Specifically, we do this using DAW bits, which are doubly authenticated bits. And here is some formalism, if you want it, but at a high level, parties are able to perform local operation on shares within the ring to, if you have shares of random bits in this ring, you can perform local operation to get shares of the same bit in GF2D. And having, having shares of these bits in both representation allows the parties to, parties are able to switch between in a particular coding in R and the same encoding in GF2D. And protocols, we, we do give protocols for generating these random bits in the paper. Another contribution of this work is that we do give away of improved double share production. So the, the basic way of producing double shares is to apply a hyperverbal matrix to a vector of double shared values S. And then to check that the resulting vector of outputs are, to check that these are also valid double shares. And so typically, the way that the, the check in these prior works is done is that so many of these out, these are double shares are opened up and checked to be consistent with each other. And so you had to do this for every time you want to, for every time you generate this vector of, vector of Rs, you have to open up so many of them. And so you, each time you produce T, T double shares. And in this work, we, a contribution of the paper is that rather than having to do individual checks every time you generate these Rs, we give a batch check that can be applied over, that can be used to check many, that can be checked, that can be used to check over many of these. So instead of having to check this R each time you, instead of having to check each time you produce this vector R, we give a check that can be done over many batches. And so you can produce all of these factors R. And at the end, we basically do a random, we do a random linear combination to check that the Rs were produced properly. And so the check is going to be independent of the number of actual shares generated. And so it basically amortizes. And so each time you apply a type of our matrix, you're able to generate two T encodings, and then at the very end, throw away some constant number of them. And the challenges of such a, of this batch check is that we are working over encodings. And so our hypervario matrix needs to preserve these encodings. And because we're doing random linear combination, we need to be careful of zero divisors. We implemented these, some of the protocols in our paper, specifically the double share generation check. And here are some of the running times. There's a small overhead in generating double shares in this encoded double shares. But it's very clear that this batch check does yield a noticeable improvement. And so when you, so looking at the total runtime, you do start to, you do start to see that we do have a overall better, overall better running time for generating these double shares. And so the recap of our contributions is that we give encodings for gaolring elements, sorry, encodings for, for these gaolring to the KD by exploiting the degree of this ring to encode these subcircuits of Z2K. And if you set K equals one, remember we mentioned this as a property of gaolring, then we can get F to the D and encode circuits over F2. Our encodings, if you think of this as, this is a framework for constructing other encodings and translating between them. We also give batch checks for encoded double shares, which give faster preprocessing for these style protocols that use these hyperverbal matrices. And a small thing to note though is that our batch check does only have a statistical security. And we also give ways of producing random bits in GR, which can be used to create doubly authenticated bits from in this ring and this field.


Tech in BC is strong, it's growing, and it's the future of BC. Innovation in BC is changing the world. BC is a pioneer of revolutionary quantum computing technology. Technology has allowed me to open doors that I didn't even know were there. Exploration is probably one of the areas that I believe is helping create new opportunities for people to be more included in their communities. New capabilities of bridging those experiences and insights of how to connect people, all of us, forward. In the beginning, individual farms, individual factories had a windmill to produce electricity, and that was the efficient approach to go. But then over time, we realized there's this incredible economies of scale and this standardization across, and we can offer this as an overall utility. We can now suddenly work and play 24-7. Technology in BC is everywhere, and it's from technology invention to reverse climate that lives are changed all around the world. We are going to invite people into our country and welcome them here to a place that is not tolerant, but a place that is embracing them. A place that says, no matter where you are from, your faith, your creed, your origin, your language, you are welcome in British Columbia. You are welcome to come and help us build what we think will become the greatest country in the world. We try to move innovation out in industry, and we're doing it with this BC Tech Summit. More people, more places, more connections from all across all sectors. This is why I love being in this industry, because it's always in the place of breaking through and making the impossible possible. We can start to solve problems that are otherwise unsolvable, impossible to solve with current computers. This opens up new technology possibilities. We are at a unique moment in British Columbia and Canada's history. We're really going to move towards the patient as a community. It's going to be determined by a plan. It's going to be standardized. We're going to measure quality. I can now finally use my iPad, and I'm very excited. With AI, our words, what we say, what we write will be a window into our mental health to be able to analyze what a person says and be able to see indications of PTSD, Parkinson's, Alzheimer's. Being technologically literate, I've allowed myself to expand my career and options for the future. We are the future. Technology will allow youth to take what they love and what they're passionate about and move in any direction. And we will say to people from around the world and people here at home, let's get to work. Let's get to work and let's build British Columbia together.


everyone Shaber 1000 here today we won't get the front end of this Corvette up in the air we got to check this collector gasket on the bottom of the header where it goes into the exhaust this thing is very loud on this side also it's a it's island really high it's island at between 12 and 1400 rpm I like to see around 800 so there's a couple things I need to check I was looking for vacuum leaks yesterday so I'm not sure what's going on with that I couldn't find any vacuum leaks I am getting the vacuum lines straightened out but as of right now there are no vacuum lines leaking so I'm not sure what's going on there but anyway I want to get this see what I can do with this exhaust I know one of the header bolts is stripped on this side so I may end up taking that header off I thought I had a a set of small block Chevy header gaskets but so I don't know let's see what we got going on here let me get this thing let me get the hood up and get it up in the air and on stands and we'll see what the collector gasket looks like if there's one on it I don't know it's pretty loud sounds like an open header on this side that's how loud it is so anyway let's get it up now and check it out okay guys before we get started look at this tire just from sentence that five years in a garage on concrete which is better than dirt I guess but then sat what two years out here they were getting dry cracked the last time I look at them but see this was on the bottom I moved the backward yesterday so I figured they're all like that showed that the monkey she's like oh we'll just have to get new ones yeah okay she's like what are they expensive huh we'll see this wheel does not want to turn it we'll turn when you're moving the car do you have this on a jack stand and I'll always keep the jack under something whenever I can just in case but see there's a header bolt it's not stripped it's in there crooked I'm not sure the collector gasket let me see if I can get you under here I don't know what this is leaking must be water but there's where the collector gasket is I don't see any signs up leaking yet but yeah it doesn't look real well I'm gonna go and take them bolts off and that pipe there should just set right on the frame what this does it goes way back here then around here it goes up into here and somehow back out that tailpipe side pipe okay but anyway currently he's the one that did this exhaust so I don't know so let me go get a wrench first of all we got to take them bolts out there's just no way getting around that you know probably have to drop that header down so I can maybe try to run a tap and straighten that straighten that bolt out up there see if I got a gasket on me just get new gaskets and bolts are pretty cheap I don't like the tires I still don't know where this water is coming from this has been let me do some checking here still don't know where that water is coming from gotta be coming out of here somewhere yeah I see some leaves down in there okay so what I'm wondering I know it looks like to bring new nuts on the back of that thing but they're probably stainless I'm back that collector so what a lot of guys will do me included we just I'm I know this head's been off of here what we usually do is just unbolt the headers from up here and move the headers back but in order to do that the right way you have to loosen that collector so what I'm thinking may have happened is they didn't loosen the collector and kept pulling this back and putting it forward trying to put it on and all that what happens when you do that is it rips that gasket and I know this gaskets probably bad so right now I'm gonna go ahead and try to get these bolts out I don't know how well that's gonna work and I got unbolt that collector the way because when you go to put these back on once you move that out of the way and try to put it back on it's not gonna be right that's probably why they got that cross threaded like that so I'm gonna have to unbolt that collector anyway I'll get new collector gaskets but what I'm thinking is I may have to pull that header clear down out of there I think this one comes up from the bottom I may have to do something with that steering column I don't know if I can get this to come back here far enough so I can get a tap in there I don't know we'll just have to see I got to get that straightened out or it's always gonna leak there the weird thing is the leak sounds like it's more in the center and then it's really loud back there in the back so it may be blown clear out back there I don't know so let me see if I can get these bolts out of here and get that collector unbolted and then then I'll bring you back I'm not gonna bore you with that it's just three bolts down on the bottom and then these six up here on top there's two there two in the middle and two on the end I'll have to pull these plug wires off that's not a big deal there's still some wires I don't know where this goes that is a hot wire it's been made up because there's the other end of it now I took that off because the other end of that's open and it's a hot wire and I didn't want to shorten out on anything so all right I got to get to work but first hot one today 90 degrees feels like 99 well time for a beer I've been on this thing for you know a good 20 minutes anyway maybe 10 all right let me get some cold liquid in me and I'm gonna go ahead and get those bolts pulled and I'll bring you back when I find out something okay guys so I got the header gasket out I didn't take the collector off yet but you know I got to I mean I just haven't done it yet none of these bolts were tight the very last one and they're not looking that great either well this one don't even this one don't even have the washer on it have washers lock washers and what you do when you put these on you tighten them down you start it up you let it run you get it up the operating temperature then you let it cool down and tighten them all back up again and when you got these kind of headers all your gear has no you're going by two to four times a year you want to go around and tighten and keep tightening them but anyway so I get this out as you can see this is the one that's in crooked that wasn't crooked right there you can see it leaking there center one of course was leaking then you get down here to the end and holy shit this is copper gasket yep how hot that was this one wasn't even in this one here wasn't even in a half turn this one was about a half turn these were about two turns each this one was the only one that was tight and of course this one is was crooked so I'm not sure I can say I may have pulled that header clear off to get to it I don't know we'll just have to see it's an aluminum head so you got to be careful with this stuff guys you just can't willy-nilly slap something like this together so I'll have to pull them plugs out of there just so I don't break them off all right I'm gonna call it quits for today so there it is pretty pretty nerve-wracking working around that tire right above that tire so I'll probably have to let some air out of it so don't explode all right guys that's it for today she barely met the mental edging gone for now and we'll see you guys in the next one I'm gonna do a garden update today it's going pretty good while an onion update not really planted a garden the tomatoes have not come up yet they take five to ten days so we'll see what happens this week with those and again we'll see you in the next one say bye bro say bye all right bye guys have a good one