I'm very pleased to welcome you to this IIEA webinar. We're delighted to be joined today by Dr. Teo Tili Kanan, Director of the European Center of Excellence for Countering Hybrid Threats, who's being generous enough to give her time out of her schedule to speak to us. She'll speak to us for about 20 minutes or so, and then we will go to a Q&A with our audience. You'll be able to join the discussion using the Q&A function on the Zoom, which you should see on your screen. Please feel free to ask questions in throughout the sessions as they occur to you, and we'll come to them at the end when asked, Dr. Dinh, when she's finished her presentation to them. Just a reminder that today's presentation and Q&A are both on the record, and please feel free to join the discussion on Twitter, using the handle Twitter that is at IIEA. And now formally introduced Dr. Teo Tili Kanan, who is the Director of the European Center of Excellence for Countering Hybrid Effects. Previously, she was the Director of the Finnish Institute of International Affairs from 2010 to 2019, and has been the Director of the Network of European Studies at the University of Helsinki from 2003 to 2009. And in 2018, she became and was nominated part-time professor at the European University Institutes of Transnational Governance in Florence. She served as Secretary of State at the Ministry of Foreign Affairs, Finland from 2007 to 2008, and she was a member of the European Convention in 2002 and 2003, and a member of the panel and eminent persons of European Security as a common project in 2015 and 2016. Dr, I'll hand over to you. Thank you very much. Thank you so much for this kind presentation, and I also would like to thank the organizers for this opportunity to address this distinguished audience. I will talk about a topic that, during the past couple of years, has surfaced European political discussion, hybrid threats. What are they? How do they affect the security of our societies? What happens to hybrid threats when there is a huge conventional threat in the form of the war against Ukraine going on? What have we seen and experienced during this, this half a year in these terms? I am representing a center of excellence, which is an international, intergovernmental center of excellence located in Helsinki, where the key task of the center and its experts is to provide information, analytical knowledge, expertise about these hybrid threats. And I will structure my presentation in the following way. I will start by paying attention to the notion of hybrid threats. Hybridity, hybridity meaning mixed form of something. So what does this refer to in the case of security threats? I try to put hybrid threats into a context asking, how come that these threats have become so very topical now during the past few years? And what do we need as democratic societies to do in order to address them and protect our societies from these threats? And last, I'm going to focus a little bit on our center, tell about its work and activities during these five years when the center was established in the spring 2017. So now I would like to use my slides and this is the topic of my presentation and we can move to the first slide, which brings light to the concept. When we refer to hybrid threats in the context of European security or broader global security, we refer to threats of a very specific type. It is malign activity caused by state actors or non-state actors, which in most cases are kind of meant to do harm to democratic states and societies. What is typical of hybrid threats is the set of instruments and tactics that are being used. So when I say here that in hybrid threats it is a question of unconventional means that are being used, I refer to means that are not typical of those means that tend to be used in the international context, political, economic or military means for power protection or promotion of one's own interests. These threats are unconventional. We talk about cyber attacks, cyber means being one of the key tools in this context. We talk about attacks and disturbances of critical infrastructures, access to energy, electricity, which of course are very topical today, critical sea lines of communication. We talk about disinformation campaigns or more broadly manipulation of the information space. We talk about instrumentalised migration, a phenomenon which we saw last year at the borders of Belarus and its three European EU neighbours Lithuania, Latvia and Poland. We talk about asymmetric forms of warfare, hybrid warfare as we call them. So many unconventional means where the target is a democratic state or society and weakening of that state is the key goal of the use of these activities. From our centre's point of view, we tend to mention that these unconventional means usually are used in concert as different tools, different instruments are being used at the same time. The activity is planned so that they are exploiting the vulnerabilities of the target country. So this is very much in the nature of what we are referring to and the use of these kinds of tools has become very common in today's international environment, just because they are so cost-effective and cost-efficient as we tend to argue. In comparison with normal military instruments, in comparison with normal political or diplomatic tools, it's much cheaper to carry out a cyber attack or produce a disinformation campaign. Still, it tends to have serious consequences for the target society. Soon when I put them into a context, I will tell that the reason why they have become so very common relates to the current international environment where there is a major rivalry going on between democratic states on the one hand, authoritarian regimes on the other. It is a rivalry about values, about models of governance, about leadership of the international order. So this is the context in which these kinds of threat instruments belong. And we can already at this stage mention that when we look at the political documents or doctrines of the key authoritarian states, Russia and China, we find these instruments there. They are a part of the so-called Russian political war. This is the Russian term and the understanding of the Russian thinking is that Russia is in a kind of broad-scale war against the West. The Russian argument being that the West is the one that attacks. And that's why Russia has to use the full scale of instruments to defend itself against the hostile hostilities of the West. And in the Chinese case, there is a similar terminology, the concept that is used by China is the indirect war where the whole Chinese society, public and private actors have to form a united front to defend China. It's political and cultural unity against Western hostilities. So the argument, the justification for the use of these tools is given in these doctrines. We can take my next slide please. So they have become a commonplace tool in this rivalry where the non-Western authoritarian states are competing about a leadership position at the international level, where we have a transition in the global balance of power ongoing, the arguments of the authoritarian regimes, Russia and China, being that it should be the end of the Western political hegemony, the international system should be more democratic, more multipolar, that their values should play a larger role in the current international order. This is the argument. There is something that we call the systemic rivalry and of course the vulnerabilities of the authoritarian systems play a role, vulnerabilities which mean that when authoritarian regimes cannot be renewed in the normal democratic way, the legitimacy of their governments, of their regimes have to be safeguarded by using other types of means. Exactly the external campaigns weakening the democracies, discrediting the democratic model, changing the international power structure to their own benefit here functions also as a tool for the domestic survival of the authoritarian regime type. We should also of course take into account that the modern technological developments creates a form, plays an important role in this context. There are much more new facilities, platforms and potential for adversarial activities and the use of these hybrid tools. And I believe the cost-efficient character of them was mentioned. So let's move to my next slide please. In the center of excellence we are looking at various cases of hybrid threats, various forms of hybrid threats, but we are also looking at trends. So what kinds of trends do we see in certain geopolitical fields, in certain functional fields of society? These are certainly no news for you, but I just wanted to pick up some trends mainly to pay attention to the diversity of hybrid threats today. So we can divide them on the basis of the time span. There are those kinds of threats that are more immediate and then there are threats that we call us or describe to be at the priming stage. So pave the way for a later operation or attack, preparing something. Well, just to mention some trends. We have seen during the past couple of years an intensifying hacking against Western governments and parliaments, their information systems. We cannot ask ourselves what is the ultimate goal with these kinds of attacks. In most cases it is not that clear if the hackers are after the kind of information that they then confidential information or personal information that they then plan to leak or publish at the later stage. Or if it's just to increase psychological pressure on societies by attacking the kind of the heart of the democratic government, parliament, the governments. This has become very frequent. If the goal is to decrease trust in the government in that country or polarise public opinion, very difficult to know. A very different trend of hybrid threat activity that we perceive takes place in the kind of at the company level within critical infrastructures where we see a kind of dependencies increasing dependencies created by in particular Chinese actors and the Chinese government. Where we're increasing foreign ownership, Chinese ownership of Western critical infrastructures cannot be described as a hybrid threat as such, but in our understanding kind of paves the way, creates a lot of dependency and potential for future hybrid threat activities, which would mean that these ownership, these critical infrastructures, these dependencies that have been created would start to be used politically against the countries and governments where they take place. And this of course has already been seen in some cases. This seems to be a systematic trend. It's linked with the Chinese Silk Road project, the Arctic Silk Road or the Central Asian Silk Road. Similar activities taking place in Africa, in Latin America, but also in the heart of Europe. As a part, I already mentioned earlier that when we talk about hybrid threats, we refer to both state actors, but also non-state actors. Non-state actors all from private companies, different political groupings, terrorist organizations, just groups of hackers are being used as proxy actors for state actors. We see more and more different types of non-state actors that promote the agenda and interests of state actors. All from the Wagner Group, private military companies, religious communities, to private smaller private companies that have been established just to kind of take care of a commercial activity for a state actor. So this really is a crucial trend among hybrid threat activities. Of course, to a little bit newer phenomena related to hybrid threats can be described first as the use of lawfare, which I will explain and the instrumentalized migration that I already mentioned. So lawfare is a term which refers to the political and strategic use of law to the benefit of a hybrid threat actor. If we think about law in its commonplace role, it is an element of stability, predictability at the international level as well as at the national level. If then law and legal frameworks are being used, not in that role, but rather in the role of promoting a state interest, law gets a very different function. This is what we see in many maritime environments where the UN Convention on the Law of the Sea is kind of artificially interpreted very much against its original spirit to promote state interests in East China, China Sea or in the Arctic or even in the Baltic Sea. This might imply the use of kind of the legal use of military exercises to block critical sea lines of communication, access to ports or harbours as an example among many others. An instrumentalized migration where migration and the commitment of Western states to international humanitarian rules and conventions is being exploited as a vulnerability and migration is used as a tool to enhance polarization in stability in target societies. We have seen in 2015 in my country Finland a Russian operation the same year against Norway and as mentioned last year by Belarus to three EU countries. Just mentioned a couple of trends to give you an impression of how diverse and different the hybrid threats activities can be. Now we go to my next slide please. And now I try to be very brief with the next two slides just addressing the phenomenon from the point of view of how we can counter these threats, how we can protect our societies, enhance our own security. Basically, we are talking about two main tools in very broad terms. We are talking about societal resilience, building broad societal resilience. And here I give you the definition of resilience, which is an ability to adapt to exceptional conditions to absorb and recover from a shock. Resilience is being built at the national, local and even international level in the framework of the European Union and NATO for instance, both by using legislative instruments, new laws, also policies. We need to pay increasingly attention to our information space for instance, against the counter this disinformation campaigns or broader manipulation of information space. But we also need to prepare our populations and societies to address this phenomenon that takes on multiple forms and that's where we are talking about psychological resilience. Of course, common situational awareness, common understanding between the private sector and public sector about the big picture that I tried to describe to you that the hybrid threats relate to and the kind of tactics, their specific tactics, by means of which they try to exploit vulnerabilities in our democracies, our values, kind of bring our values against us. Next slide mentions another tool which for a long time was a little bit distant, at least from the small states amongst us. When we now talk about an effective policy of deterrence, that deterrence does not refer to nuclear deterrence where the concept originally comes from. But in addition to resilience, we must also create, take into use more proactive tools to signal the countries that are targeting us that there will be a cost on their behavior. And this is exactly what we are doing at the EU level, at the national level by imposing sanctions, by strengthening our own narrative and the willingness, messaging the common willingness of us to protect our societies in a broad manner. I'm fast now with these slides because I want to use the remaining couple of minutes on the hybrid center of excellence, which we then can also discuss more in detail in the Q&A session that I could take my next slide and present the center of excellence to you. So we are talking about currently about the center of the size of 31 countries, on Wednesday we will in fact get our 32nd participating state, this center was established in Helsinki five years ago as I mentioned and then there were 11 members. The understanding behind that establishment was that, as these threats are so different, diverse, and as we really have to understand their logic, we have to cooperate closely as democratic states, but also strengthen cooperation between the key intergovernmental bodies, the European Union and NATO. So we have to kind of find the right instruments to counter hybrid threats and those instruments need to take place at different levels, as I said. So the center was established to kind of enhance this understanding and awareness and expertise by those 11 states and when Malta joins on Wednesday or confirms its accession that we can already place earlier, we will be 32 countries and the center covers a major part of the European Union and NATO then. And the next slide will show you how we function here. So the secretariat where we are around 40 experts, we are focusing on these different forms of hybrid threats, we are focusing on the state strategies and policies that create these threats against our societies. And so 40 experts representing 17 different nationalities as we have a lot of second-dead experts here in our secretariat, mostly with people with civilian backgrounds, some people with military backgrounds, academic experts as well as experts from the government. The center is funded by its participation fees. Finland as the host country pays half of our core budget and the rest comes from the other participating states. We do a lot of different types of analytical activities. We publish a lot on our website, public publications, but also publications with limited release. We provide a table of exercises and different types of trainings to the administrations and do capacity building in other forms. But of course we also work closely with the European Union and NATO and try to facilitate their mutual cooperation as it is a part of our mandate. We are not a part of EU or NATO, we are an independent or autonomous center of excellence. Of course we are led by, if we take the next picture, we are led by a steering board as you can see, consisting of representatives of the soon 32 participating states. And you see the flags there and you see our units with kind of green color and then the administration with its teams with blue color. Of course I have been in this position since autumn 2019 and there has always been a close cooperation with Ireland. We have had important visitors from Ireland and it has always been a pleasure to cooperate even if Ireland is not a participating state for the time being. My final slide, I have used some extra minutes now, but I wanted to just kind of show light on the kind of three dimensions of our work just to make the picture clearer for you. So we look at these threats, how do they look like, what is the peculiarity with hybrid threats, what is the kind of their specific tactics because it's a very tactical instrument when they are targeted against the vulnerabilities in our democratic society. It's freedom of speech, our commitment to human rights norms, kind of free media environment. This is what is being exploited there. We look at hybrid threats in specific geopolitical regions such as the Arctic or the MENA region last year. This year we are focusing on the Eastern partnership countries. But we also as the second section here shows we are focusing very much on the authoritarian states and their philosophies, their approaches to these hybrid threat instruments in order to be able to counter them. And we also pay attention, increasingly attention to the use of non-state actors to try to block also that route from being used. And finally the core of course is to create knowledge about our vulnerabilities. And that's where we also focus on our democratic processes. We counter election interference, counter foreign interference in our democratic processes and debates. Now I'm sorry I used a couple of extra minutes. I'm very happy to answer and address any types of questions and comments. Thank you so much Mr. Chairman.


All you and jobs is probably one of the most rewarding things I've ever been involved in. And I bring that energy to theCUBE because theCUBE is where all the ideas are and where the experts are, where the people are. And I think what's most exciting about theCUBE is that we get to talk to people who are making things happen. Entrepreneurs, CEO of companies, venture capitalists, people who are really on a day in and day out basis building great companies. And the technology business is just not a lot of real-time live TV coverage. And theCUBE is a non-linear TV operation. We do everything that the TV guys on cable don't do. We do longer interviews. We ask tougher questions. We ask sometimes some light questions. We talk about the person and what they feel about. It's not prompted and scripted. It's a conversation. It's authentic. And for shows that have theCUBE cover it, it makes the show buzz. It creates excitement. More importantly, it creates great content, great digital assets that can be shared instantaneously to the world. 31 million people have viewed theCUBE and that is the result of great content, great conversations. And I'm so proud to be part of theCUBE with great team. Hi, I'm John Furrier. Thanks for watching theCUBE. Okay, welcome back everyone. CUBE coverage of AWS, Amazon web services, public sector summit in person here in Washington DC. I'm John Furrier, host of theCUBE. We're here with Sandy Carter and Lynn Martin, VMware vice president of government education and healthcare. Great to see you, both CUBE alumnus. Although she's been on since 2014. Your first time as well, I think 2018, maybe? 2018. 2018, great to see you. Great to see you, thanks for coming on. Yeah, thanks for having us. So VMware and AWS have a huge partnership. We've covered that announcement when Andy and Pat Gelsing was the CEO. Then lots happened. A lot of growth, a lot of success. Congratulations. Thank you. What's the big news with AWS this year at public sector? So we just received our authorization top rate for FedRAM high. And we actually have a lot of joint road map planning. We are kicking off our job today with the Department of Defense and IL-5 for the defense customers is also in process. So a lot of fruits of a long time of labor. So I'm very excited to be here. Awesome. So explain what is the FedRAM authority to operate mean? What is that all about? So I would say in a nutshell, it's really putting a commercial offering through the security protocols to support the federal government needs. And there's different layers of that depending on the end user customer. So FedRAM high crosses across all the civilian and non-classified workloads in the federal government. Probably applicability for state and local government as well with the new state ramp focus. FedRAM high will meet or exceed that. So it'll be applicable across the other parts of the government as well and all operated in a controlled environment jointly. So you get the VMware software stack on top of the platform from AWS and all the services at AWS. So more VMware faster deployed usage, faster acceleration? Yeah, so I would say today the government operates on VMware across all of the government state, local and federal. Some workloads are still on-prem, many. And this will really accelerate that transformation journey to the cloud and be able to move workloads quicker onto the VMC on AWS platform without re-architecting your applications. Without giving away any kind of VMworld secrets because that's next week. What is the value proposition of VMware cloud on AWS? What is the main value proposition you guys see in the public sector? So I see three and then Sandy chime in there too. I would say the cost in general to operate in the cloud versus on-prem are significant savings. We've seen savings over 300% on some customers. The speed on the application movement I think is a huge unique benefit on VMC on AWS. So traditionally to move to native clouds you have to really do a lot of application work to be able to move those workloads where on VMC on AWS you move them pretty fast. And it also leverages the investments that the government agencies have already made in their operational tools and things of that nature. So it's not like a full reinvestment for something new but really leveraging both the skill sets in the data center and the IT shops and the tools and investments you've bought over the past. And then the third area I would say is really getting the agility and flexibility and speed of a cloud experience. So what's your reaction to the partnership? You know, we were just talking in a survey to our customers and 67% of them said that the velocity of the migration really matters to them. And one of the things that we do really well together is migrate very quickly. So we have workloads that we've migrated that have taken weeks, months, as opposed to years as they go over, which is really powerful. And then also tomorrow, VMware is with us in a session on data-led migration. We were talking about data earlier. And a VMware cloud on AWS also helps to migrate over like SQL server database, Oracle databases so that we can also leverage that data now on the cloud to make better decisions and real-time decisions as well. It's been really interesting to watch the partnership and watching VMware transform as well. Not only the migrations are in play with the public sector, there's a lot of them, believe me, healthcare, you name every area. It's all those old systems are out there. You know what I'm talking about out there. But now with microservices and like, say containers, you got Tanzu and you got the whole cloud native VMware stack emerging. That's going to allow customers to refactor. This is a dynamic that is kind of under-reported. Migration's one thing, but refactoring- I think that the whole Tanzu portfolio is one of the most interesting things going on in VMware. And we also have some integration going on on VMC on AWS with Tanzu. We don't have that pedogram yet for the government market, but it's on the roadmap and plans. And we have other customers and I would say, some of my non-federal government customers were able to move workloads in hours, not even days are we literally back and forth and very impressive on the VMC on AWS platform. So as we expand things in with the Tanzu platform, Sandy talked about this yesterday in our partner summit. Everyone's talking about containers and things like that. VMware is doing a lot of investment around the Kubernetes plus the application migration work and things of that nature. I'd love to get you guys reaction to this comment because I've seen a lot of change. Obviously we're all seeing it, but I've actually interviewed a bunch of AWS and VMware customers. And I would call some of the categories skeptics, the old school cloud holding the line. And then when the pandemic hit, those skeptics flip over. Because they see the value. In fact, I actually interviewed a skeptic who became an award winner who went on the record and said, I love AWS, I love the cloud. I was a skeptic because he saw the value, the time to value. This is really a key dynamic. I know it's kind of thrown out a lot in digital transformation or IT modernization, but the agility and that kind of speed it becomes the number one thing. What's your reaction to the skeptics converting and then what happens next? So I think there's still a lot of folks in IT that are tree huggers or I call them servo huggers, right? Data center huggers, pick your term. And I think that there is some concern about what their role will be. So I think one of the differences delivering cloud services to your internal constituents is really understanding the business value of the applications and what that delivers from a mission perspective back to your clients. And that's a shift for data center owners to really start thinking more from the customer mission perspective than, oh, are my servers running? Do I have enough storage capacity, blah, blah, blah. So I think that creates that skepticism and part of that's around what's my role going to be. So in the cloud transformation of a customer, there's all this old people part that becomes really the catalyst. And I think the customers that have embraced that and really leveraged that and then retooled the business value back to the end users around the mission had done the best job. Yeah, I mean, Cindy, we talk about this all the time. It's really hard to get the best to breed partners together and then make it all work. But with cloud, it becomes easier than doing it very bespoke or waterfall way. Yeah, I have to say with the announcement yesterday, we're going to have a lot more partnering with partners. So you and I have talked about this a few times where we bring partners together to work with each other. In fact, Lynn is going to go meet with one of those partners right after this interview that want to really focus in on a couple of particular areas to really drive this.  You know, people have really strong vSphere skills, vSAN skills, operation tools, yeah. And so they want to preserve those. I think that's part of the beauty of doing VMware Cloud on AWS is you get to take those skills with you into the new world as well. You know, I was going to just ask that next question. AI ops or day two operations is a big buzzword. Yeah. And that is essentially operation mindset. Yeah, that's what I was- DevOps, DevOps 2.0 is coming. Emily Freeman gave a keynote at what our last event we had with Amazon public showcase. Revolution and DevOps. DevOps 2.0 is coming, which is now faster. Security's built in the front end. So all these things are happening. So now it's coming into the public sector with the GovCloud. So I have to ask you, Lynn, what are some of the big successes you've had with on the GovCloud, AWS GovCloud? So I would say we've had a lot of customers across the state and local side, especially, that weren't waiting for FedRAMP. And those customers were able to move. Like I mentioned this earlier and you guys just touched on it. So I think the benefit, key benefit, one of our best customers is MIT, right? Absolutely. MIT, God bless them. They've been on every cloud journey with VMware since 2014. And we're moving, I think it's three years now. That's right. And talk about a skeptic. So although Mark is very revolutionary and tries new things, he was like, oh, who knows? And literally when we moved those workloads, it was minutes. And the IT shop day one, there was no transformation work for them. It was literally using all the tools and things in that environment. So the progress of that and the growth of the applications that have been able to move there, things that took two to three years before were all done within six months and really being able to expand those business values back out for the services that he delivers to the customers. So I think you'll see quite a bit across state, local, federal government, we have U.S. Marshals, I think that's right. Thank them very much. They were our sponsor that we've been working with the last few years. We have a defense customer that's been working with us around IL-5, you know. And if we could also thank Coldfire, because Coldfire is one of our joint partners, talking about partner and partners, and they played a critical role in helping VMware Cloud on AWS and get the Fed Ramp High certification too. They were our three P.O. We hired them for their expertise with AWS as well as helping the VMware team. Well, the AWS partnership with VMware has been a really big success. And I remember the naysayers when that was announced, it really has worked out well for you guys. I do want to ask you one more thing and we don't mind. One of the biggest challenges that you see the blockers are challenges from agencies moving to the cloud, the government cloud, because people are always trying to get those blockers out of the way. Whether it's an organizational, it's a culture, it's a process, technology, what's your take on that, Lynn? I think a lot does have to do with the people and the organizational history. I think somewhere you need a leader and a champion that really wants to change for good. Pat used to call it tech for good. I love that, right? To really get things moving for the customers. I mean, one of the things I'm most proud about supporting the government business in general though is really the focus on the mission is unparalleled. In the sectors we support. If you say education or government or healthcare, all three of those sectors, there's never any doubt on what that focus is. So I think the positives of it are like how do you get into that change around that? And that could be systems. There's less with VMC on AWS as we mentioned because the tools are already in the environment so they don't have to use it. But I do think there's a transformation on the data center teams and really becoming moving from technology to the business aspects a little bit more around the missions and things of that. What's interesting is that I mean, I actually love this environment even though it's kind of hard on everyone. Education and healthcare have been disrupted in unprecedented ways and it's never going to change back. Remember healthcare, HIPAA, data, silos, silos, education, don't spend on IT. Now- I thought education was the most remarkable part. Unbelievable. I started working in February before schools started with one of the large cities. Everyone could guess. And just the way they were able to pivot so fast was amazing. And I don't think anybody, I think we did like five years of transformation in six months and it's never going to go back. I completely agree, yeah. I mean, education, we just did a piece of work with CTOs around the world and education is one of the most disrupted, have you said, healthcare. And then the third one is government and all three of those are public sectors. So the three most disruptive sectors or mission areas are in public sector, which has created a lot of opportunity for us and our partnership to add value. I mean, that's what we're all about, right? Customer obsession, working back with some of the customer and making sure that our partnership continues to add value to those customers. While we love the tech action on theCUBE, obviously we'd like to document and pontificate and talk about it. Digital revolution, every application now is in play globally, not just for IT, but for society. I mean, public sector more than ever is the hottest area on the planet. Absolutely. And I would say that now our customers are looking at ESG environmental. They want to know what you're doing on sustainability. They want to know what you're doing for society. We just had a bid that came in and they wanted to understand our diversity plan and then open governance. So they're looking for that openness. They're not just artificial intelligence, but looking at explainable AI as well. So I think that we have a chance to impact environment, societies, and governance.  But what's happening with space and what you can monitor, disasters, understand how to deploy resources to areas that might have challenges, earthquakes or fires or other things. All new things are happening. Absolutely. And all that data, you know, people like to say, why are you spending money on space? There's so many problems here, but that data that comes from space is going to impact us here on earth. And so all the things that we're doing, all that data could be used with VMware Cloud on AWS as well. Well, you watch closely. We got some space coverage coming. I got a big scoop. I'm going to release soon about something behind the dark side of the moon in terms of space sovereignty coming. A lot of action, cybersecurity in space. That's cool. Really heavy right now. Yeah. But aren't you glad that VMC Cloud on AWS isn't hidden on the dark side of the moon? Yeah. Any customer can access it today. Congratulations on, Lynn, thanks for coming on. You guys are doing great. Thanks for sharing. Thank you so much. Congratulations. Okay. Cube Coverage here continues. AWS Public Sector Summit in Washington, DC, live for two days of coverage. Be right back. Thank you.


Hey guys, it's Nate, aka The Foot Account, and welcome back to the channel. I think EA have one objective throughout this whole football-ish promo, and that is to mud our clubs and drain our coins from whatever we have to zero until we have nothing left because they just keep releasing even more SBCs, and with that, even more prices keep dropping on the market. Everywhere that I look right now, prices just keep going lower. So that's what I'll look at in today's video, is can they keep going? Are prices going to keep dropping? At this rate, it seems like they are. We'll look at that, and how you maybe can make some coins with prices dropping like this if you can time the market just right, and also how you might be able to make coins every single day on fodder as they're releasing all these SBCs. We're going to take a look at that and more, and what to expect today on a Sunday in FIFA 23 with footballers content. I'm coming. If you're excited for it, hit the thumbs up, and of course, if you're in your run here, hit that subscribe button. Let's go right away and look back at yesterday's content. Do a little bit of a roundup, and look at what they dropped yesterday because we had once again another good, cheap, and just kind of fun card dropped with the footballers promo. Patrick Bamford, we knew this was going to be the Bamford day, right? We now know every single day who's going to be dropping because of the objective. An 82-rated squad, right, or with an inform is what this was. Very easy to do, very cheap, and then you go and you play a couple of games, and just like with Luis Diaz, it's very quick and very easy to do, and you can get to playing with this Bamford upgraded card with 99 dribbling and four star skill moves in no time, right? I believe all you have to do is score a goal and four separate matches, and here's where it's starting to get really interesting with these objectives. You can actually combine. You could have done Luis Diaz and Bamford, and got them both done today with both of the SBC cards. You can also start to combine some of the new objectives that they dropped yesterday as well with even more footballers, players, and a lot of really good packs. So at least EA is trying to mud our clubs right now and take our coins all the way down to zero, right? Because of all the content that is out, at least they're giving us gameplay objectives where we can go out and try draft in squad battles, which we're already playing to get these guys completed for objectives, right? You get some extra packs for doing so. So this is very nice from EA to get some extra cards, some fun cards, right? The Saudi guy here, Megidi, five star skills. You've got the Dan Juma, of course, at the end of it, and you've got a lot of packs in between. So a big W from EA Sports, the Super Loans team pack is kind of like whatever. But I think this objective is a big W as well for the continuation of the grind. They give you a draft token. You can go to draft, you know, when you're winning and you're playing those draft games, you get the packs, the same thing with squad battles. So here's my take. If you are playing weekend this weekend and you have not actually started grinding, you know, the squad battles games to get any of these objectives done, maybe hit the pause button on that right quick. Unless you want these cards right away, you still technically have 12 days to get all these objectives done and all the SBCs are still available as well. You don't have to stay on top of this every single day. If you don't want to, I mean, I'm sure you're not going to be able to combine all the squad battles games for every single one of these cards. But like, let's say if you could do the first three, right? Maybe score a finesse goal, score a goal. We'll see if they continue on this path of just like score a goal in a couple of different games or assist or maybe, you know, score from across with a certain player or something like that. We'll see if they keep up with that trend. But you might be able to combine some of these objectives so you don't have to play as many games if you don't want that card right away. But still, it's a W grind right now. This content is absolutely incredible. And it didn't stop with the objectives yesterday in SBCs. We had yet another big time SBC. The 87 plus base or fee for World Cup hero player pick came back. This is the one last week that we were so excited about. I got Captavia from this. It's the one of five player pick, 84, 85 and 86 rated squads. You did have to have that 87 rated player requirement in it. But this SBC is really hyped, right? I think it was more exciting last week when people had fodder to actually do it. The problem right now with this SBC is and it's only 19 percent up voted on foot bin, we're all broken out of fodder. Or at least most of us don't have a ton of fodder. If at least if you do have some extra, you probably have it more on the higher end than the lower end, right? Because all the lower end fodder and all these like 83 doubles, the 85 mix, the 82 times 20, right? That's all low end fodder that's required for that. So this is at least craftable with high rated fodder. If you do want to go ahead and do that, but 311,000 coins. I think most people right now are realizing their fodder can be used in other places for better purposes, right? Then using it in this SBC, which is why it's got such a low upvote percentage. Now, speaking of more SBCs, let's talk a bit more about today. And I want to show you guys how you might be able to make profit every single day with certain cards, because we've seen this price fluctuation now two days in a row, because we're getting the same type of content refreshed every single day with an additional player SBC. And maybe another SBC kind of put out there, right? Look at 82s, 83s and 84s, but specifically the 83s. Remember on last night's video where I was buying 83s like 3.2, 3.3k, and what did they go to yesterday, right? OK, Henderson's a bit of a weird example because, of course, there was an extra Liverpool requirement in Diaz. But let's look at Ruben Neves car. Ruben Neves yesterday, I was buying him when I was recording the video at 3.3k. Here we are again, 3.5 right now.  But what you can see is around the content time, every single day on these 83s fodder prices are spiking because people are going out and doing, you know, Bamford or the Luis Diaz that was dropped yesterday. And the more SBCs that get dropped, yes, this fodder is going to continue to trend upwards, but you can trade with this every single day. You get 83s on bid or on snipe today on Sunday morning for like three low threes like 3.2 and 3.3k. You're going to be able to sell some of these cards for 4,000 coins plus to some lazy buyers around the content or an hour after the content drop today on Sunday. So that's what I would really, really look for. 82s to 84s are going to be the best. 83s are in so much demand. 82s are in so much demand. You can see this right yesterday from like 12, 1300 coins. These guys go up to about 1700. Now, again, also know that right now we're in the middle of the weekend, which means people are playing weekend league and there's more tradable pack supply than there's going to be throughout the rest of the week. So these card prices, you're like, Nate, they're going between like 3,000 to 4,000 coins. That's not that big of a deal. Well, a couple of things. First thing is it is weekend league. So you have a lot more supply and a lot more people are opening tradable packs because they get their games done, they open their packs. Now, a lot of people, I think, are still opening their packs right now because they need those gold players, gold rares, gold non-rares, maybe the 82s and 83s to get all the SBCs done right now. So I think some people are saving packs, but I also think some people are opening packs as well because you just need that lower end stuff on this game to at least get anything done. And when this weekend ends, right today, tonight, tomorrow, when the weekend league is ending and there's less packs being opened, that's when I think you're really going to start to see the fodder prices start to take off because if EA does not put tradable packs out in SBCs, I know that the 75 plus packs inside of like the 83 double and the 75 times five are tradable, right? If you guys have been doing any of these like this pack right here, the 75 plus rated rare player, sometimes you hit an 83 or an 84 out of this. And it's like, oh, boom, I just got something that's worth like four or, you know, eight thousand coins can go and sell it, right? There's a little bit of supply coming in from that, but not that much. I think a lot of your supply is going to dry up even more so as we exit the weekend. So if you're looking to invest at all today, if you're looking to buy in any fodder cards, whether it's for a fluctuation or whether it's for maybe a hole until later into the week, I really think this low tier fodder still has room to go up, even though it's so expensive already. So just kind of know that you can daily trade with these cards. Today's squad battle rewards, right? We're going to have the the rewards given out. I forget what time it is exactly. But think about how many people have been playing squad battle rewards. It's actually very soon after this video is going to go live. Squad battle rewards are going to be out and that's going to bring some supply to the market. It's going to be a great opportunity to get on bids for 82s, 83s and 84s. Buy some of those and you'll be set for the content that comes out today and maybe even set for a couple of days down the line, depending on how many you want to buy. So that's what I wanted to point out in regards to the SBC fodder because there is so much potential to buy it and flip it every day or just buy it and put it in your club for a cheaper price. That way, you know, when an SBC comes out like today, when the Kulisepsky comes out, probably going to be an 83 rated squad because he's an 86 rated card. You're going to be able to do that SBC easy or if you want to do an 82 20 today or whatever it is, you're going to have you kind of have to right now. It's not about getting the fodder at the best price possible. It's like, OK, can I get this fodder at a reasonable price before it goes up later on today? Because I know there's an SBC that I'm going to want to do. So that's kind of what I would watch out for. But seriously, get on the bids and look to sell for lazy buyers. Right. When I talk about lazy buyers, some of you guys know what I mean. Some of you may not. Like you see here, money I was between seven K and eight K yesterday. I bet there are people selling 84s at like eight and a half to nine thousand coins because sometimes when people search the market, they don't exactly search for the cheapest price. They think, OK, I'm just going to search for this guy. And then whenever I see one, I'm going to buy one. And for some, you know, they don't pay attention that much to prices and stuff like that. They might just search for money. I mean, and if you search for money, I want to see, OK, a bid at six K, 10 K. Oh, you know what? Boom, I'm going to go buy this one at nine thousand coins because it's cheaper than the ones that I all saw here. People do that a lot on this game. Listing for lazy buyers is so crucial to help you make more coins on this game and it can make you a lot of coins throughout the entire year in FIFA. So that would be one big tip I would give you guys right now, specifically on the lower rated fodder, on the higher rated fodder. I'm still watching my ninety ones. I'm still invested, guys. I still have all of these. Really, what I'm waiting for is that Play of the Month and Bop SBC and if EA were to drop any other icon SBCs today or something like that. Messi is sixty eight K. What's Lewandowski checking all these guys? You just you love seeing their prices continue to go up. Sixty seven K for Lewandowski right now. These ninety ones, all the higher rated fodder continues to hold price as well as it should. There's nothing to bring it down at this time. So keep holding on to that lazy listening stuff as well. Lazy list that stuff high. I've got mine listed at like seventy seven thousand coins listed up there. Pretty hot. Look, I just got a lazy sale on LaMella at fifty thousand coins. I bought that at forty K list for lazy guys. Perfect example right there. Now, Sunday content. What else are we going to get today? Right? We know Kudusevsky, he is, of course, next in line. Hopefully gets the five star skills. Like I said, I think he's going to be an eighty three rated squad requirement today, just like Luis Diaz, because he was an eighty six rated base SBC card when he dropped on Friday. I think Kudusevsky will be the same. Then the other question I have is what more can we get from EA sports with all these SBCs that we have out right now? The only other leak we have is for Furpo. We have not seen the Furpo footballers card yet. I don't even think we have a footballers car design here in the store search, because obviously there's none out on the market. But Furpo is the only leaked card. If we're going to have any more leaks, I mean, those, of course, could be dropping today, I'm guessing Furpo would be an objective. But who knows at this stage, if they give us more objectives for more packs, they play to style, play to ball. Maybe there's going to be like a play to upgrade. I don't even know. Man, they keep dropping more objectives with more packs. I mean, we won't say no, because right now we just need all the fodder we can get and however they're going to give it to us, we would love to have it. So there's our chance for Furpo today. And I just I don't know if they're going to drop another icon SBC guys. I just don't know how much further this can go on, how much longer this can go on with a big icon upgrade SBC still available for five days. All of these SBCs are refreshing every single day. And then get in the base or hero player pick yesterday. Maybe an icon player SBC, but we just had Cruyff. I mean, seriously, a lot of question marks from me today. Besides the Kudusevsky, not entirely sure what we would get because there's going to be a quiet day of content soon. There always is, right? We always come down from the crazy high. But at least for right now, we are still on that mountain top of FIFA content just being absolutely insane every single day. We're going to talk about the market in just a second because we have not yet. I want to talk about the store really fast to every single day. EA is making bank in here right now because they know specifically with this provisions pack, people are buying this pack every single day. And if that's you, that's not a problem because this gives you a hundred gold common players. And I completely understand the 500 FIFA point value of this. If you're someone who spends FIFA points on the game, this saves you a lot of time from going and buying those commons and a lot of coins technically because commons are what, five, six hundred coins right now. So instead of this, you just pay 500 FIFA points and boom, you have it. But EA is so smart with what's going on, man. They just have people turning to the store this year like none other. And also right now, if you want to pack anything cool, think about it this way, EA is not dropping anything in packs. So if you want to pack something cool and have that rush, what you have to do is go to the store and spend a lot of FIFA points on one of these review packs, which they dropped the 400 K pack yesterday, eighty seven percent chance of a Winter Wild Cards, eighty six of a Centurions, eighty five of a Future Star. Crazy, crazy luck on that pack right there, of course, because of the guaranteed players from the promos. I have not opened any of these. I probably am not going to open that. It's just a lot of coins for my liking. Sometimes we do those gamble packs in the store with coins, but when it's that much, that is a lot of cost. I didn't make that many coins yesterday to be able to say that I can afford opening that pack today. So maybe a new store pack today, keep an eye out there in the store as well. Now, let's talk about the market, because again, we talked about it a lot yesterday. Prices are starting to drop and we saw the continuation of that yesterday on this game. And it's going to happen even more into today. One card we look at all the time is Golden Bopay, right? And I want to show you guys Golden Bopay on the market at the moment. 640, about 645,000 coins. Just look at this graph since Friday. Friday, this guy was 730K, which was already down a little bit, by the way. Boom, big drop off Friday down to 694 and look at yesterday. Same thing. Started the day up in the 690s once again, and then boom, content drops 650, and he's still slowly sliding down a price. Honestly, guys, this is probably going to continue to happen. If the content does not slow down, you're going to have drops like this just about every single day. Usually, the drops are a bit more accentuated on the weekends, especially we had a striker drop yesterday. I doubt many people are substituting a Bopay in their teams for Bamford. But besides the points of phone card at least, you know, you're going to see prices continue to drop like this. And a Bopay is a card that we look at all the time as kind of like a barometer. So if a Bopay is dropping, then prices everywhere else should be dropping on this game. Let me just give you an example. You know, cards that aren't dropping right now in price, especially if it's on a mid to lower tier. I'm trying to like look through a couple cards right now for maybe something that's not down that much. If something is not down a lot, that would be like a warning sign to me. Like if you have a card tradeable besides like a Trent Alexander Arnold, like obviously this card is up because the Premier League links because of the Luis Diaz links. But let's say you got some some random guy from like, I don't know, for the Foot Future Stars promo. Like Enzo Fernandez is still 1.4 million coins. That's still up there, right? Musiala is still 1.4 million coins. I think that a card has not dropped off at all yet. Gavi's still 590K with all the Premier League hype that we have right now.  I would look to get out of that card because if it hasn't dropped yet, it has more drop coming in the near future. It really does. I just think that these drops are going to continue as the amount of coins being drained off this market every single day is really, really crazy. And it's going to keep taking coins off this game. And that's going to make prices continue to fall lower on all aspects. You had a lot of the top tier cards we mentioned in last night's video as well.  Look at Yaya Turei, 3.7 million coins. He's now down at 3.15. Now, is that down too much? Will he bounce back a little bit? You're going to have some fluctuations in there. But a lot of your pro level cards on the top tier have been dropping too because of qualifiers being played and people selling their teams afterwards. And of course, that just kind of, you know, is added on top of the already crashing market. So just continue to be very, very careful with all cards on this game because I do believe prices are going to drop some more today.  As more and more coins are drained off of this game as well. Now, another thing I want to look at are these foot fantasy cards because a lot of them have been dropping as well, but for different reasons. Hazard, 600k. Elclasico is today, man.   Elclasico is today. I might have to pick one of these up because look at Hazard. He was 630 yesterday all the way up to 670 down now into the 620, 620,000 coin range. These cards are dropping a lot because investors are selling them either before the game or during the game. Most of these guys are going down after a game. Even Emery Chan, who did not is not getting an upgrade for a performance, but Emery Chan and Dortmund, they won the game. So he's going to get a plus one whenever EA decides to upgrade these cards. Even still, his price went from 340k down to 300,000 coins. I picked up three right here. He's kind of starting to go back up. And I hope that he has a very similar price rise to Esok, who performed very well on Friday, exploded in price up to 400k and then just kept rising into yesterday. 440,000, then dropped back down. Of course, after Banford was released, another Premier League striker. Keep a close eye on these cards. Ben Acer is one, you know, kind of like a, you know, a horror story, if you will. 420,000 coins. Milan, you lose yesterday to Udenese. He goes all the way down to 300k. I picked one up there, sold them at 330. He's kind of now back down. You can absolutely fluctuation trade with these cards. Like the Ed and Hazard I just mentioned, like El Clasico is today, right?  Don't try to go all out. But these guys are still live cards. And if Real Madrid scores first today, this guy is going to go up in price. I bought a Dina Talley yesterday after Udenese scored. These heroes, guys, I think people forget that the heroes get a plus one after one win. That's all that it takes.  I always do this with live cards, man. I always sell way too early with lives. I bought Dina Talley at 1.91. He was being panic sold as pros were selling off their teams. This guy was being panic sold a ton. Picked him up at 1.9 and I ended up selling him at 2.07 because that was when Zlatan Ibrahimic scored the penalty. And I thought Milan were going to start kicking back and come back. They didn't. They ended up losing three to one. This card is now a 2.2 million coin card and I lost out on like 120,000 coins of profit. But these cards move. If you want to figure out where all these guys are getting their upgrades at, just head over to the players tab, drop down dynamic to fantasy. And you can see every single live card. And this is where you can kind of keep track of these cards. And you can also see like if a player player or not. Boom, Marquez plus one, New York Red Bulls one. Saliba is injured. This is a specific card we need to talk about. Saliba dropped off a ton because there was news that came out yesterday that Saliba is going to be out for like four to five weeks, which is longer than just like the one or two weeks that we initially thought it was. Of course, we do have international break upcoming, which definitely impacts these cards. But yeah, just be really careful with these foot fantasy cards. They can be big money. They can also be big losses. And but again, the same kind of thing holds true. And I also bought a couple of Melliers yesterday. Got a cheap one on bid, but some low fifties on Melliers for the Bamford Lynx. The same holds true with just being able to flip rare cards in the panic selling. I bought a Salah at 630, sold at 700 because fluctuations on a rare card. This Goretzka, I'm looking, I'm trying to get 1.5 something. He's 1.6 right now. He is down like 300,000 coins. This Kyle Walker is down a ton. And I know there's a lot of pro people that are selling off teams out there. So it's risky because, you know, it might not work out. Kiesa went from 700K back to like, what is he right now? Like 750, maybe even higher than that. So these cards do move out of pack specials you can trade on this market right now. You just have to be careful and you have to find big drop offs to get some profit on a bounce back on a rare card. So it's risky business out there right now. I do believe the market's gonna fall further today. So be careful, but you can make some coins with fodder and hopefully EA Sports just do something else that surprises today, all right? And make some coins off that fodder. Get on those bids, stock your club, and you'll make some coins today with those cards as well because that's what everybody needs right now in this game is fodder. If you enjoyed today's video, smash the thumbs up on it. Comment down below if you have any questions and subscribe if you're new. It's been Nathan Foot account and catch you guys tomorrow. Peace out.


So suppose H is a normal subgroup of G. We saw that we could define coset multiplication A H B H equals A B H. Consequently, the cosets of H have an associative binary operation with an identity and an inverse. And this motivates the following definition. Let G be a group and H a normal subgroup. The quotient group G mod H is the group of cosets of H under coset multiplication. So for example, suppose G is a group with 30 elements and H is a subgroup with 5 elements. Let's find the order of G mod H, and let's consider what are the possible orders of an element of G mod H. Since H has 5 elements and G has 30, then there must be 30 divided by 5 or 6 distinct cosets. Because remember, given a subgroup H of G, every element of G is in exactly one of the cosets of H, and every coset of H has the same number of elements. And so that means that the quotient group G mod H has order 6, and so an element A H of G mod H must have order 1, 2, 3, or 6, what are the divisors of the order of the group? Now Lagrange's theorem says that if a subgroup exists, then its order must be a divisor of the order of the group. But what about the converse? If a number is a divisor of the order of a group, then a subgroup of that order exists? Well, maybe. So here's an idea that we might consider in the investigation to follow. If you can reach your destination despite any roadblocks, you can reach your destination. So let's see if we can find a subgroup of the multiplicative group of integers mod 11 of order 5. So remember, every element of a group generates a subgroup, and the order of a subgroup is a divisor of the order of the group. So to begin with, we note that the multiplicative group of integers mod 11 has 11 minus 1, 10 elements. So its subgroups could have order 1, 2, 5, or 10. So we can find a subgroup by considering powers of any element. Well, let's consider the powers of 3 mod 11. And we find these are, and we're done. We found a subgroup of order 5. And so if we pick an element of order 5, we're done. But we don't want to really rely on being so lucky as to have picked an element of order 5. Remember, if you can reach your destination despite any roadblocks, you can reach your destination. So let's put a roadblock. Let's suppose we don't pick an element of order 5. So again, we can form a subgroup by considering powers of any element. So let's consider the powers of 2 mod 11. And these are, and we see that the powers of 2 actually generate all of the elements of the group. Now, since 2 to the 10th is congruent to 1, then 2 to the 2nd to the 5th is also congruent to 1. And so that means 2 squared 4 has order 5. And so if we pick a generator, we're done. We can find that element of order 5. And correspondingly, the subgroup of order 5. But again, if you can reach your destination despite any roadblocks, you can reach your destination. So suppose we don't pick a generator. Let's close off that possibility. So again, if we pick an element of order 5 or a generator, we're done. So suppose we pick neither and generate a subgroup H. Well, the only other possible order is 2. And so we find that the element 10 generates a subgroup, 1, 10, until it has order 2. And since the subgroup has order 2, that means there have to be 5 cosets. And so our quotient group has to have order 5. And so that means any non-identity element of our quotient group must also have order 5. So A H in G mod H must have order 5. And so we'll pick a random coset, about 4, 10. And we find that 4, 10 has order 5. But 4 itself has order 5, and so we don't want it. Because stop me if you've heard this. If you can reach your destination despite any roadblocks, you can reach your destination. So in this case when we found our coset of order 5, it turned out that the element that produced that coset also has order 5. So let's throw up a roadblock that keeps us from taking that path. So we find a different coset, about 2, 10. And we find that 2, 10 has order 5, but 2 itself does not have order 5. 2 to the 5th is not congruent to 1. But now let's think about this. 2H to the 5th is 2 to the 5th H, which is H itself, because again 2H has order 5. And so that means 2 to the 5th is an element of H. And that's because A H is equal to H, if and only if A itself is in H. So we'll give it a name, and in a spate of creativity, we'll say that 2 to the 5th is, how about H? And we can actually compute it, it turns out to be 10 in fact. But wait, there's more. Since the subgroup H has two elements, then every element must have order 2. And so 2 to the 5th to the 2nd, well that's really the same as 2 to the 2nd to the 5th, must be the identity element. And so we've overcome all of our roadblocks. Since A H has to have order 5, then if A itself has order 5, we're done. So suppose we don't pick an element of order 5, say 2. Then 2 to the 5th is an element of H, and 2 to the 5th to the 2nd is congruent to 1. But because the exponents are counts, we can rearrange them in our usual way. 2 to the 5th to the 2nd is the same as 2 to the 2nd to the 5th. And so 2 to the 2nd or 4 is our element with order 5. So even though we close off every possible road to an element of order 5, we still found one. And so the question is, can we do this in general? Well let's find out.


So, this is a joint work together with Nivek Yoboa and Niveli Shai, right here, you guys. And the focus is on what's referred to as a circuit size barrier. So here, suppose I have Alice and Bob with some inputs and want to compute some circuit scene. So, if we don't care about security, the communication that's required here is very minimal. I can just send my input over, computation will be performed, and the output sent back. Interestingly enough, this is a, you know, crypto conference, we want to do this securely. And so by security here, I mean that nothing beyond the output is revealed. So interestingly enough, when we go to this security setting, all, essentially all known techniques for achieving this require communication that grows with the entire circuit size. Here, as opposed to inputs and outputs, there can be a very large gap here. And this is what I mean by the circuit size barrier. So essentially, all of the tools that we know how to use, even if you consider, for example, restricted classes of programs, things just like branching programs, Boolean formulas, still require this entire circuit size amount of communication. So the one exception to this is the recent breakthrough works in fully homomorphic encryption, which essentially allows you to get security while mimicking the original procedure, but underneath a layer of encryption. So here this breaks the circuit size barrier, it gives you something comparable again to just inputs and outputs. But of course, fully homomorphic encryption is also non-ideal in a certain different ways. For example, even though we get these great asymptotics, concretely, these have very heavy machinery, high concrete costs. And in addition, despite a lot of work and a lot of different candidates that have come up over the years, essentially all of them rely on the same class of assumptions boiling down in one way or the other to some sort of noisy encoding over lattices. And in particular, there's no candidates to date based on sort of retro 20th century assumptions. So let's rewind one year ago, Eurocrypt 2015, where I presented exactly this slide and I work in fact with the same authors on what's known as function secret sharing. So don't worry about what that is now, of course you should look it up afterward. But the important part that I want to say here is this giant region in red, which is essentially one of the things we showed is that if you were able to construct this object, this function secret sharing tool, for classes of programs sufficiently rich, for example, NC1 and above, that this would give you a succinct two-party computation protocols, essentially breaking the circuit size barrier for comparable classes of circuits. So you'll see this, this isn't red. We took this in fact as a negative result, it's some sort of barrier that essentially if you wanted to build this kind of function secret sharing, then probably you're going to need to use something like fully homomorphic encryption. So I'm happy to report in this work, we essentially turned the tables on this negative result by constructing exactly this notion, this function secret sharing, based not on fully homomorphic encryption, but based just on standard decisional Diffie-Hellman. Okay, so we achieved this for the class of branching programs, which in particular includes this NC1 log space in a number of different things. And actually I should take what half step back, so what we achieve is not exactly the same thing as function secret sharing, in the sense that we have a small probability of error in the reconstruction procedure, but as it turns out, this is still enough if you boost within the application, it's still enough to give you, for example, succinct MPC. Okay, so the core theorem of this work is actually going to be a little bit more convenient to talk about the dual notion of function secret sharing, which is that of homomorphic secret sharing. So keep in mind, I come with some secret and I have a secret sharing scheme such that if I want to now get secret shares of a function of this secret, that there's some procedure of homomorphically evaluating on the secret shares independently, without communicating back and forth. Okay, and the resulting values, these output shares, are exactly an additive secret sharing of this target function evaluation, F on my input. So here throughout the talk, W is going to represent an input. Okay, so a couple of notes here. First of all, you can actually consider more general reconstruction procedures here. It'll be a bit convenient for us and gives us some further applications to consider explicitly just addition. And one of the benefits of that is that, so these elements, these output shares really are elements of the output space of the function. So for example, my branching function, my function F outputs a single bit, then these shares that we have to exchange are literally one bit, not even an encryption, they're just one bit. Okay, so this is homomorphic secret sharing. And as I mentioned, we achieve this with a class of branching programs, so F's coming from branching programs, with this noticeable failure probability. And this failure probability is, you can trade it off here in exchange for run time. So note in particular that this delta is going to have to be noticeable, one over polynomial. Okay, so in the rest, by the way, Lambda is also the security parameter for the DDH. Okay, so as a function of this core result, we get a collection of different applications following from DDH. The first of which is of course, secure two-party computation. And here with the, for the class of branching programs, we essentially can match basically what you could hope for in terms of secure computation for the communication. Okay, going beyond branching programs, for a much, much richer class of circuits, we can basically use this branching program as a mini tool in order to shape the communication complexity to sublinear. Okay, so this, even for this large class of circuits, which I'll talk a bit about afterward, we can kind of break this circuit size barrier. An additional application that I won't have much time to talk about, but actually this is one of the applications that does require additive reconstruction at the end, is that of two-server private information retrieval. Okay, so here you have basically a client who wants to make secret branching program queries onto a database. So I've mentioned this a couple of times, but I really want to drive this point home, that branching programs are actually a pretty rich class of computations. So for example, if somebody tomorrow made it illegal to do any computation beyond this, I would still be pretty happy to live in this world. For example, things like approximations, essentially all cryptographic primitives have some sort of instantiation within this. Okay, so for the remainder of the talk, I'll go through the construction. I'll actually talk mostly about a simplified version, and then a little bit about how we get beyond that. I'll go through applications, and then I'll conclude. Okay, so let's get started. Okay, so it's going to be convenient for us to, instead of going directly and working with branching programs, to work with the following class of programs known as restricted multiplication, straight line programs, or RMS. Okay, so these programs have various values in memory, and you have inputs, and you're allowed to do four different types of instructions. The first is to take an input value and load it into memory. You can take two values in memory and add them together, you can take a value in memory and multiply it by an input, or you can output a value that's currently held in memory as an element of any ZM of your choice, for example. Okay, so what we're going to do is we're going to build homomorphic secret sharing that supports evaluation of these types of restricted multiplication programs over the integers, and we'll get correctness to hold as long as all of the intermediate computation values, these integers, as you go along, are sufficiently small in magnitude. So as a special case of this, if you just think about zero, one binary values throughout computation, this is already rich enough to capture log space and branching programs. I have a very cool side about that, but definitely no time to go through it. Okay, so even if you want to just compute one of these branching programs, for example, you can get some benefits by working with a larger plain text space than just zero, one. And also out of interest, so this, if you allow these larger plain text space, this now captures an entire exotic complexity class known as reach few L. Okay, so let's do this warm-up. Remember we're in the world of DDH, so we have some DDH group and a generator. And for the time being, suppose that it were the case, that if I take G to the W, that this is a secure encryption of W. It's not, I hate to break that to you, but suppose for the time being that it is. So here's how we're going to generate the secret shares. So I come with my input W. The first thing I'm going to do, by the way, this line denotes that this will be one guy's share, this will be the other guy's share. The first thing I'll do is give additive secret shares of each of the values. So just random values that add to the correct value. And the second piece will be to give this sort of pseudo encryption of my input to each of the parties and note here that this is the same value on both sides. Okay, so how can we do homomorphic evaluation on this? Let's step through the four different things that we have to be able to support. So loading of value into memory, we're going to think about the invariant that we'll maintain is any value in memory is currently held as an additive secret share between us. So loading an input is already trivially taken care of because this is part of the original secret sharing. Now that we have this, it's straightforward to see how can we add values in memory. I have an additive share of this, an additive share of this. I can just add them locally, and that gives me an additive share of the sum. Okay, so multiplication, let's skip over this for a second. And let me just say that outputting the value of memory is also reasonably straightforward.  Okay, so the tricky part is how do we do this multiplication? And remember that here, this is where we're going to use the fact that we have, as part of this input value, W, we have this encryption, or pseudo encryption. Okay? So we'll take this G to the W that each of us hold, and raise it to the additive secret share of our memory value X. Okay, so take a look at this. If I multiply these two values, what do I get? Quite audience. All right, I'll tell you the answer. You get shares, multiplicative shares now of G to the product, G to the WX. Okay, this is good. This is progress. In fact, we're trying to get this WX, we want to get shares of it somehow. But what we want to get in order to continue with computation is that we need additive secret shares. So how can we get from these multiplicative shares to additive? It sort of seems like we're stuck, right? Essentially, this would require us to take discrete log. Or does it? Okay? So again, our goal now is to get back to these additive secret shares. And one of the core technical ideas in this work is the following share conversion procedure. Okay, so our goal, again, we have these multiplicative shares of G to the Z, and we want to somehow get to additive secret sharing of this exponent Z. Okay, so let's look at this graphically. The top part and the bottom part are going to represent the views of the two different parties. And each of us, so here, graphically, think about this as stepping along the different powers of this secret group, DTH group, G. And the fact that we have a multiplicative sharing of G to the Z means that we can derive values that here differ on this path along by exactly Z steps, okay? So what we're going to do is to consider a set of special random points, these red points here, whose density is approximately delta, and whose identity we can efficiently test and agree upon. So this can be achieved, for example, just by sharing a pseudo random function and a point, some G to the I is said to be a red point if this evaluation of the PRF is zero. Okay, so now our share conversion procedure is going to be as follows. So starting with whatever your share is, say this guy starts here, this guy starts here, just iteratively step along on this path each time multiplying by one copy of the generator G until you hit a point that's a special point, one of these red points. And the output of this will be exactly the number of steps that it took for you to reach that point. Okay, unless, of course, so we have this escape condition that if you go beyond a certain amount of point and you didn't see one of the special points then just output zero, for example. Okay, so why does this help us? Well, there's three different cases about where these points potentially could lie as opposed to where our values are. The first case is the good case for us where there's no point in this zone in between our values and there is a point in this zone before a board. So in this case, essentially this is good because each of us is going to output our distance with respect to the same special point, which means that the values that we output will differ additively exactly by this value Z. So this is the good case, but there's two additional cases that would be bad for us. So the first is if there is a point in this red zone, and the second is if there's no points in either of the zone, in which case at least one of us is going to have to abort. But, and never fear, so you can set the probability of these events to be essentially as low as you want, okay? So here, what does this probability space correspond to? It's roughly going to scale with the size of this window times the density of these red points. So for any value that I want to shrink this error down to, what I can do is I can just make these points less and less dense. And as a trade-off, I'll shrink the error in exchange for needing to take additional steps, so to travel further along this path before you're expected to hit one of these points. Okay, so this is the share conversion procedure. And actually, kind of a note out of interest is that this procedure is a little bit reminiscent to some applications or some techniques in crypt analysis. For example, there's a technique of Van Orscha and Wiener, and I think it's kind of cool that we actually turn this into a constructive technique. Okay, so summarizing this warm-up construction, as you may recall, so loading to memory, addition, and generating output were not a problem. And to do this procedure of multiplying an input together with a memory value, we first started by taking G to the W, raising it to the additive share of X, and then running the share conversion procedure. And note, by the way, so the error of the share conversion scales also with the size of the payload. So it's important when you're designing the scheme, this is where we get this restriction of correctness only as long as the plaintext remains small. Okay, so this is fantastic, I hope you think so too. But, of course, this is assuming in this kind of magical land where G to the W was actually secure encryption. So I'm not gonna spend too much time talking about how we get this beyond, because I think that this warm-up actually gives most of the core technical ideas. But let me just give you a little bit of a flavor of how we remove these restrictions. So the first step is that instead of taking this G to the W as some sort of encryption, we replace this with L-ga-ma, and it will be the case that we can mimic a similar sort of step of going from this encryption using the additive shares, this time using sort of linear algebra in the exponent by giving together not only shares of X, the memory value itself, but also will end up maintaining as an invariant that you have additive shares of the secret key for the L-ga-ma times X. Okay, and then, so I'm not gonna explain why, but hopefully I'll pique your interest. So we'll also need an encryption now of the input times the secret key, and in order to make the share conversion procedure work out, we need to keep the payload small, so we use some bit decomposition tricks. Okay, so kind of combining these tools in with a little bit of work gives us a scheme that's secure, but now, so we've shifted the assumption and now we have L-ga-ma, which is great, but note that we're still giving an encryption of the secret key. So here this is secure, assuming that L-ga-ma is circular secure. And the final step is removing this circular security assumption, and there's two potential ways you can do this. So the first is sort of the typical approach in fully homomorphic encryption where instead of giving an encryption of the secret key under itself, you can consider a sequence, sort of a leveled version, where in each one I give you an encryption of one key under the next. And this, so this blows up the share size now by the depth of computation, you need a new key for each multiplication method. However, unlike fully homomorphic encryption, actually in our construction, we can get rid of circular security altogether, basing instead of in the place of L-ga-ma, turns out we can use the encryption scheme of Bonnet, Hallevi, Hamburg, and Ostrowski, which is provably circular secure exactly in the way that we need based on standard DDH. Okay, so one last comment before I move on to applications. As I've described it, this secret sharing scheme is individual for each person. So if I want to generate shares of my input, I need to, for example, generate my own L-ga-ma secret key and do things with respect to that key. And the question is, can you hope to get something with homomorphic computation across different parties' inputs? So for example, say that I have some sort of general generation procedure that gives us a public key and shared, so shared public key and separate evaluation keys, such that any party who comes along can now use this public key in order to share his input, so that later on these servers, for example, can compute across the different shares. Okay? So this will be important for the next piece, which is, now let's shift gears and talk about applications. Okay, so kind of the whole thing that brought us into all of this is this question of secure two-party computation and suppose that what we want to evaluate is a branching program. So using this public key version of HSS, the first thing that we'll do is jointly run the key generation procedure. So now we share a public key and each of us will take one of the evaluation keys. Now, given this, the parties will secret share using the homomorphic secret sharing scheme, their inputs, and now we can locally evaluate using the homomorphic evaluation procedure. So remember what we result in here are secret shares that agree are the correct values except with some probability delta. So of course, one thing that we can do is just run this multiple times independently. And interestingly, in the case of secure two-party computation here, we have an issue not only with correctness, so but also with potentially with security if you reveal whether or not there's errors. So, but don't worry, you can take care of that by essentially taking each of these multiple copies and running another MPC just to securely output the majority value. Okay, and a quick taking a look at the communication required for these three different parts and using a little bit of tricks with hybrid encryption techniques so that we can cut down some of the costs here. Essentially, we get back down to what I promised. So scaling as inputs plus poly and the security parameter times the output. Okay, so going if you're going beyond branching programs, we can actually apply these sorts of techniques directly into larger classes of circuits. Okay, so the intuition is that I want to view my more general more general circuit structure here as a collection of larger branching program gates. And if I have a circuit for which I can do this, for example, essentially all natural non canonical, diabolical circuits can be put in this form. Then now, by running exactly what I told you in the previous slide, we only need to pay for the size of the inputs and the outputs for each of these gates. We don't have to communicate with respect to the entire branching program size. Okay, of course, there's a little bit more work. We have to add take care of the error, but we can basically take care of that by adding the error encoding and decoding straight into this branching program gate here. Okay, so to summarize our results, we give a construction of this Delta homomorphic secret sharing based on DDH for the class of branching programs. This gives us various sorts of low communication secure two-party protocols for computation and also gives this two server generalized private information retrieval. So a couple of reflective comments before I talk about open questions. I think it's very interesting this error parameter Delta in some sense maybe it can be viewed as an analog to the noise that occurs in FHE. Indeed it gives some sort of limit as far as how you can compute. But interestingly, so for FHE if you want to be able to handle to improve the error, you increase the size of the ciphertext typically. Whereas in our construction, in order to battle the error, you actually will just increase your runtime. Another note is that this public key HSS version can actually be viewed as sort of a weak form of threshold fully homomorphic encryption. So the difference, the why is this a weak version is that the parties have secret evaluation keys. But one of the things I guess that we show is that standard threshold FHE is maybe a little bit of an overkill for these applications of secure two-party computation. Okay, so very quickly some open questions. I think it's a really fascinating area that's really just being opened up right now as far as we can tell. So beyond branching programs, this is an obvious question. Is there some way of supporting, for example, multiplications of two memory values directly or doing some sort of FHE style branching bootstrapping procedure? So our construction is really limited to two parties and the reason is exactly because of this share conversion procedure. This stepping along really relies on the fact that we have values that are differing by Z but the payload. Are there ways that you can extend beyond two parties? If you guys were in the spooky session just before here, they showed some GMW style techniques that allowed them to go to additional parties. Unfortunately, it seems that those don't quite work in this case. Can you do a similar approach but under different assumptions? Factoring, for example, RSA seemed very in line with this. Of course, all sorts of optimizing complexity, improving the error. There's a lot to be done there. So with that, I'm happy to report that as of yesterday, we have a complete full version of the paper up on Eprint and I invite you to take a look. Thank you.