As-Salaam-Alaikum-Khawwateen-U-Hazrat. Wasim Hassan welcomes you to lecture number 41 of brand management, MKT 624, at the Virtual University of Pakistan. Today's topic is brand-based culture, the meaning developing an organization which is fully compatible with the strategies that you want to have in place for developing and leveraging your brand. I did give you a very brief introduction to the topic in my previous lecture. And you will recall that the discussion is going to revolve around the importance of involvement of all within the organization. A brand-based organization is not very different from a traditional organization by way of human resource and other resources. What we are going to talk about today is the culture that we need to develop in order to be able to go through all the successive phases of the branding process, the meaning the strategic process and leverage of a brand. Unless we have a compatible organization which is fully geared toward achieving the objectives that we cannot really go for those. So in other words, we are talking about an organization which is very customer-centric and which really involves all its people toward the branding process. Despite the fact that the branding remains the domain of the marketing people. This organization or this culture which is very brand-based is basically driven toward creating a setup in which you like to go for the cross-functional relationships and interactions in order to have the maximum utilization of the human resource and the talent toward making your brand a success. In order to do all this, there has to be a method which can ensure that a cross-functional setup becomes a success. And a method whereby we can make a cross-functional activity or these set of activities a well-structured management process. That is what this kind of culture is all about. While the thrust seemingly is toward creating the mechanism of the joint working. And relationships, there has to be a lot of emphasis on conviction. And on the ownership of the concept on part of all the individuals who are involved in the way that this kind of organization or who are going to be part of the overall culture. In other words, unless there is a very strong conviction on the part of all those who are going to be working for the company to achieve company objectives. There is just no way that the cross-functional working and cross-functional interaction can be a great success. The culture that I'm talking about and the organization or the organizational setup that I'm talking about is very beneficial in relation to the brand management or the brand management strategies. The kinds of the benefits this setup offers could be summed up like the following. First of all, it really throws a lot of light on all the relationships that the people have with each other. And the significance of those relationships as those are viewed from a very strategic standpoint. And the strategic standpoint relates results which you are out to achieve and you must achieve as a bigger company team. So in other words, it really lets you look at yourself or yourselves as part of an overall scheme of things in which the relationships are very explicitly developed and defined and then executed. That's the beauty of this kind of a setup. Another thing which this setup really does to you in a very good way is the measurement of the brand's performance. And that is something which we just talked about in the previous lecture.  Let me recall your attention to all those major and dominant points which I talked about. And you will realize how important it is to have this kind of a setup. The measurement of the brand's performance cannot be given a practical shape in terms of the corrections and in terms of the adjustments. And also in terms of improvements, even if you don't really have to make any adjustments unless you really have people who are like-minded. And who are also into the same mode of thinking and the same mode of action. How is it possible that you really can bring about a change unless that person is fully in the picture and unless that person is fully involved into a certain process which is well structured, which is well defined and in which everyone knows the significance of the relationship and the significance of the execution. And given the fact of execution, the objectives which he or she is supposed to be achieving. So performance measurement becomes easy and straightforward. This is the beauty of this kind of an organization. It also offers us the benefit of looking at the customer, the product and the brand as the things which just cannot be separated. And therefore, all involved within the organization can have the same focus. And when the focus is uniformed, there's no way that the different people who are working for the same objective will work differently. I mean, they will work in such a way that their efforts converge at the point of achievement. It makes the statement about the commitment of the top management. Because without the support of the top management, this kind of culture just cannot nourish itself. So in order to nurture the elements of this culture, it is very important that the organization really has the support of the top management. The top management can support this culture building in so many different ways which I'm going to talk about in a moment. Another benefit is that we become part of the process which is improving itself all the time. And a process where not only the plans, but parts and actions and improvements and different kinds of developments are all owned collectively by all the people within the organization. It doesn't really remain the monopoly of the marketing people which generally is the complaint about marketing people on part of the non-marketing people. That you guys like to monopolize the philosophical thoughts and the whole marketing and branding process. So to make sure that the people within the other parts of the organization are also part of the planning process and the process in which you are living the day in, day out, and in which you all can collectively own the thought process, the action process, and the resultant, the development process. This, what I've talked about, can really be witnessed in any organization which really has a very powerful brand. I don't want to give examples of any brand name or a company name, I leave it to your imagination. You look around and you will see so many different organizations operating within different categories, having powerful brands and hence becoming powerful in the process. What happens is because of the power for which the brand enjoys, there is a sense of pride of being the part of that organization. And that certainly is an organization which is compatible with branding and is the one with a culture which is very compatible with the brand management strategies. That is why the people like Hugh, while they get out of the business schools, like to go for the companies which are very well known because those are powerful companies and those are the companies with very powerful brands. It is that pride which really attracts you toward those companies. And once you become part of those companies, you become part of that culture. So in other words, it also becomes the responsibility of those companies to attract people like you who are willing to mold themselves into that kind of a culture. This goes without saying that the company also has the responsibility of educating and training the people like you, the ones they entered the gates. Well, that's something that we are going to talk about later. Back to the benefits of this kind of culture. Another one is the level of motivation. When you see the people in a particular company full of motivation, that really is a reflection of satisfaction. And the motivation really leads you to work your fullest. So motivation, when it runs across the organization, it makes sure that the implementation of the brand-based strategies takes place to the fullest. That is a very important benefit which this culture offers you. Another benefit of this culture is that it really binds you around the position of the brand because everybody is fully in the picture. And everybody was involved during the process of creating the company's vision, which really led towards the brand's vision. And the brand's vision is the one which gave rise to all the marketing strategies. And therefore, you have everyone within the organization owning that position. And because of that, it becomes very easy for everyone to look at the marketing and the branding strategies from the same angle as you do. In other words, you really can deliver the promise of the brand and the contract of the brand the way it is intended. Because you have total support of your colleagues from different departments. People from the production side and people from the accounting and finance. So let's talk only about these two departments and you will know what I'm talking about. With that support from the colleagues and the members of the overall bigger team, it becomes much easier for the organization to work around that given position of the brand. So delivering on the promise becomes a collective responsibility, so to say, of the total team. The whole focus is on just one point that whenever your customers think of satisfying their needs, they must think of your brand first. They should not think of anybody else's brand. And if you really succeed in creating those kinds of customers, it means that you really have an organization which is compatible with your goals. Another beauty of the organization is that it does not really require extra human resource. You work with the same people. You do not induct new people. You just define and redefine your relationships within the organization in a way that you end up working in a more cohesive manner. And you work in a manner that the achievement of goals becomes easy. There are no conflicts and rather there are convergences. There are no divergent points of views. That is the beauty of the organization. So in other words, it is something which is not just about marketing. It is something which is about the total organization because the culture has to be developed across the different lines. We basically are talking about cross-functional interactions. And it really takes the blame of the marketing people who are, like I said earlier, blamed about monopolizing the marketing philosophy. And therefore you are in a position to go about achieving your objectives in a much more cohesive way. Which in turn means that the achievement of the brand's position and delivery of the brand promise become much less difficult, if not easy. In other words, it is about creating a culture that must support the brand's positioning and brand's promise the two very fundamental and important strategic dimensions to your brand. To be able to deliver the promise, all processes, functions and resources are integrated and reinforced. This is the crux of what I have talked about so far. And these resources and functions, they just cannot be reinforced and integrated unless you have the support of the top management. Top management must come into play and that is what we are going to talk about. The management has to believe in the power of the brand and the management has to believe that the brand has to be managed across so many different functional boundaries. Now this is not to say that management, meaning the top management in most of the cases is not aware of this factor. The factor means that the top management has got to be committed that they have to take certain actions in order to bring the power of the brand to life. That is where the importance lies. In the organizations that have been successful in this kind of an effort, the committees are the small groups responsible for creating this kind of culture so that you really can achieve your objectives is generally headed by the head of the marketing department. Either this group or committee is headed by the marketing manager or by the chief, the branding officer, whoever you have within your organization. There are certain organizations which really have huge portfolios and in those organizations you may have the chief branding officer also. So depending upon who really is the head of the marketing effort, you should head the group which is responsible for bringing into the integration the areas relating the development, research and other strategic functions responsible for strategy making. And of course the chief executive of the company has got to take interest in this kind of an effort. Without the support of the chief executive, there is just no way that this small group but nevertheless the very important senior group within the company can be as successful as it should be. If we believe that brand management strategies are good for the long-term health of the brand and to the company, then the support has got to be generated at the topmost level. What will happen is if we have the support at the topmost level, it automatically will trickle down and then we will have a total executive support within the organization. In order to have the few with the winning brand management strategies we can talk about the support that is needed to be given to those strategies. That support is given in the form of committees. You form certain committees comprising of people from different areas meaning from different functions and they get together in order to make sure that all the strategies are taken into the very realistic light and the execution of those strategies takes place the way that it is planned. Let us start talking about the possibility of the chief branding officer. Now, like I said, I am going to talk about different possibilities which basically relate to some restructuring within the internal organization. You can have a chief branding officer responsible for the brand strategy and its implementation. What this means is that this person should be responsible for the total performance of the brand. Having said that, if an organization opts not to have a chief branding officer, the organization must have what you call the marketing manager. So without getting into the terminologies or the designations, what it really boils down to is that the head of marketing has got to be responsible for the brand strategy and its implementation. In other words, which is total performance of the brand. Now, in order to make sure that the performance takes place the way that it is planned and envisaged, you get into the different kinds and levels of committees and subcommittee. To begin with, the most important committee at the highest most level that you may have in any given organization is what you may call brand management steering committee. This steering committee basically relates to the strategy making. When I talk about strategy making, what I mean is the committee basically is responsible for developing all the requisite linkages which have to be there in place to make sure that the strategy relates to all the functional areas. In other words, the functional areas do end up working for the strategy which basically is a marketing strategy and the linkages and the relationships are there. Knowing that all the strategies flow out of the brand's vision, it becomes imperative on part of the marketing people to involve all others with the meaning from other functional areas to give their inputs toward those linkages. And it goes without saying that this committee, which is headed by either the chief executive officer or the head of the marketing comprises of other members at the highest level from their respective areas. The meaning you have to have the head of the production or operations, the head of finance, the head of any other department that you may have within the company. And there are so many different departments. So to summarize, the committee is headed either by the chief executive or the head of the marketing who may be the marketing manager or maybe the chief branding officer and is comprised of all other heads. The meaning it is a very high level and powerful committee. It is basically responsible for developing all the linkages for the strategy which is already in place. And it goes without saying that the strategy making is a collective effort which starts from the marketing department because I'm talking about the branding strategy. And when it comes to this committee, it doesn't really mean that the strategy making starts from there. What it means is that the strategy which already has been crafted and gets total support in terms of the inter-functional linkages from all the departments that are going to be involved to delivering the brand's promise. And delivering brand's promise means that the product that you manufacture has got to be delivered to all the means, meaning channels and then supported by communication and all that to your target audience. That is how these linkages are going to work in relation to this committee at the highest, most level. Once you have this committee in place that has done the job of the strategy, the making and the strategy assurance in a way, then you have the next level of committee which you may call the Brand Management Directors Committee. This committee is headed by the marketing manager or the head of marketing, whatever his designation is and is comprised of other members who are from the middle tiers to the senior tiers of the organization. Remember one thing, it is not that this committee is again headed by the marketing manager who also heads the steering committee. The steering committee is basically headed by the chief executive and if the chief executive opts out of it in terms of presiding the meetings and all that, he can appoint somebody else who generally is the marketing manager or the chief branding officer. So back to the directors of the Brand Management Committee, it is headed by the head of the marketing and is comprised of people from middle to senior levels from different functions of the company. The basic objective of this committee is to make sure that the Brand Management strategies are executed the way those were planned. So from the standpoint of execution, the committee has a very multifunctional kind of constitution because it is going to involve the responsibilities from so many different areas. It has to be very multifunctional at the execution level, not at the strategy level. So that basically is the difference between this committee and the one I talked about earlier, meaning strategy and then down to the execution level. After this committee, you may have another committee or rather you should have another committee at a further level below and that is what you may call the Brand Management Team or Brand Management Teams. These teams are basically headed by the Brand Manager and are comprised of the members who are holding equal or similar positions within various functional areas of the company. Headed by the Brand Manager like I said earlier, the basic function of this committee is to make sure that the designated objectives are divided and subdivided at the lowest possible level in order to ensure their execution. Because of the level the committee or the team with the Works Act, most of the meetings which the company is going to witness are going to be the meetings relating such teams. And in relation to the execution, all I can say is that the team which you're going to have under one set of circumstances may not be the team for another set of circumstances. That is why I talked about Brand Management Team or Teams, meaning that you are going to change this team in relation to the needs which keep emerging regarding the execution process. Having talked about the different kinds of structures within the organization or rather restructuring of the internal resources spread across the different functions of the company that you are going to come up with these committees and subcommittees based on your needs. That is what it boils down to. This is not to say that every company must have a steering committee and then a committee below that by the name of the Brand Management Directors Committee and then the Brand Management Teams. This is just to give you an idea the way a cross-functional setup should work and the way a cross-functional setup should bring all its human resource into a well-structured and the well-spelt out form of relationships which are the optimal relationships to deliver your Brand Management Strategies with the final objective in mind that your brand must be leveraged and your brand must gain a lot of power because that gives the brand value and that translates into the profitability. That is the crux of the matter. So to further elucidate the point, I can say that the basic effort is the word developing relationships that have authenticity and legitimacy in a very well-structured form. Whether it is that or the well-structured form which really lets your brand management strategies drive themselves and in the process offer your brand a lot of strength and power. All good companies depend on the cross-functional workings because of the cross-functional working that the people from various areas start owning the part of the planning and action process to the benefit of the overall company. It is because of the links, these members of the different committees have their original functions that they are in a better position to train and educate their people back there. By educating their people, they are in a better position to make sure that all the objectives are achieved, meaning the execution which is that their people are responsible for does take place in the most befitting manner. This is a great benefit offered by this cross-functional approach and I can give you a couple of examples of how this really works. Just look at the operational people coming up with an idea which might change the marketing strategy somewhere along the line and the marketing people getting convinced that whatever operational people are talking about makes a lot of sense and had it not taken that into account the problems would have emerged. This is the one example. The other example is if you have the cross-functional teams and the people really own all the planning and action processes, then somebody from accounting and finance may point out something to the benefit of the pricing strategy and you may bring about certain improvements. Another example I've given you in relation to the cross-functional working. My point is that when you involve people from different functions and they look upon themselves as the very active members of those committees that are steering the strategy and its execution, then they assume this responsibility to educate and train their people so that they really can execute the way it is desired. As for new recruits who just joined the companies, I have a few words to talk about, it is very important for the companies to offer those people who have a broad outlook. This is not to say that the people should not really have the specialization in one particular area. Take your own example. If you are wanting to join a company as a brand manager, you've got to be a specialist in the area of marketing. But then what is important is that you must have a mindset and you must have a willingness to really educate yourself in relation to brand-based cross-functional relationships. If you really are going to lock yourself up into the brand management area only then the chances are you may not be as successful as another person who is willing to learn and really improve himself about the cross-functional relationships and all those touch points which have the potential to improve the brand management strategies. Therefore, no matter however someone bright is, unless that person has a versatile approach to divert the management or the issues, or for that matter the brand management issues, there is no way that that person can be very highly successful. So the emphasis on being versatile while still being a specialist in your own area, which is brand management. Now the next step that I really want to talk about is you have the strategy in place. You also have the committees formed for execution. Now what is important as a next step is that you've got to communicate with all that is decided in those meetings of the committees to all the people involved within the organization. Without communication, you just cannot educate your people all across the company and without education, there is just no way that you really can achieve your objectives. It remains something very far patched. So the ultimate objective of the brand-based organization, so to say, is to make sure that the people all across the company really share the brand's vision. They really can uphold the brand's picture and they really can own the brand's positioning. When that happens, it means that everybody within the company is on the same wavelength and you shouldn't really have any problems toward execution of all the strategies involved in place. There are a variety of approaches which are employed by the companies under different circumstances toward educating their personnel. Some of the approaches which are popular nowadays can be talked about here. The one is that you have internal groups focusing on the education through lectures. You have somebody from one of the functions talking about the importance of the cross-functional relationship. It could be the head of marketing. It could be any other head of any area from within the company. It could be accompanying the publications. You go for those publications once a month and through those newsletters or whatever you may call those, you educate your people about the objectives which are to be achieved. You can also talk about the decisions the company has taken and the involvement of the various people from different functions who took those decisions in the hope that the people from those very functions will start owning those decisions and then educate themselves through the material that you communicate. You also can get into some programs in which you invite speakers from the outside world the meaning professionals who really specialize in one area or the other and identifying that you need to have somebody talk on a certain issue. You can accordingly make a decision to invite the best suited person for that issue. You can also have interactive training modules in which the knowledge is imparted to all involved within the organization regarding the differentiation and the segmentation and the positioning and so on and so forth. This is not to develop marketing specialists with a view that you have a shortage of those. No, this is with the view that the people should try to learn different concepts so that they can apply those concepts when it comes to the application of those in the light of their own particular functions. If you are talking about differentiation in your training program and you really want your people educated who are not from the marketing department rather from other departments you would like them to look into those aspects in their respective functional light which means because somebody working in the production area has got to work on that to get the point of differentiation and when that person knows that this basically is the logic and the rationale behind creating and then highlighting this point of differentiation he is going to work his heart out because he is part of the process which was initiated to educate that person and to train that person. So having felt the kind of indebted to the company for the education which was imparted this person is going to work in a very motivated form. Some companies they go to the extent of carrying out research within the organization what they do is they like to study the perceptions of their employees regarding their own brands the objective here is to compare those perceptions with the perceptions of customers in the marketplace you will recall the measurement mechanism while going through the market research the test of customer loyalty or pricing or anything of that sort whether you try to identify what really were the perceptions and once you also have identified the perceptions of your own people within the company you can compare those and look for the gaps and if there are any gaps that is going to pinpoint the area of leading emphasis in terms of education and training the interaction with staff under such conditions really helps the companies to bring their staff members really around the brands positioning and then achieve the brand management strategies that's the ultimate goal and you know what it means in order to communicate very effectively we also have a few tools at our disposal just to make sure that the communication really does its job the first tool that we have at our disposal is that we let the staff know the results of our research this may sound rather the foreign to many of you why should the marketing people share the research findings with the others within the company because generally what happens is there are a lot of questions and criticism and the opinion making in the process because you are sharing something with others and they feel very liberated in order to give their opinions and that is something which generally people do not like but then that also has a positive side and the positive side is when you start sharing your research findings with your colleagues all over the company that really brings them into the picture what really was the basis of developing the brand's picture and the brand's positioning and all the related strategies for managing the brand now this is something which gives your colleagues a lot of confidence in the absence of why you came up with the strategies that you have come up with the support from your colleagues different disciplines and functions may not be as enthusiastic as it would be if you share all those facts and figures letting your colleagues know how your brand stacks up against the competition and what really are the preferences on the part of the customers and what is it that really drives the loyalty towards a certain brand and what is it that is going to drive their loyalty towards your brand given your brand's picture throws a lot of light on the basic factors which make them feel very confident about the creation and the existence of your brand and this is how they assume the responsibility of making that brand a success and that is how they contribute so positively towards the brand management strategies the second tool is all about making sure that employees understand the results company is seeking but what this really boils down to is a continuation of sharing the objectives with different people within the organization when you share the objectives you make them very clear in terms of the results that you are wanting and in order for the results to come you have to gain support of the people at all levels and therefore communication in this respect plays a very important part don't forget that decisions about the responsibilities and objectives were already taken it is only that you are communicating those to all the people within the organization at various levels for different levels of objectives to be achieved and for different results to be achieved the role of the cross functional teams gains importance all over again here it is because of their role and their links with their original departments that this communication becomes effective and easy in order to have their people achieve the results which are to be achieved another tool that we have at our disposal is letting your employees know the action plan what this really means is that employees within the company have to be guided about their actions everybody is a part of the action plan no matter what area he or she is working for tell them specifically about the changes in their routines and procedures and any changes to that the effect have got to be formalized because otherwise people are going to come up with excuses that is for sure you have got to educate those people about those routines and the changed procedures not only educate them verbally you also have to formalize those with the help of things like the standard operating procedures and any changes to those procedures this is one of the factors that was talked about in one of the earlier lectures and I hope that you do understand the importance of the standardized procedures the objective here is to translate all the actions on the part of the employees into targets and then measuring their performance against those targets it is because of this reason that you like to share the action plan with employees this not only brings you their support but this also makes sure with the help of defining the targets their performance let me summarize the concept of the brand based culture in the light of the lecture I have given today there are two concluding dimensions to the whole concept the one is that we have to have the top management brand management strategies a success the second concluding dimension is that all employees of the organization have got to be educated for the common goals unless employees are educated about the strategic intention the strategic goals and all the actions that they are a part of there is no way that they are going to work for the overall strategies and there is no way that they are going to harness the total potential of the brand to work complete profitability and leveraging the lecture comes to an end Allah Hafiz until the next one


The next talk is about zero-knowledge arguments for matrix vector relations and lattice-based group encryption and this work is by Benoît Libert, Saint-Lin, Fabrice Mouartem, Roi Nguyen and Roi Xiong Wang and Roi will give the talk. Can you switch on the microphone? Okay, thank you and hello everyone. I'm going to talk about construction of lattice-based group encryption scheme and the zero-knowledge arguments necessary for that construction. This is a work with Benoît Libert, Saint-Lin, Fabrice Mouartem and Roi Xiong Wang. Okay, so first I will recall some background on group encryption and discuss our difficulties towards realizing lattice-based group encryption. Then I will state our results and describe the techniques that we use to overcome the difficulties. Okay, so let me start with group signatures, which is an important anonymous authentication mechanism proposed by Kelvin-Vanhest in 1991. In this setting, we have a group of users and each member can anonymously sign messages on behalf of the whole group. This means that group signature app is hiding the source of the message within a group of registered signers. Group encryption is a primitive introduced by Kyat, Sunit and Yung in Asia Crypt nine years ago. It is an encryption analog of group signatures. Okay, so we have a group of registered receivers and each sender can encrypt messages to anonymous group members. Okay, so in this way, group encryption armed to hide the destination of the message within registered receivers. Another interesting feature of both group signature and group encryption is that the users are kept accountable for their actions. In case of this build, there is tracing authority and opening authority who has some kind of secret key and who can identify the signer of the message or the receiver of the cybertext. Okay, so more formally, a group encryption scheme allows encrypting while proving that the following hold. First, the cybertext is well formed and it is intended for some registered group member who will be able to decrypt. Second, the opening authority should be able to identify the receiver should the message arise. And thirdly, the plan test should satisfy some properties like being a witness for a public relation or being a private key for a given public key. Okay, so this additional requirement may be useful for spam protection. As spotted by KGY, some possible applications of group encryption are in the context of 5.1 filtering for anonymous strategic third parties in cloud storage services. Group encryption also implies hierarchical group signature, which is a general form of group signatures. Okay, so let me now briefly review some previous work on group encryption. In the work that introduced group encryption, KGY also provided a modular design that based on ordinary digital signatures, anonymous secure public key encryption and interactive zero-knowledge proof. They also demonstrate concrete instantiation based on number theoretic assumptions. Okay, so the KGY scheme only considered interactive setting, but the scheme can be made non-interactive in the random oracle model via the phasomy heuristic. Two years later, Cataloeton introduced a non-interactive construction in the security standard model under parent bay assumptions. Subsequently, NM&E and CHO chairs suggest various improvements for constructing group encryption. Okay, and Libert et al. proposed a refined traceability mechanism that allowed to identify on the cybertext intended for specific group members without affecting the anonymity of all the other members. Okay, so for the time being, on existing realisation of group encryption rely on traditional number theoretic assumptions. So usually we don't want to put all of our eggs in the same basket. So it's maybe worth considering construction from other assumptions like a lattice base. So lattice base crypto is interesting and lattice assumption is still resist against quantum computers. Okay, so let me move to the context of lattice base crypto and in particular consider lattice base groups of natures. And this is a very active topic in the last six years. The first construction were proposed by Gordon Cat and Wacontana Tan in Asia Crypto 10. Since then various improvements have been made in terms of security, efficiency and functionality. And the most recent scheme already achieved the logarithmic size in the number of group users and work of dynamic groups when the first construction only achieved a linear size and only can handle static groups. Okay, but no lattice base group encryption so far. So we ask the question, what's the main difficulty here? Okay, so given that both of the primitives can rely on almost the same component like ordinary signatures, public encryption and supporting zero knowledge proof. Okay, so in the next I will describe that the main difficulty lies in the problem of constructing a suitable supporting zero knowledge proof for group encryption. Okay, so let's consider the existing zero knowledge protocols that's used for handling lattice bedulations. In previous work, under protocol in previous work can be categorized into two main classes, snorly and stent-like. Okay, snor protocols were originally proposed for handling discrete log relation, but it was then so very useful for lattice relation by Lubaszewski who introduced the rejection sampling techniques. On the other hand, stent-like protocol was first proposed in the context of code bay crypto and it was first considered in the lattice setting by Kawachi Tanaka and Sagawa and then it was empowered by Lindaton with TechnicCon, the combo season and extension. We observed that Zika two classes of techniques mainly deal with linear relations in the sense that the equation that contains only terms of the form of public matrix multiplied with some secret vector where the secret vector may satisfy some additional constraint like asmonics or have some special arrangement of entries. Okay, so the typical example of the kind of relation is the ISS relation and the LW relation. In the ISS relation we have an equation A times X equal to U mod Q where the matrix A and vector U are public and the secret vector X is small. The LW relation as represented by the equation A times S plus E equal to B where matrix A and vector B are public, vector E is small secret noise and the secret S may be small. Okay, so this also holds Zika two classes also work for encryption scheme based on LWE and signature scheme based on SIS problems. Okay, so now let me go back to the context of lattice bay group signature and see how the techniques work well for group signatures. A modular design for group signature is concise and encrypt and proof. It consists of the following. First, each user has a signature system on his identity ID and that signature is issued by the group manager who manages that group. In the process of generating group signatures then each user he asks to encrypt his identity ID to a cyber taxi and that is done using the public key of the opening authority. Then the signer has to prove in general knowledge that the following holds. First, he has a secret valid message signature pair with respect to the manager's public key. That means that he is a certified group member. Second, C is a well-formed cyber text of ID with respect to the public key of the opening authority. That means that he has done the encryption honestly and the opening authority can recover ID should the needs arise. Okay, so if we use SS Bay signature and LWE encryption then the relation underlying this statement can be represented by linear equations and it can be handled by previous techniques. Okay, so now if we consider the context of large group encryption then things become more complicated. Okay, so the modular designs by KTY he has followed. His member has a key pair SKPK for an anonymous encryption scheme and the manager signs the member's public key PK and public the pair PK and the signature system. When the sender wants to send something to the group, so a message meal, then he uses PK to encrypt message meal that satisfies some relation R and obtain a self-taxed C. The sender also encrypts the public key PK under the public key of the opening authority and obtain a self-taxed CLA. Okay, that's for enabling the opening feature. Then the sender has to prove that the following two parts. First, C is a correct encryption of some message meal with respect to a hidden public key. And second, the sender knows a valid signature system on that PK with respect to the public key of the manager and that COA is a correct encryption of that PK with respect to PK-OA. And also the message meal satisfies some relation R. Okay, so we observed that the statement in the second part are similar to the one appearing in the context of lattice-based group signature and it can be handled with previous techniques. The challenging part is essentially the first part where everything except for the self-tax is hidden. Okay, so even the public key that the sender used to encrypt the plan test is hidden. Okay, so if we use some LWA-based encryption for this, then the problem would boil down to proving an LWE relation with hidden but certified matrix as you have the form X times S plus E equal to B mode queue. Where this matrix X here is also hidden but we additionally have to show that we have some signature on it. Okay, so we call this quadratic relation and we identify this at the main obstacle on our way towards realizing lattice-based group encryption. And our common difficulty likely requires some new ideas. Okay, so now let me state our result and describe the techniques we use. In this work, we introduce a yellow knowledge argument for quadratic relations. So it's including the relation that I described where matrix X and vector S may satisfy some additional relations. Our approach is to develop sense protocol and to improve its capability from handling only linear to handling quadratic relations. In the process, we propose some new techniques that may be of independent interest. Okay, so once this most difficult part is realized, so we can use to build the first lattice-based group encryption scheme. The scheme is proven secure in the KTY model under the SIS and the LW assumptions. Okay, so now let me recall Stan's clever ideas. Stan's protocol is a yellow knowledge protocol for the syndrome recording problems where given public matrix A's and public vector U, we have to prove that we know a secret binary vector X and we have fixed him in way W. So Stan did it with two main ideas, first permuting, which means to prove the constraint of the witness using random permutation, specifically the proven sense to verify a permuting vector pi of X. Okay, so we observe that the following equivalence holds vector X has the constraint binary vector with weight W if and only if pi of X does. Okay, so if the verifier sees that pi of X has this constraint, he should be convinced that X is a valid witness. And moreover, because pi is random, it completely protects the actual value of X from the verifier's view. The second idea is markings. That means to prove the linear equation using a random masking vector R.  Okay, so let's go back to our quadratic relation. We will employ a two-step solution. In the first step, we will pre-process the given quadratic relation so that we obtain somewhat more familiar form. Second, we will exploit Stan's idea, especially the permuting idea, where we will set up some kind of permutation into a similar equivalent like the apparel and then exploit the random permutation. Okay, so in the first step, we transform the term matrix X times vector H into the form of a public matrix times a secret vector. To this end, we do the following. First, we write this one at the sum of all of the product Xi si, where Xi at the columns of matrix X and Xi at the entries of vector S. Okay, so all of them are elements of ZQ. Second, we look at each of the terms Xi times Si and use a decomposition matrix to break on the entries of vector X into binary and obtain an equation that Xi times Si equal to that public matrix multiplied with a vector whose entries are X ij times Si, where X ij are binary and Si are still element of ZQ. Next, for each of these terms, X ij times Si, we do the same decomposition process and obtain the form that... Okay, so it can be represented as a public vector multiplied with a binary secret vector. So, combining all of these sub steps, we will obtain the form X times S equal to Q times Z mod Q, where this Q is a public matrix and vector Z is a binary secret vector. Okay, so this looks quite familiar, but actually the harder part is still ahead. Why? Because vector Z is still quadratic. It still has some kind of quadratic nature because each of it... NG is a product of a bit from matrix X and a bit coming from vector S. Second, the component bits also additionally satisfy other relations. Okay, so now we go to the second step when we handle this vector Z. We will employ a divide and conquer strategy where we view the whole problem as a bunch of sub-problems. Where for each sub-problem, we aim to prove that a secret bit Z has the form Z equal to C1 times C2 while preserving the possibility of demonstrating that the component bits C1 and C2 satisfy other equations. To this end, we will use a permuting technique that's based on two bits. Okay, this follows. First, for every big C, we denote by bar C the bit 1 minus C. Then for every two big C1 and C2, we define a vector... a binary vector of length 4 that we call extension of C1 and C2 whose entries are the following. First, C1 bar times C2 bar. Second, C1 bar times C2. Third, C1 times C2 bar. And fourth, C1 times C2. Okay, so now for every two bits, B1 and B2, we define a permutation called T of B1 and B2 that transform an integer vector of length 4 that we call V whose entries are V00, V01, V10 and V11. Two, the vector whose entries are V, B1, B2, V, B1, B2 bar then V, B1 bar, B2 and V, B1 bar, B2 bar. Okay, so why should we come up with some kind of artificial permutation? Okay, the final goal is to obtain an equivalence. Okay, for all of C1's... all of the big C1, C2, B1, B2, we have the equivalence. But the V is the correct extension of the big C1 and C2. If and only if the permutation T, B1, B2, of V is the correct extension of two bits, C1, XOR, B1 and C2, XOR, B2. Okay, so how does it work? Let's consider an example to see what's happening here. Suppose that C1 is 1 and C2 is 0 then V, which is the extension of C1 and C2 would be the vector consisting of the entries 0 times 1, 0 times 0, 1 times 1, and 1 times 0 would be exactly vector 0, 0, 1, 0. Okay, so we look at the entries of this and we denote by V, 0, 0 is 0 V, 0, 1 is equal to 0 V, 1, 0 is equal to 1 and V, 1, 1 is equal to 0. Now, let's consider the permutation. Suppose that we will permute with the two bits B1 equal to 1 and B2 equal to 1. Then the permutic vector T, B1, B2, of V will be the vector V, 1, 1, V, 1, 0, V, 0, 1 and V, 0, 0 which is the vector 0, 1, 0, 0 in this case that is exactly the extension of two bits 0 and 1 and 0 is exactly C1, X of B1 and 1 is exactly C2, X of B2. Okay, so how can we make it useful? Actually, this already gives us a solution to the sub-problem. To do this, we first extend this secret bit Z to vector V, which is the extension of C1 and C2 the two component bits, then we permute this vector V with random bits B1 and B2 and give the verifier the permutic vector. Okay, the verifier can check that the right hand side of the equivalent host which convinces him that the left hand side also holds and which convinces him that the original bit Z must be well formed. Furthermore, the random bits B1, B2 here essentially act as kind of one-time bits that perfectly hide the value of C1 and C2 from the verifier's view. Okay, so secondly, we also have to prove that the same big C1 and C2 satisfy all the equations. So to do this, we set up a similar mechanism where all the appearances and use the same one-time bits at all of Z places. So that's the main idea. So once we have the solution to this sub-problem, then we can also obtain the solution for the whole problem. Okay, putting everything together, so our Neustern-like techniques allow us to handle the quadratic relations. And to instantiate our group, let's say group encryption, we use the following ingredients. For encryption, we use an anonymous CCA2CQ public key encryption that obtained from the ABB identity-based encryption via the CSK transformation. For signature, we use the signature scheme that will appear as a conference in my college, Fabriz, we present it to you tomorrow. The signature scheme interacts with zero-knowledge proof. And finally, combining with known Sturn-like techniques for encryption and signatures, we obtain the zero-knowledge protocol that is required for the group encryption construction. And that's it. Thank you. So unfortunately, we're quite late, so let's skip the question session and give people a chance to switch tracks. Thank you.