Back in the chapter on iteration, we used a for loop to iterate through, or traverse, a list of data items. This program takes a list of integers, and then, with a for loop, takes each item in the list and prints it out. Like this. This list is a collection of integers. We can think of a string as a collection of characters and use a similar for loop to get each character in the string and print it out. And here's the result. Another way to traverse a string is by using a for loop with an index. We'll take an index that starts in the range from zero up to but not including the length of the string, which is exactly how the positions in a string are numbered. And each time through the loop, we'll print the character at that particular index. And here are the results. Unlike our first for loop, one advantage of using an index is that you don't have to process every character. For example, we could process every other character by starting our range at zero, going to the end of the string, and incrementing the index by two every time. And there's our output. Or you could find where the first space in the word is by using the find method by running the index in the range from zero up to space index and printing those characters one after another, and that would give us the first word in the string. It's also possible to use a while loop to traverse a string. If you're going to do that, you need to set the index to its initial value before you enter the while loop. Here we're using a compound condition for our while, as long as the index is valid and we haven't reached the first blank in the string, we'll print the character at that index and then we'll move to the next position in the string. Remember that while doesn't automatically add to the index. You have to do it yourself or you'll end up with an infinite loop. And when we run the program, we again get the first word in the string. And there are three different ways to traverse a string with a for loop by item, with a for loop by index, and with a while loop.


Alrighty, we should be live. Now we're really live. Welcome everybody. Welcome everybody. We're just going to wait one or two minutes to let everybody get joined properly and get settled in and then we will go ahead and get started with content. For the time being, we are just going to wait one or two minutes. So definitely just hang tight and we will get started shortly. As we wait, feel free to use the chat function. I just threw out a little message. You can let us know where you're joining us from today, what kind of work you're managing, scheduling for. It's always fun for us to get to know you all a little bit better before we actually get started. Helps pass the time and it actually helps us to get to know you all better before we start with any questions. Tori and I have worked at 1iWork for quite a bit of time and we have talked to so many users, so many different companies and we've seen a ton of different setups. So definitely just chat us, let us know what kind of work you're managing for and also where you're joining us from.  So we schedule for lots of users all around the United States, but also all around the world. And even when it is really cold in Minnesota, where when I work is based, I always had somebody chatting in from the Bahamas or somewhere really cool. So definitely let us know. Awesome. Welcome everybody. Welcome Jennifer from Scottsdale Medical Network scheduling. Awesome. Paul from Dallas. We've got a couple from Texas. Welcome everybody. And Caroline from the UK. Like I said, we schedule for users all around the world and I see a ton of users in the UK. So welcome from across the pond. And LA for non-profit. Thanks everyone for chatting. It's a really great way to just use this time where everyone is, you know, jumping in even last minute. So I don't want to take up too much time, but I want to make sure everyone's ready to go before we get started. Awesome. I'm seeing so many different kinds of businesses today hopping on. Again, we schedule for not only one type of business, but for tons and tons of different types of businesses, different use cases and setups. So we can probably find a good setup for everyone. And of course we could help figure that out as well. Welcome Joyce from Virginia. Awesome. Wow. So many cool use cases today. Thanks everyone for those of you who chatted in. So nice to get to know you all and welcome to the webinar. It looks like just as I said that we had one more person jump in, but it looks like we probably are pretty good to go ahead and get started. So I just wanted to welcome you all one last time to the When I Work live Q&A. We're so happy to have you all join and we're excited to help you get started with When I Work. So during the next 30-ish minutes, we are going to be answering your When I Work questions.  But the content that we will be talking about will be directed by the questions that you all ask. So the questions are going to be flowing in and we're going to get to as many as we can, we promise. But if your question doesn't get answered or you would like some help for something else, anything, you can always chat with us after. So listen for more information on how to get in contact with us. We're going to go over that probably during the webinar and then definitely at the end as well. If you're totally new to When I Work and just checking out your account, going over the plan that might be right for you, we will go, we will show how you can upgrade your account and go over different plans at the end if you really liked the tools that we're going to show you today. And if you're joining us to kind of ask questions on your existing account and you're already, you know, grooving on your account, we welcome you as well and you're welcome to ask questions here as well. So basically anyone here is welcome and invited. So the way that this works now that I said that way that this works is we're going to use that Q&A bubble. So not that chat bubble that we've been using just now to get to know each other. We'll turn that off and then we'll use that Q&A portion. That tool is going to be where you can put all of your questions that you have today. Tori is going to be going through those kind of asking out loud as many as we can get to. And I'm going to be sharing my screen and kind of giving you a visual demo to the answers to your questions.  So with that, you can pop all of your questions in that Q&A section. And I'm going to flip my screen over to my When I Work account. Bear with me. The hardest part, hardest thing I do. All right. So this is my When I Work account. I am logged in right now as the main admin or just essentially the user that created the account. When your employees log in, if they do log in on a computer like I am now, they're going to see a view pretty similar to this, but they won't have access to seeing everything that you can or changing any the schedules or settings like I can on this account right now. But just seeing this is pretty much a good idea of how your employees will see the tool and see their schedule as well. The top menu bar here is kind of your main navigational section for When I Work. It'll bring you to the different landing pages for our different tools, like our scheduler, our attendance tools, so clocking in and out, and then of course, WorkChat, our in-app messaging system. And then on this side of the top menu bar, this is where you can add any information into your account and change any settings. So that's kind of a really rough overview of When I Work. So we can just go ahead and get started with any questions that we have. Awesome. We got a first question that came in. I feel like it's a good way for us to get familiar with the scheduler and some of the different tools that we have. So this person is asking, what's the best way to set up a bidding scheduling system for my team? And then they followed up with they need to be able to bid by seniority and job type. They are also bidding on schedules that are for a period of 12 days. So just, yeah, if you could highlight some of the options available and When I Work for that would be awesome. Definitely. I will go over how you can create an open schedule and a schedule where your employees can bid or request on those shifts. But just for a background on how the When I Work scheduler works is that you will be creating your schedules within the scheduler tab here. And some users choose to create shifts for their employees and then actually just publish those shifts out directly to their employees. So you can see the day and the employee that this is the sell for. You just click into there and add in a shift that your employee can work. But not all workplaces work like this. And that's why we created an awesome tool called OpenShift and OpenShift requests. So our OpenShift section here, it's just this green strip up top. This is where you can add in all of the shifts that you need covered for your workplace, but shifts that you don't necessarily want to publish out directly and assign directly to your employees. You can just publish out the shifts and then have your employees either request or bid to work those shifts or grab those shifts first come first serve. So the way that you would set that up is essentially just doing it the same as scheduling out directly for your employees. But you would use the OpenShift section up here. It's just that green section and you can add as many shifts as you need for your day. If you have a specific type of shift, you can add as many as you need. And then what you can do then is you can either publish out those shifts. And if you publish them out just as so, your employees would be able to grab the shifts first come first serve based on their qualifications. So that would be the schedule that they're tagged to the tags that they are assigned to you and the positions that they are assigned to. If you want to set up more of like a shift bidding or shift request setup, you can too. So your OpenShifts don't have to be first come first serve, grab them if you want them. You can put a little bit more control over your OpenSchedule or OpenShift schedule. And the way that you would do that is just for each of the shifts that you need to have picked up and covered, you would require a pickup approval for that shift. So essentially your employees who are qualified again by the positions, schedules and tags that they are assigned to, your employees could request to pick up a shift. You or a different manager could then go into your shift request section up here. And then you could essentially allow one specific person who signed up out of the list of employees who signed up for the shift to take that shift. So this is a really great way to make sure that the right users, the right employees are actually working the right shifts and you can make sure that the right seniority and the right employee is actually covering the shifts that you need. And it just looks like you are muted. Yeah, seriously. That's what I get for not wanting people to hear me type. All right, so we have a couple questions on availability. So the first one is just a basic, how can my team upload their availability? And then somebody kind of has more specific question about availability. So it is how are availability preferences managed differently than requirements? For example, an employee is available on Monday from 9am to 11pm at any location but prefers working mornings at a certain location and prefers to not work with particular coworkers? Definitely. Those are good questions. And I really, really like the availability tool, just a background on why I like it. I think it's just really helpful for both you as the manager and your employees. You know, you are getting employees who can work the shifts, who are going to show up, who are going to be happy with the shifts that they are receiving, and your employees are just going to be happier for it. So I think it's just such a mutually beneficial tool. And I love all the use cases I've seen with the availability tool. So the first thing I'll show is actually how your employees can go ahead and input that availability. And then I will show how you can input the availability and then how you can interpret the availability and schedule shifts for your employees based on that entered preferences. So again, the first thing I'm going to show is how your employees can input this availability.  They would just be presented with a calendar just like this and they would then be able to add their preferences. So either they would choose I'm unavailable to work and that is an unavailability preference or I prefer to work, which is an availability preference. They would choose which one they need and they would choose either all day or a specific time within that day. And then they can also repeat that preference as well. If you want your employees to input any other information about their availability, I would suggest using the note section. So more information on maybe where they prefer to work, who they prefer to work with. I would indicate that on their on the notes or you could also add this within your work chat or your chat messages. You can also hide these availability preferences and not everybody can see them and you can hide everyone's schedule from each other. So not everyone would be able to read those preferences and things like that. So once they've added these preferences back in the scheduler, you can actually add preferences in for your employees as well. So you'd be editing your employees availability preferences. So you can always do that for them on their end. When you actually go to schedule your employees in the scheduler, you'll see these little green and gray tabs on your employees cells. And a gray tab indicates an unavailability preference and a green tab indicates when your employees prefer to work or can show up for their shifts. So when you hover into those shifts, you can see that any shifts that kind of are conflicting with the unavailability preferences will be grayed out. So you can make sure that you pick a good shift or a shift that isn't grayed out for your employees. So you know that they will be able to show up for those shifts. And then a green, this is a preferred day. You can see that all these shifts are good thumbs up and you can assign those shifts to your employees. Back in the unavailable day, an unavailable preference is just that it's just a preference. So it's not an official time off request or any official request to not work. It is just that guide to help you manage the schedule and to help employees get shifts that they are able to work. So you can definitely schedule over an unavailability preference, no problem. You will get a little red tab indicating that you have done this, but there's nothing wrong with this.  So the time off tool is those official time off or PTO requests from your employees. And if those are, if those requests go through, they'll show up just like this in the schedule and it'll block out the employees from actually being scheduled for the day. So that kind of difference between the time off tool and the availability tool is important. And just to make sure that your employees know that before they start using the availability tool.  If it's not right for your business, if availability isn't the way that you roll, that's fine too, and you can turn that tool off. So you're just muted one more time. I was pressing the space bar, I swear. No more muting, I'll just be quiet. So just a follow up to the availability preferences. If you're using the auto scheduling feature, can that respect availability preferences or unavailability preferences? Oh, great question. We, for those of you who don't know, we do have an auto schedule tool. If you are using these open shift section, and you don't want to publish out the open shifts for your employees to grab or request, you can actually use a tool that we call the auto scheduler. This is going to push out all of your coverage in your open shifts section to your employees based on their qualifications and based on their preferences and time off requests. And then when you do click the auto schedule tool, you'll be able to configure those settings. So if you do want to respect unavailability and availability, you can turn those on and off. So it's also a really good tool if you're using the auto scheduler words today. If you are using the auto scheduler, it will take those preferences into account. If you do configure that within your settings, and this is super helpful. If you just want to take that extra step out of scheduling and make it super easy, fast, and streamlined, I think it's just such a good option. Great. All right. So I have somebody that's asking about our annotations feature. So how can I annotate all weekends as the business being closed without having to do it day by day? Awesome question. I don't get too many questions about annotations, but they're so helpful for just bringing your schedule and when I work to kind of the next level. I really like this tool as well. So the annotations show up as these little thought or speech bubbles on a certain day within your scheduler. When you click these on, you can always choose which schedule they show up on, a title for that specific request, or, and then you can choose what you want the annotation to be about. You can include a little message. So this one would be business closed. You can choose a start and end date for that annotation, and then click save. And that will basically block out your day if you don't work Sundays, for example, it would block out that day and your employees would know that no shifts will be scheduled on that day. So even if you don't want to use business closed, annotations can also be used to not allow time off, which is a really cool tool. So if you want to make sure that there is a specific day that you don't want any employees to be calling off, you can use the annotation tool for that as well. And then you can use your announcement tool as well if you just want to let your employees know something important for that day. And this is bringing you to the next level for your schedule, just making sure everyone's on the same page. So I really like that tool as well. Awesome. And so annotations can be created for a single day or date range. There isn't an option to set them to repeat. So like if you need to set an annotation for every like weekend, those would have to be created, but you just need a single one for both days on those weekends that you would just adjust the date. But for each weekend, they would have to be created at this time. Yes, sorry, I forgot the main part of the question. I got so excited about annotations. But yes, you're exactly right. So if you are doing that weekend, make sure that you do, you can do the entire weekend at once using the date range, but you would have to be creating those every week. But if you just sit down, you can schedule as far ahead in the future as you want. So if you just want to take a bit of time one day, create those for the next couple of months, you definitely can do that with our scheduling plan. You can schedule as far ahead as you need. Awesome. Now we have a question kind of relating to the attendance, the time clock and attendance platform. So somebody is asking, is there a clock in and out area for shifts and also breaks? Yes. All right. I know we had a couple, I was chatting to somebody earlier who I knew was going to have a question about the attendance tool. So I'm really glad that we are going over it now. And I really like the attendance tool. It is going to just create that streamlined employee management system out of when I work. If you are using the scheduler and then tacking on attendance, you'll be able to create those shifts for your employees when your employees should work and then having the clock in and out for the times that they actually work. And this is just really going to work well together. So I'm just going to actually hover over the attendance tool and click into my time sheets to show you all more. So in when I work, employees can clock in and out three ways. So the first way would be having them clock in and out on their personal computers. They would just log into their accounts just like I am right now. They would hover over the attendance tool and just click clock in. The second way would be an onsite specific option. You would lock a device, so a computer or a tablet as a time clock terminal. You can lock it here if you're on your computer and you can lock it on the time clock terminal app if you are using an iPad or an Android tablet. And essentially your employees would come into the workplace, locate the device, and they would type in their code or their email and just click clock in to clock them in. The third way and I'll show more about this option would be to have employees clock in and out on their mobile phone. I tend to see this as the most popular option, especially these days where we want everyone to kind of be touching their own devices and employees and managers tend to love this option as well, but that would be mobile clock in. Your employees would essentially just see a big green clock in button at the bottom of their when I work app and they would just be able to click that button and that would clock them in. When your employees clock in and out, you'll be able to see their times populating onto their time sheet. So when they do clock in, you can see that their clock in time will appear and then when they clock out, the same will happen. Within the detail section of their time sheet, you'll be able to see all the information about their clock in. So how long their break was, which schedule and location they clocked in at, and then of course, what shift or what position they are working during that time. Then at the end of your payroll summary, you can see all the different payroll periods here. You'll be able to close the period and when I work produces a payroll summary for you. So it's really slick and a really great option. And we also do have quite a few payroll processor integration. So if you have any questions on that, we can definitely go over those as well. But I did actually want to quickly show how you can turn on and off the different clock in tool options. And that would just be hovering over the gear icon and clicking to attendance settings. If you don't see your attendance settings showing up, that might be because you haven't activated your attendance tool yet. So if you don't see these, make sure to hover into your attendance tool and just click on it and it will guide you through a guided setup first if you haven't attached or started this tool yet. So if you're interested, definitely just click on the attendance tool and will guide you through a little bit of onboarding and turning on that tool. Once you've done that, you can see the attendance settings and this is where you can turn on the different clock in methods. So if you want your employees to clock in and out with their mobile app and not their personal computer, you can do that. You can turn on both or one or the other, whatever you really choose, and make sure to save your preferences as you go. And when you turn on these different tools, your employees will see the clock in and clock out button populate onto either their phone or their computer. And then I almost forgot to talk about breaks, but we do have unpaid breaks that your employees can clock out for. So if you have clocked in for a shift, your employees will actually see a take break or take lunch icon. So when they are clocked in, that take break or take lunch icon will appear and they can take their break at any time. So when they do that, again, back in the time sheets, you'll be able to see when they actually clocked in and out for those breaks. In this case, I added it on my time sheet. But if you hover over it in your cases, you'll be able to see when your employees clock in and out. All right. I'm not muted. All right. So we have a question. So it's mostly around a work chat and messaging, but I'm going to just read the question because it's a little specific as well. So we have technicians working with us. It'd be ideal if they could access our central support team via live chat versus text message as they do now. Would your in-app messaging system work as a live support team chat for troubleshooting? That's a really good question. I know I was just thinking about that. I was trying to figure out a way to pare it down, but it's just a good question. It's just a good question. So background, we do have an in-app messaging system where your employees or anybody added into the account specifically will be able to chat back and forth with each other or create new channels or speak within the main channel for your workplace. So only anybody who is added into your account will be able to use the in-app messaging system or work chat like we call it. So if you did want to create kind of like a hotline or a big messaging system, you could use that for support, having people on live, texting back and forth, not texting or messaging back and forth. You definitely could do that, but just keep in mind that only people that are added into your account would be able to use work chat. So if you want to add everyone in like as a support team, you can add a support team in there, add in all those employees and they'll definitely be able to use the work chat and be kind of live for any troubleshooting messages that need to happen. You could even create different channels for maybe different types of messages. So yeah, that would definitely work as far as I'm concerned, as long as you kind of know that all the team needs to be added into your Oneiwork account. So I think we got time for one more question. Annabella is asking, will attendants know if an employee works at more than one location so that they are able to successfully clock in from any location or the location associated with their shift? I think I understand the question. So I'm just going to draw over all the different things that I'm thinking in my head. And we do have ways to kind of monitor where your employees are scheduled so your employees can clock in and out at the right locations. So in the scheduler tab here, you can see that I have two different schedules created right now, one for each of the retail locations that I have for my account. So here you can see Rachel is actually scheduled for three shifts at a different schedule or a different location. So this is one way that you can make sure to not double book your employees for shifts. So you can see that you wouldn't be able to schedule her first shift at this location at these times, but this time would work. So you can see that now Rachel has one shift scheduled at the east end schedule and one at the central schedule. And you can toggle back and forth between these schedules just to see all the shifts scheduled at the different schedules or locations. When your employees are clocking in and out for their shifts, you can turn on location restrictions so your employee can only clock in and or out at the location that they're scheduled at. And this doesn't have to be monitored just by schedule location or different schedules. You can also use our job site assignment or job site tag on your shifts to indicate where your employees shifts take place. So you can see this is location A where the shift is taking place when your employees try to clock in or out. In this case, they would have to be at their job site location. So hopefully that answers the question. And if it doesn't, I will actually right now go over how you can get in contact with us because I think that was a good question. Anything that has to do with like clocking in and out restrictions and locations we probably can handle. But I will show you how you can get in contact with us right now. And I'm going to change my screen one last time. All right. So I did quickly as we end want to go over the plans that we offer. We've made it super simple and super easy to choose the plan that's right for you. We essentially have that small business plan for up to 100 users. That's going to include all the scheduling, communication tools that I showed you. And then if you need any time clock or attendance tools, that just comes with simply the attendance add-on. So you either would just use just the small business scheduling or small business scheduling plus attendance add-on if you want to use the awesome clocking in and out tools. I'm not going to go over those too much. But if you want to check out what your price might be or what is in each plan, you can find that information from our pricing page or from your account and billing page directly within your account. So it's super easy to go to that page, see which tools you might need, toggle on your tools and your billing frequency, and then your amount of employees. And then you'll be able to see what your monthly cost might be. So you can actually just do that all from right within your account on your own time. No need to get in contact with anybody. It's super simple and easy to guide you through on your end. But of course, if you have any questions as you go, that's why we're here. That's my job. I would be happy to answer any questions you have as you go. For example, if you have any other questions about job sites, multiple schedules, how to clock in and out, or just the best use case setup and plan for you and your business, we are here to help. You can contact us through this need help tab or the little chat icon at the bottom right hand corner of your screen. And then of course, if you don't have an account yet, you can get in touch with us at gettingstartedatwheniwork.com and we'll be able to answer any questions that you have as you go anywhere that you get stuck or if you need any advice. We're here to help. And we should have a little bit of information. Oh, Tori already put it in there. Awesome. So if you navigate to the chat bubble, this is where Tori just threw out all of the resources that you need to get started. This is essentially just a getting started onboarding packet that we have created for you. So if you want, you can copy and paste all of that information to your computer or whatever. And these are the links to getting started for an account, our help center, our team training center, and other options on how to get in contact with us. So definitely give that a look, copy and paste that. It's just going to give you everything you need to get started. So with that, thank you all for your questions. Thank you for attending today, taking your time to actually be here. We really appreciate it. It's great getting to know you all and the different setups that you are looking for in when I work. And again, let us know if you have any questions as you get started. We'll be very happy to help. Thanks, everyone. Bye.


The Navy has resources for your family to get the most up-to-date information and even contact you while out to sea. The Navy ombudsman is one of those resources. Ombudsmen are volunteers appointed by the commanding officer to serve as an information link between command leadership and Navy families. They're trained to disseminate information, Department of Navy information, command climate issues, and good deals around the communities such as events, tickets, entertainment, etc. They also provide resources and referral and are instrumental in providing assistance before requiring immediate command attention. To find your command ombudsman, go to ombudsmanregistry.org. From the Defense Media Activity, I'm Petty Officer Brandy Wills.


OK, we can start. So welcome in the multi-linear map session. So the first talk is cryptanalysis of the new CLT multi-linear map over the integer. And Sol is going to give the talk. Thank you for your introduction. I will talk about cryptanalysis or the new CLT multi-linear map over the integers. This is a joint work with Jeong Hee-cheon, Pierre Allen, Buk-gu, Chang-min Lee, and Bryce Minoan. And first, let me define a multi-linear map. A copper multi-linear map is a map from a product of group GI to a group GT, which satisfies a linearity in each component. Its security is based on MD-DH problem, which is given copper plus one encodings of MI and encoding of M, determine whether M is a product of MI or not. Multi-linear maps have lots of applications. Basically, it is used in multi-party key exchange with providing low-level encodings of zero. Another crucial important application is indistinguishability of classification. When it is used in IO, it does not need to publish its low-level encodings of zero. Currently, construction and analysis of multi-linear maps are being repeated. Among them, we looked through multi-linear maps over the integers. In 2013, Corona, Rufo, and Tibuship proposed a multi-linear map over the integers. But it turned out to be insecure by so-called CHLRS attack using low-level encodings of zero. After then, there are several attempts to make it repair, but they were quickly proven to be insecure. At Crypto 15, the same asserts set out to repair their scheme. It retained the structure of the encodings from 2013, but it added a new type of noise to sort CHLRS approach. So it has conceptual simplicity, relative efficiency, and wide range of pre-sumed hard problems such as subgroup membership and decision-linear problem. However, CHLRS 15 is not secure anymore, in the sense that we can find all secret parameters in polynomial time with list packed to security parameter lambda. Until now, CHLRS 13 looks secure without providing low-level encodings of zero. But CHLRS 15 is fully broken for all possible applications due to low-level encodings zero are provided by the letter. Before describing our attack, let me sketch first the CHLRS 15 multi-linear map scheme. The construction of CHLRS 15 is as follows. Choose distinct secret primes, PI and GI, with GI is much smaller than PI. Let XRL be the product of PI, and choose invertible G in mode X0, and keep these values secret. The public parameter is N, which is used in zero testing. A level K encoding of MI is defined using CRT, and it is similar to a cybertext of integer homomorphic encryption scheme. Now we move on to the crucial zero testing procedure. We define UI as follows. Then UI equals GI over GI kappa in mode PI, and it equals to zero in mode PJ. And we define also VI as a product of zero testing parameter and UI in mode N. And V0 be the product of PGT and X0 in mode N. Then the top level of encoding E can be rewritten as a linear combination of these constants UI and X0. And the size of VI is similar to N over PI, and V0 is much smaller than N. Therefore, the zero testing value of E can be written as a linear combination of VI and V0 over N. The important point is this. If E is an encoding of zero, our eyes are small enough so that the right-hand side of the zero testing value is much smaller than N. In this case, this equation holds over the integers, not mode GN, and the reduction does not happen. Once X0 is known, the scan becomes equivalent to CRT13 in terms of security. So CHLRS attack is applied well in this case. Suppose X is an encoding of zero, and Y and C be some encoding. Then we can multiply these three encodings and reduce its size using mode X0. Then the zero testing value can be written as linear combination of VI and V0. From X0, we can also compute V0. If you view these zero testing values as in V0, then it can be written as a matrix expression as follows. Remark that the VI is a regardless of an encoding. So by varying X and Y, we can obtain the matrix equation as follows. And it includes some diagonal matrix which is related to an encoding C. Therefore, some eigenvalue computation of related matrix, we can have CI. Then C minus CI is a multiple of PI. By repeating this procedure for another choice of C prime, we can have PI. However, X0 is secure in CRT15. So we can now reduce the size of encoding after the multiplication. Remark that the size of E is deeply related to the size of A. So if E is large, then A is large. So A V0 exists the modulus N. Therefore, the right-hand side of the zero testing value goes over N, despite E is an encoding of zero. From this reason, the previous attack does not work. More serious problem is that the correctness of testing does not work. Therefore, we need to reduce the size of encodings in order to perform zero testing. Let me explain how to reduce the size of the encodings in CRT15. When two encodings are multiplied under X0, the correctness comes naturally as long as the numerator does not go over PI. However, X0 is secret, and the size of encoding is growing. So to reduce the size of encoding, CRT15 publishes letters in each level, which are encodings of zero of increasing size. The size of the smallest letter is about secret modulus X0, and the largest one is about X0 square. This explains how the size reduction process works. Using the letter, the size of encoding can be recursively reduced under the size of X0. The right is corresponding encrypted values. Since letters are encodings of zero, the size reduction does not alter the encoded value. So we can multiply encodings while maintaining each size under X0. Let me explain the effect of letter in the aspect of CHLRS approach. As in previous, we are given encodings X, Y, and C. Then we multiply these encodings and reduce its size using letters. To compare with previous, there are two additional terms, TI and A prime. By varying X and Y, we can obtain the metricization as follows. But there are NAR unknown matrices. So it looks hard to obtain secret information as before. Now I give a brief description on how to resolve this problem. The goal of our attack is to compute V0 and so recover X0. This starts from the observation of the equation, and it consists of two steps. The first step is to remove TI using the zero setting value of letter. And then we compute V0 from several equations module unknown V0. Let me explain the first step. For a time-level encoding of zero E, the zero testing is done after the size reduction process. So it can be written as follows. And the goal of the first step is remove the box indication. If we define a map pi using constants VI and V0, then the box value equals pi value of some letter-related one. Moreover, the function pi has two good properties. The first proposition indicates that pi is the same as the zero testing value of E when E is an encoding of zero and E is small. The second proposition says that pi is an additive homomorphic as long as the associated allies do not go over PI. The conditions on allies are also required for the correctness of the scheme. So we may regard pi as an additive homomorphism. Now we can remove TI. From the additive homomorphic property of pi, we deduce this equation. Therefore, it is enough to compute individual pi xj. Pi x0 can be computed directly from zero testing procedure. For the next one, we may reduce its size using x0 and apply the additive homomorphic property. Continuing this process, we can get all pi xj's and so pi values of any time-level encoding of zero, even though its size is large. This completes the process step. I remind you that CHLRS approach gives this matrix equation with additional two matrices, T and A prime. Through the process step, we remove matrix T in this equation. Now we move on to the second step. As I mentioned before, once x is known, the CLT15 is not secure anymore. So the goal of the second step is to compute v0 and so x0. Similar in previous, we will build a matrix which consists of pi values of some product of encoding. Suppose x be an encoding of zero and y be some encoding. Then by the process step, we can compute pi xy and it is written as a linear combination of vi and v0 over the integers. If we view this value in mode v0, everything behaves as like in CLT13 since the additional noise av0 disappear. So it can be written as a matrix equation includes some n-dimensional diagonal matrix vi in mode v0. Remark that we are regardless of an encoding, so we can vary x and y and build a matrix equation. Unlike the CHLRS approach, we made a matrix with dimension n plus 1. Then it spreads into lower-dimension matrices in mode v0. Therefore, it is not a full length when embedded into Gv0. So v0 divides a determinant of w when the determinant is computed over the integer. By repeating this procedure for another choice of y prime, we can compute v0 and so x0. It leaves all secret parameters in CLT15. Our attack consists of computing many values of pi and computing some determinant of matrix and GCD. So it takes polynomial time in security parameter. Until now, there are three types of multilinear maps are suggested, but they were all proven in SQL when used in key exchange. Specifically, for GJC13, we understood well after y. Recently, three papers are published to crypto-analysed GJC13 without low-level encodings of 0. One is applied only for a basic IO scheme. The others are applicable for all IO, but they break quantumly or only for up to degree lambda Q. Therefore, crypto-analysed multilinear maps without low-level encodings of 0 and design a new multilinear map with reduction to standard hard-problem style, worthwhile. Thank you for your attention. So while the next speaker is getting ready at the end, searching for his mic, is there any question? So congratulations for your attack. And when we designed the scheme, we did not expect that it could be broken like this. And yeah, the technique is very clever, the technique of extending the evaluation of the encoding over the integers instead of only modulo n. So this is very clever. And my question is, do you think that it should be possible to again repair the scheme or doing the CLT scheme for key exchange? Because for obfuscation, it seems to be fine. But for key exchange, do you think that it should be possible to again repair the scheme? Pre-repair? Then I try to analyze. OK. Other questions? So I actually have one. Did you try to implement it in practice on the servers like this parameter set with the CLT-15 paper? Did you try to implement it in practice? We only implemented on very small parameters. OK. OK. OK, so another question. Let's thank the speaker again. OK, so second talk of the session, it's a crypt analysis of GGH map by Yupu and Yujinja. And Yupu, who is giving the talk? No. Thank you very much. The title is Crypt Analysis of GGH Map Background. Multiliner map is a leveled encoding system. Can multiply but cannot divide back and goes further to extract limited information. We know that this can be achieved by zero testing. And it is a solution of a longstanding open problem and a novel primitive which has many cryptographic applications. GGH map is the first candidate of K-linear maps for K larger than 2. It is from ideal lattice structure. It is a major candidate of multiliner maps and the best paper of Eurocrypt 2030, two classes of applications of GGH map are applications with public tools for encoding and applications with hidden tools for encoding. In this paper, we show that applications of GGH map with public tools for encoding are not secure and that one application of GGH map with hidden tools for encoding is not secure. On the basis of weak DL attack presented by the authors themselves, we present several efficient attacks on GGH map aiming at multi-parted key exchange MKE. We know that this is an open problem. And the instance of weakness encryption, WE, based on the hardness of exact three-cover X3C problem. A note, WE is another novel cryptographic primitive published on stock 2030. And the instance of WE based on the hardness of X3C problem is its first instance. This is the situation about major candidates of multiliner maps, GGH, CLT, and GGH-15. I should say that GGH-15 and GGH are quite different from different structures. Then here is our work. Now, our contributions. Contribution one, we use special modular operations, which we call modified encoding, zero testing, to dramatically reduce the noise. Such reduction is enough to break MKE. Moreover, such reduction negates KGMDDH assumption, which is a basic security assumption. Notes, the procedure involves mostly simple algebra manipulations, and rarely needs to use any lattice reduction tools. The key point is our special tools for modular operations, contribution two. Under the condition of public tools for encoding, we break the instance of WE based on the hardness of X3C problem. Notes, to do so, we not only use modified encoding, zero testing, but also introduce and solve combined X3C problem, which is not difficult to solve. In contrast with the assumption that multiliner map cannot be divided back, this attack includes a division operation. That is, solving an equivalent secret from a linear equation modular some principle ideal. The quotient, the equivalent secret, is not small, so that modified encoding, zero testing, is needed to reduce the size. This attack is under an assumption that two vectors are co-prime, which seems to be plausible. Contribution three, for hidden tools for encoding, we also break the same instance of WE based on the hardness of X3C problem. Notes, to do so, we construct level two encodings of zero, which are used as alternative tools for encoding. Then we break the scheme by applying modified encoding zero testing and combined X3C, where the modified encoding zero testing is an extended version. This attack is under two assumptions, which seem to be plausible. Contribution four, we check whether GGH structure can be simply revised to avoid our attack. We present cryptanalysis of two simple revisions of GGH map. Aiming at MKE, we show that MKE on these two revisions can be broken under the assumption that 2 to K is polynomially large. Notes, to do so, we further extend our modified encoding zero testing. These two simple revisions are natural revisions and cover neighboring structures of GGH structure. What is main techniques of our attack? Main technique one, modified encoding zero testing. For the secret of each user, we have an equivalent secret, which is the sum of original secrets under noise. These equivalent secrets cannot be encoded because they are not small. Then we compute the product of these equivalent secrets rather than computing their modular product. Then our modified encoding zero testing is quite simple. It contains three simple operations, avoiding computing original secrets of users and extracting same information. That is, it extracts same high order bits of zero tested message. The following table is a comparison between processing routines of GGH map and our work. It is a note of our claim that we can achieve the same purpose without knowing the secret of any user. Now, this is the table illustrating processing routines of GGH map and our work. We can see that there are several differences, same purpose, main technique two, solving combined X3C problem. The reason that X3C problem can be transformed into a combined X3C problem is that the special structure of GGH map sometimes makes division possible. Now, here is a simple illustration. If we have equation A times B equals C, then we can solve B to be equal to A to minus 1 times C. We can solve combined X3C problem with non-negligible probability and break the instance of WE based on the hardness of X3C problem for public truth of encoding. Main technique three, finding alternative encoding tools. When encoding tools are hidden, we can use redundant information to construct alternative encoding tools. For example, there are many redundant pieces beside X3C. Encodings of these redundant pieces can be composed into several level two encodings of 0. Suppose that this is a product of two encodings and this is another product of another two encodings. If their positions are intersected, then the subtraction is the level two encoding of 0. Only one level two encoding of 0 is enough to break the instance of WE based on the hardness of X3C problem for hidden truth of encoding. Also, this technique can be adapted to other applications of GGH map, where although encoding tools are hidden, a large number of redundant information are needed to protect some secrets. Now, GGH map and two applications. First, parameter setting. Here we can see that R is a polynomial ring. RQ is another polynomial ring for integral Q. Mod Q operation is redefined. Then I emphasize that six elements G, Z, A, B1, B2, H from R are kept from all users, where G, A, B1, B2 are small. H is somewhat small, somewhat small. Z is random. Then we use principle ideal generated by G. Y is level one encoding of 1. XI, I equals one or two, are level one encodings of 0. PZT is level K, zero testing parameter. PZT is always public. Y and XI are called tools for encoding. For MKE, they are public. While for WE, they can be either public or hidden. Suppose a user has a secret V from R, which is a short element. He encodes V into capital V, and he publishes capital V. Then GGH K linear map includes K, Y, XI, PZT, and all noise encoding capital V for all users. Application 1, MKE, suppose that K plus one users want to generate K, E, Y, a common shared key by public discussion. We know that this is a public open problem. To do so, each user K, zero uses his secret V, K, zero, and other users encodings capital V, K to compute such a modular product. We can see that this is a zero tested message. Then K, E, Y is its high order bits with no relation with K, zero. Application 2, the instance of WE based on the hardness of X3C problem. A piece is a subset of the set 1, 2, 3K, containing three integers. X3C is a collection of K pieces without intersection. The X3C problem is such a problem. For arbitrarily given, many different pieces with an X3C. Find it in encryption. The encryptor generates E, K, E, Y as follows. He samples short elements V1, V2, V3K from R, computes the modular product V1, V2, V3K, Y2K, PZT, ModQ takes E, K, E, Y as its high order bits. Then he can use E, K, E, Y as the key to encrypt any plain test. Then he hides E, K, E, Y into pieces as follows. He randomly generates many different pieces of 1, 2, 3K with an X3C. For each piece, I1, I2, I3 encodes the product, V1, V2, V3, into capital V, I1, I2, I3. And publishes all capital V, I1, I2, I3. Decryption. The one who knows X3C computes the zero test of such a modular product. Then E, K, E, Y is its high order bits. Then the detail of our modified encoding zero testing. Now, here is our special tools for modular operations. And here are our three steps and our conclusions. Then other details of our work on our manuscript. I think they are a little bit, a little bit. And my time is coming. So thank you all. Is there any question? OK, so I have one question. So you have one attack when no public encoding is given for publicly encoding value and for witness encryption. So did you try to look at obfuscation because there is no public value to encode? It's also already encoded as for the X3C. Yes, I tried, but not successful. Yeah, any other question? OK, so let's thank the speaker again.


Welcome to the wide world of eSports, a show devoted to all things eSports. I'm your host, Katharine Norr. Today, our topic is eSports health and vitality, leveling up your wellness game. My guest is Gary Kleinman, the founder of Skins GG. Welcome, Gary. Hey, nice to be here. Nice to talk to you in Hawaii. Fantastic. Well, okay, so we want to hear about Skins GG. What is it? What is it? It's a health and wellness platform for gamers. The history behind it quite simply is if you look at traditional stick and ball athletes, athletics and sports going back 25 years, they did not have any health wellness or nutrition. In the traditional sports now they all have health wellness and nutrition and that's, you know, whether it's Pilates nutritionists and gaming in eSports with the growth and the dollars involved. It's going to go into that direction as well because of the extended time people, not only game, but the dollars involved and the franchises and what have you. We got ahead of it and created a platform for health and wellness. So when I say a platform, we have, you know, a wide variety of products, but in addition to that, there's a job board because our tagline is we power your performance. And we look at performance not only as gaming performance, but life performance. So you can get a job through our site. We're adding a couple of neuroscience games to the site, which we can talk about. So really our ethos is to power the life of gamers across all their touch points. Well, Gary, this is really interesting to me because I spent many years as a triathlete and runner. I did a number of marathons and one of the most important things that we used to fuel our performances was like electrolytes and various gels that we use because if you. It was interesting if we had a bad performance. A lot of times it was because of our nutrition and because of our hydration and electrolytes. So, I was very interested in skins GG because of the fact that you are providing that very essential in game nutrition for athletes as they play. So tell us about the nutrition that you offer for during play and, you know, whether it's competitive, you know, like esports or versus gaming. Yeah, so we look at our market, if you will, is esports, obviously professional gamers, but also the casual and competitive gamer. I mean, a gamer is a gamer. And there are a lot of physical ailments that are kind of unique to gamers and that's pain, discomfort, focus, anxiety, sleep deprivation, healthy eyes. So we looked at a whole range in all of our products are scientifically tested. The pain relief is actually based upon a formula from an Israeli pharmaceutical company that developed it for anti inflammatory conditions like IBS and psoriasis. We found by adding 1000 milligrams of CBD and had tremendous efficacy for topical pain relief. But the end game experience is we have an energy product that is not going to give you a higher crash. It's just going to elevate your focus. It's interesting that you brought up electrolytes because we have a new product. Hopefully we'll launch it in a month. I've been eating or tasting, if you will electrolytes, signing off on flavors for the last three days. But most people don't realize you will because you just gave us that interesting history about your athletic background. Hydration and electrolytes are actually two separate functionalities. Hydration is really about fluids. Electrolytes is magnesium, calcium, sodium chloride, and that's what really fuels your cells. And we looked at this and said, what do gamers need? They need to fuel their cells. They need to stay focused and electrolytes will do that. It also does several other things and without getting it too scientifically, but it's really, really important to replace your electrolytes. Most of the hydration products in the market, in fact, I venture to guess every single hydration product or electrolyte product is a powder you put into water, you shake it up, and you drink 32 ounces of water over whatever period of time. And it's the combination of that that people take. And that's true, whether it's a liquid IV or noon and some of the other products that are out there. I looked at that with our product innovation team and said, one of the things we don't want people to do or we find that people don't want to do, especially gamers, is to get up in the middle of the game and have to go to the bathroom because they consume so much fluid of 32 ounces over whatever period of time. Our electrolyte boost is a concentrated powder that you do not need water.  And we have a wide variety of flavors. It really tastes like candy, even though there's no sugar in it. It's a fascinating recipe formulation that a food scientist came up with. And I love it.  So it's really about allowing people to perform and do what they're doing longer without the intrusion of getting up, going to the bathroom, drinking and what have you. Sure. And you know that it sounds like it's quite portable. Is that right? Yes. It is very portable. And because it's not water dependent, you can put it in a backpack. You're talking about a four gram serving. So it's a tiny pouch.  So let's go back a little bit. Why did you create the company? What led you to an esports gaming type company rather than address a different market? I tripped across esports about six and a half, six years ago. I read an article about a Canadian female gamer who played a League of Legends tournament, Madison Square Garden, and the article said there were 17,000 people there. And I obviously thought that that was a typographical error because I just could not fathom 17,000 people watching somebody play a video game when I'm even throwing my kids out of the house saying shoot hoops and stop getting bed sores and all the kind of things that parents have a way of saying to their kids. And I have for many, many, many years owned an entertainment and sports marketing company and I was fascinated by what was going on numerically, if you will, and the engagement in esports. So I took several months to really learn what was going on in gaming. And my takeaway was that esports or and or gaming is not about the game. It's about the community around the game. And that's pretty powerful. The communication, the engagement, what have you. So I ended up creating a digital media network called WAM that was about the lifestyle and culture of gaming. OTT platform still runs on Comcast and a few other services. Well, what kept coming up as we're doing production content, the doctors were telling us that their practices were exploding with injuries from gamers. Gamers were telling me, Hey, you know, I've got sleep deprivation. I'm gaming till one in the morning that I can't sleep I have to get up go to work, practice whatever it is.  And as gorgeous as these gaming chairs are, they're not really ergonomically sound for extended gaming so they're at all these physical and psychological conditions that was coming from I said, Well, who's addressing that. That is a lifetime issue and since gamers start young, you know, 14 year old that beds gaming eight hours a day is going to have an early onsite of carpal tunnel syndrome. So we looked at this and said, Let's address that come up with products that have tremendous efficacy that will power the performance of gamers give them a healthy lifestyle, educate them about nutrition, and really foster health wellness and nutrition in the gaming world that previously has been Doritos and Red Bull and all the other kind of kind of food groups that we don't cosign as good. So that that was really the the the origin behind it we just produced a three volume e book on the top 25 gaming injuries how to prevent them and or how to treat them, which I'm more than happy to share with whoever wants it they can email me more than happy to send that out. So there is a tremendous amount of need for education about your body and the demands that gaming has on it.  It's it's the antithesis of that. And then you start seeing all the universities and colleges that have academic scholarships for gamers, the your physical well being has to be elevated to compete at that level. And that's why we created the products. That's why we created the the job board for somebody to upload their resume will match them with every gaming job based upon their skill set, not their job title, why we're creating six neuroscience games to help people understand where they, they look on what their skill is on spatial awareness, speed, accuracy, target discrimination and things like that. So it's interesting that you've entered the eSports ecosystem in this area. I've previously had the gamer doc and psych sensei as guests, and, you know, you happen to provide the products and, you know, so that's really interesting. Have you had eSports athletes come to you with stories about how your product has help your products have helped them, or about their specific challenges. Yeah, without a doubt. I think that the the the hero product, if you will, is the topical pain relief.  And our topical pain relief is is phenomenal. It just works minutes. Some of the stories I get from gamers, you know, that have the product is they say my my grandmother takes it because it helps her rumored toward arthritis or some of you my father has tennis elbow so he's grabbing it kind of thing you know we have a few sponsorships with influencers. One significant one is a fellow by the name of Troy field was a professional volleyball player and a significant streamer. Troy practices volleyball in the morning and he ladders his shoulder up with the pain relief. And then after he streams it's on his fingers and his hands. So it works for inflammation anywhere but especially for gamers, because you know you've got, and you might know better than I believe the statistic is that a gamer is utilizing 200 moves, a minute, or something like that, with their, you know their hands their eyes their fingers and what have you. That repetitive motion is just going to cause discomfort and pain, and we address that so yes we have lots of anecdotal evidence and a lot of people, I get text messages all the time saying I need more samples and more samples and what have you so yeah it it does work. I think the other area that I'm, for whatever reason, I love it is that the healthy I product, you know we don't really understand the damage that the blue lights having on us on everything. When we game or on the computer we're on our phone so be able to reduce that and to reduce eye strain is critical because macular health, especially as you age is just so important nobody really thinks about that. And that's a whole nother area that our formula is great it's based upon a national Institute of Health formula for healthy eyes. It's interesting that you mentioned people that are not gamers who use your products effectively. So I realized your target market, it are the e sports athletes and gamers, but are you finding more and more that you have an extended target market in you know amongst those who are not gamers. Yes. You know we look at that part of the pond as our halo audience. And if you look at households around the world, the penetration of a gaming device is up in the 90% because of the growth of mobile gaming. Right so there are a lot of people that game that really don't self identify as a gamer, because they're playing words with friends, eight hours a week but if you were to ask them they're not a gamer, but they are right because they're playing eight hours a week. They're competitive they want to beat their friends they want to get better at it but they're as much of a gamer as somebody on a call a duty team in in significant ways. The benefit of gamers is pretty significant there's three billion people gaming every day around the world but in direct answer your question. Sure. People that game with their parents and their parents are tennis players are going oh my god. I got to put that on my elbow. And I get it from some of our at the agencies that we work with that they're not true gamers and the true definition of the world even though they they game. And then someone said oh my god this is like incredible that the one thing about gamers. And I think it's a challenge in the early onset of health wellness and nutrition in gaming is gamers to a large extent think they're invincible. Right so they don't really acknowledge pain or they go and it's no big thing as they get older. I don't see that manifest and go wait a second, I need to treat that as you know again most people don't realize the average age of a gamer is 37, and it's split basically, you know 50 50 male female. And I love, and I don't know if you have this experience went on with non gamers and they all say here, what do you do you're in gaming I don't understand health wellness and gaming why do they need it and all that kind of stuff. What do you mean the average age of a gamer, and they'll go 1617 you say 37 and it's like, well what do you mean 37 right. So that market is very very right for nutrition and that's true. We don't have a vitamin series out yet I think we will in time. So a lot of vitamins are going to be critical. One of the things with our electrolyte boost product is we can add more vitamin so it has lysine in it vitamin C plus magnesium and all the other electrolytes. But that's an easy product for us to put vitamin E in it. We can put non caffeine energize in it, because there's some really cool ingredients now. In two weeks I'm speaking on eSports at the supply west ingredient show in Las Vegas. So I'm going to have a kick talking to them about what they should be creating from a healthy substance for gamers because gamers, gaming is just going to grow. I mean it's not going anywhere. So the average age of a professional eSports athlete would be more in the range of 18 to 25. Do you see your products as extending the, the life of a competitive eSports athlete. I wouldn't go so far as to say we can extend it as much as I would love to say that these drugs are miracles and I can give you three more years of gaming. That would be hyperbole and I'd sound like an ad guy. But I do think what we can do is make the years that you're gaming more comfortable, pain free, teach you how to stretch, and that may give you longevity as a gamer, because you will reduce your incident or probability of injury, you'll sleep which may have an impact on how long you can game, but I'd be hard pressed to say, use our suite of products and you get three extra years of a COD team. No, but I think what we do by the wide breadth of things that we offer is that we can make gaming more comfortable. I think we will make you healthier. I think what ends up also happening is people, as they're using our products, they become more aware of their general health and wellness. So they're probably going to drink less sodas and they're probably going to maybe have an extra salad as opposed to a pizza, because when you start thinking about health wellness and nutrition, and you start thinking about how do I reduce the inflammation in my body. I think our products help do that, but it's also an insight of some of the other things that you can do in your life. And that will I do believe will make it easier to play longer, but I wouldn't, as I said, say we're extending the career. But if you want to say that we are be more than happy to use that quote. So we're looking at products that help health and wellness of Esports athletes. How does health and wellness in gaming compare with that for traditional sport. Great question. Right now, it's nascent. There are very few, albeit some esports organizations that are bringing in nutritionists that have a very, very low level education program. Right.  There's so much more to it. And that's why if you were to look at the 25 injuries that the gamers sustain, most people would be hard pressed to come up with 25, but there are 25. And our ebook has pictures of them and certainly recommendations and suggestions of how to treat and how to prevent. So the growth and the opportunities in gaming. And when we talk about the opportunities in gaming any sports, you know, gamers have a tendency to age out early right any sports professional as you said, they're aging out fairly early well what do they do, you know their traffic controllers the FAA literally is is recruiting gamers for air traffic controllers makes perfectly good sense. That's a long career, right they can do that forever in a day. Even with the military they're hiring gamers for the drone program. They outfly the pilot so even though you sports athletes may age out in their early to mid 20s. There's an entire career opportunity that's based upon that skill set that they're going to need this foundational health wellness knowledge and implementation so that they can do that longer. And the very first show that I had was interviewing major general Frank Muth, who start was one of the people who started us army sports and we talked about how the US army uses those skills in across different military operations and, you know so I think, I think it has such broad application and it seems like your company is interested in educating that segment of the population to understand a little bit more about health and wellness. Absolutely a high priority in the ethos of our company. It is also our biggest challenge, because we're talking to a group of people that really haven't made the connection that my my wrist hurts or my back hurts or I'm not sleeping. And where is that solution that has been created for me so we're bridging that gap I mean the one comment I did want to say, I'm not green who is a Hall of Famer from the Green Bay Packers and the e sports coach at Lakeland University. He's not he's that one of our advisor. But what he has done as the e sports coach at Lakeland is literally taking his entire protocol from a football you know being a running back with the Green Bay Packers, and he puts his teams to the exact same training and the diet and the nutrition. And he replicates it he said because you, you have to have that to really be at the top of your game and I think e sports athletes and especially those that want to be e sports athlete. You know earlier, the maximized their physical and psychological well being in order to compete at the level. Because as you will know, the more money that goes into the sport, the more competition there's going to be, which means if you want to succeed, you have to be the best version of yourself, and health wellness and nutrition is a critical aspect of that. So you sell your products outside of the United States and do you have to get any particular approval for you to sell like any government agencies have to like, certify your products. So we do not currently sell outside of the United States but we are finalizing distribution in China, as we speak. The challenge is not that we can't sell out of the country. The shipping cost is prohibited. So for shipping you know for us to send something to Canada is almost three times the cost of the product. So it doesn't make sense you need to figure out the fulfillment. In terms of government approval. The entire supplement world is dietary supplements that is not FDA required. We can't make certain claims as a result of that. We do have some products that we're looking at that will have OTC or drugs sign off, which will then have to go through the FDA approval process. But most everything that you see in all the energy drinks are not FDA approved and nor do they need to be. The only other thing that we have in our pain relief is CBD and CBD has depending on who you talk to is sanctioned not sanctioned the FDA has not formally approved CBD in any particular form. So federally it's not supported, but it's everywhere and anywhere so it is legal, but depending on where you are CBD is an issue, you can't sell CBD products on Amazon. Right so, and people are, they just call it hemp. There's a lot of confusion between what is and THC CBD and what have you, but that's the only ingredient that we have to be careful with our CBD is farmer grade CBD it's 99.9% pure CBD there's no THC is that you're not going to get high you're not going to get buzz and it's it's really just a tremendous anti inflammatory agent with the other base formula that we have, but from the legal requirement now it's it's all good you can ship you can send it to Canada you can actually send CBD to Canada you couldn't two years ago, and I do think in the next two years CBD will be legal with the interesting thing with professional sports so golf, not a problem with CBD baseball is not a problem the NFL and we're affiliated with the NFL Alumni Association and the retired players Congress is the NFL has no restriction on CBD, except the players cannot commercialize it pictorially. Okay, use it they, but they just can't endorse it in a commercial which I will figure that one out. I don't know. I think some of that without any two political is the pharmaceutical companies. They want to own the CBD space, as opposed to right now it's kind of anybody and everybody, but I think another two years. CBD will be everywhere, but there was a there was a period of time with the CBD you, if you had it you couldn't get a bank account. Oh, I see CBD because it's not federally supported. Now that's not an issue so we're you know baby steps. Exactly. Well, you know I know I'm interested in your products and I'm sure a lot of people watching are. How can they find them. www.skins.gg just go on there we buy it and go out the next day. Okay, fantastic. Well Gary, thank you so much. I appreciate your being on the show. And thank you to our viewers for joining us today. Next week my guest will be Mark depth, the director of UCI esports to talk about collegiate esports. See you then.


What's good, Joshua boros back again with another video. So we got to talk about this man WWE stopped selling saucer banks in Naomi's merchandise on the WWE shop comm This is kind of adding to my theory that this is not a work I know when they initially said something on SmackDown they pretty much threw them under the bus They pretty much made them seem As if they didn't care about the WWE universe. They didn't care about the fans. They didn't care about the business They threw them under the bus. I'm gonna give my thoughts and opinions on that later, but This is one of those things where it's like we really hadn't seen something like that in it For some people when we was watching it during the live stream The live stream reactions I did Friday Some people were saying oh this gotta be a word because they don't ever do this But more things have happened this weekend that alludes to it not being to work So we're gonna check out this article by web is Jericho calm and we're gonna go into what was said Monday night's raw was thrown into disarray when Sasha Banks and Naomi walked out due to being unhappy with creative Subsequently it has been reported that the doer has been taken off of all live events until the end of July and On SmackDown Michael Cole would announce they have been suspended indefinitely and that there will be a future tournament to crown new WWE women's tag team champions Now indicating that their WWE careers genuinely hang in the balance the pair's merchandise have been removed from WWE shop which doesn't even happen when WWE release talents Therefore it appears the company is doing this as a power play to limit their royalties As you can see when you search for their name on the WWE shop They'll say sorry nothing found for Sasha Banks and sorry nothing found for Naomi check out these other items instead So they're not playing they are legit trying to make sure they Get rid of anything that could potentially gain Sasha in Naomi some extra funds There has been some talk among wrestling Insiders that both women contracts are expiring this year So given their suspension it's possible neither will return to WWE television again However, as Sasha Banks has mainstream fame due to featuring in the Disney plus series Mandalorian and Naomi is related to marriage to Roman Reigns seems doubtful WWE won't at least try to resolve the issue before then nevertheless WWE does hold significant power over both women as the company can simply freeze the pair's deals to ensure They can't work elsewhere, and this is one of those things where they can do that They can freeze their contracts if they wanted to and now they just sitting on the shelf, you know It's really it's really a weird situation here. Like this is Probably never really happened to this magnitude The article makes a great point that even when people that get released their stuff is still up on the shop But they took their stuff off the shop, and that's another reason why I believe this is not a work because Even though you get wrestlers get royalties from that The company also gets paid off of that by merchandising as well. So they would lose money by taking Taking their merch off the store Granted it just I don't know how much of merch Sasha and Naomi is selling, but I'm pretty sure it's still somewhat decent So they they're willing to cut their losses there I've also seen footage on on Twitter where on the intro opening package on like for any WWE event they'll show like flashes of different moments and different wrestlers Well, apparently Sasha was on one of those moments, but they completely took her off I think Sasha was on there and I think maybe Naomi had a appearance But I know Sasha had like an appearance on the opening graphics and they completely took her off So it's like, huh? They took taking her off the open on opening graphics. I know I believe Sasha and Naomi have like switched up the Twitter handle They don't follow WWE. I don't think they have like WWE info in their bio or anything like that on Twitter Like it's one of those things where it's like damn like this doesn't seem like a work more and more and more as I think about it It seems more like this is WWE or Vince McMahon Really trying to make an example of anyone that even thinks about walking out This is not the first time someone's walked out We all remember what happened with CM Punk and even then with the CM Punk stuff They didn't really do anything Substantial until I want to say they fired him the day of his wedding something like that Which was super petty in it in in itself. So I don't know man. This is This is really interesting and I don't know where this is gonna go Honestly, like I know a lot of people are still in the camp of oh, well You know WWE was wrong for this They they shouldn't have done this. I know look at he has said they shouldn't have in like tried to embarrass them live on television I know See a punk is in support of them. You know saying yeah, we need to support these women Basically saying like they can get rid of you at any moments like you're you know the show will keep going on type Situation so and then there's other people there saying no this was unprofessional of them for what they did how they handled it and Some people feel like This is what happens when you're unprofessional Some people make the point if you just walk out on your job You you expect them to show you any love and compassion or care If you just leave your job when you're supposed to do something or you have an obligation to do something So some people make that point as well for me personally. I Do think it could have been handled better on both sides. I'm not Stand up here saying I'm pro Sasha and Naomi for how they handled it But I can understand their frustrations with the women's division in the women's tag division So I understand why they felt like that I understand. I like, you know what screw this We're out so I can get the frustration But I can also understand WWE standpoint for them They're like, yo, you're gonna still be in the main event granted. I'm guessing it's more So they Sasha wanted something substantial for the women tag division, which is understandable But they were you know WWE side of things like what we were still gonna put you in the women's main event Yeah, man, I don't know. It's there's really two sides to this both sides of point I do think WWE made a mistake of trying to bash them publicly live on television. I don't think that was necessary I think they could have just Kept it kind of low-key or if anything be like, you know what we're having a tag team division Well a tournament for the tag team division even though if you want to be honest, bro It's it's not looking too good even for that, you know, someone posted a picture of the roster and Charlotte's gone off for television, you know written off television Naomi and Sasha's gone There's only like maybe five or six people left on the rock not even that It's not even it's not even that many people left on the smackdown side of things like the roster is super depleted at least maybe five people So I don't know how they're gonna do this I think they should just get rid of the belts because there's not enough people unless you incorporate NXT to potentially be involved But outside of that man, I'm even then it's just like, I don't know what they're gonna do Yeah, putting the tag titles on somebody else having a tournament It's not gonna change the fact that those belts not have not been utilized correctly in a sense A building them up as something really substantial for the women's division in my personal opinion I think having them fight do drop in Nikki ash over and over and over can get kind of boring and redundant in my personal Opinion, so I don't know man. This is not it's not giving me work vibes. I think this is legit WWE is going rogue Sasha and Naomi went rogue and it'll be interesting to see if they say anything In the future, I know Sasha there was footage of her at a concert saying, you know, just having a good time Like fuck it and I don't know what Naomi's been up to in that sense as well So comment down below. Let me know do you guys? Think this is a work because some of you guys feel like this is all a big rules Or do you guys really believe this is there's some real tension here? Some real issue between Sasha Banks Naomi and WWE let me know down below man, but I appreciate all the love and support on the channel road to 90k almost forgot appreciate y'all kicking me. See y'all next week. Peace


So it's important to talk about how given some rings we have how we can construct new rings from old rings And in this video I want to talk about the ring of matrices So in linear algebra and also in in group theory in this lecture series We've talked a lot about matrices groups of matrices. We can talk about groups of matrices under addition We can talk about groups of non singular matrices under multiplication but if we combine matrix addition and multiplication together we can actually form rings of Matrices so for example, if you take the set of n by n real matrices or the set of n by n Complex matrices these will make rings under the usual matrix addition and matrix multiplication These are also rings with unity since the identity matrix I Sub in so this would be that the matrix with ones along the diagonals and then zeros everywhere else, right? The identity matrix is given that name because it's the multiplicative identity And therefore these rings of matrices the real matrices and complex matrices These are rings with unity on the other hand though These rings are not commutative since matrix multiplication is Non-commutative if I just choose two arbitrary matrices We cannot expect that a times b is equal to b times a now. There are some special cases that a times b is equal to b times a with matrices here when we say something like non commutative What we're saying is as we're not saying it's never commutative It just means there's no guarantee of commutivity of commutivity here. There are and then for matrices There are some matrices for which a times b does not equal b times a it's easy to find this If you just pick two random matrices, you most likely will find out that they do not commute with each other So these are non commutative rings with unity, but matrix rings are very important rings to study in ring theory in fact If you have any ring whatsoever because there's nothing particularly special about the ring of real numbers or complex numbers here If r is any ring, then we can form the matrix ring which will denote m sub n by n of r to be the set of all n by n matrices with entries coming from the number r from the ring r Now addition of matrices is defined analogously to where terms are added together component wise Okay, so for example, if we have any ring, you know, we'll do two by two matrices for examples. You have any ring a b c d we'll do something like that. I'll call it like a one b one c one d one If you add this to the to the matrix a two b two c two d two Where here we're assuming that a i b i c i and d i these are all just elements of a ring When it comes to adding that matrices together Well, what you're going to do is you're going to add together the one one position So you get a one plus a two you add together the one two position So you get b one plus b two you're going to add together the two one position Which gets c one plus c two and you're going to add together the two two position Which is d one plus d two Like so in which case to add together matrices just by Component wise you just have to add together the components You have to add together the a's the b's the c's and the d's And so if you want to construct matrix addition all that requires of your scalar is that you can add scalars If you can add scalars you can add matrices great rings have addition so we can add together the we can add together the The matrices now what if we want to think about like multiplication? What does it mean to multiply together two matrices? Well by the usual rules of multiple matrix multiplication We take like the first row times the first column this finger multiplication here You're going to get a one a two plus b one c two Then you would take the first row times the second column You're going to end up with a one b two Plus b one d two Then you're going to take the second row first column You end up with c one a two plus d one c two And then lastly you can take the second row times the second column You're going to end up with c one b two plus d one d two If you follow the usual rules of matrix multiplication, you would end up with this product Now this right here works for any ring Because in order to do this product if you take a row times a column We have to be able to multiply together elements right we have an a one times an a two We have to know what that means we have to have a b one times a c two We have to multiply and then we have to add which in a ring we can multiply and add so in a ring If our scalars are from that ring then we can multiply together matrices now I have to caution you here that The ring might be non commutative. Okay, the the the the the elements themselves might not commute We know that matrices in general don't commute But what if the scalars themselves don't commute? Well, that's okay because when it comes to this when these when you come to these products Notice how it's always one two one two one two one two You always when you have your products you always have the scalar from the first matrix times the scalar from the second matrix Plus a product where you have a first scalar second scalar plus a product from a first scalar second scalar This example I did two by two matrices But you can see how very naturally this could be brought into three by three four by four any end by end matrix So even in a non commutative setting we can make matrix multiplication be well defined Just be very cautious of the order of operations here If the ring r is a ring with unity then Then um, this matrix ring will have unity as well because it'll just be the identity matrix In the usual sense. So if r is a ring with unity, then this will be a ring Then the matrix ring will be a ring with unity now even if the ring though r is commutative If you have if n is greater than one that is you have two by two three by three four by four Your matrix ring is not going to be commutative even if the ring is but important to emphasize here that the matrix ring Is well defined even if the ring is not commutative Only thing we require for the ring is that the addition makes an abelian group And that we also need multiplication to be associative and distributive. We don't need commutivity We don't need identities if you have a multiplicative unity then so will the matrix ring But commutivity will never be guaranteed when you have matrix rings


This is LIS Podcast number two, titled Introduction to Finding and Using Information for Your Assignments, podcast by James Fraser. For further details, go to www.cumbria.ac.uk-lis. Hello my name is James Fraser and I'm a Learning Advisor at the University of Cumbria. In terms of information gathering, there are a few things to think about when you're first given your assignment. It's a good idea to start gathering your information as soon as possible. It always takes longer than you think and it's good to try and avoid those feelings of panic because you've left things too late. If you've got a reading list from your tutor, you can use the library catalogue to try and find the books on the shelves or on the computer if they are e-books. But one way to help yourself get higher marks is to try and go beyond your reading list and show your lecturers that you have shown some initiative. It's good to show evidence in your bibliographies that you have used a wide range of information sources, for example books, journal articles, good quality websites and maybe some newspaper articles. I've just mentioned websites. There is a lot of information available from the web and perhaps a person's first instinct is to go straight to Google and type in the title of the assignment. However, this usually results in hundreds of thousands if not millions of hits, most of it which will be of dubious quality. I know that later in this podcast series, we will look at the issue of evaluating information to help you make sure that the information you choose is of appropriate quality for university work. Instead of going straight to Google, there are some things you can do before you even turn your computer on. Some questions that you could ask yourself in the first stages are firstly, how much information do I need? This will often be determined by the length of your assignment. If your essay is a thousand words long, you won't need as many references as if it was five thousand words. However, there's no hard or fast rule about how many items should be in your bibliography and if you are in need out, you should talk to your lecturers. But it's better to have a few good references from books and journal articles and sources that are trustworthy than loads of references from poor sources like Wikipedia or commercial websites. The second question to ask yourself is what kind of information do I need? Do you need facts and figures or do you need thoughts and opinions on a topic? Different sources of information will give you different kinds of information. For example, encyclopedias and textbooks will give you factual information, whereas scholarly books and journal articles often provide a theoretical overview of a topic. Lecturers like you to use journal articles for your assignments for a variety of reasons, but mainly because they contain up to date information and the articles themselves are written by specialists who are qualified to a high level in their subject areas. The next instalment of this series will look in detail about how to go about finding good journal articles for your assignment. For further details on this podcast and to listen to others in the series, please visit www.cumbria.ac.uk-liss.


In this video, we will be focusing on the following two topics, rump and front end. Each one has a different purpose to help the cow produce high-quality milk. Depending on the quality of each characteristic, the cow will increase or decrease in value and productivity. According to the PDCA scorecard, each characteristic that you see mentioned has a different point value. When looking at the rump of a dairy cow, the judges should look at the angularity of the hips and pins. These are the round bones that stick out towards the top line of the cow. The hips, or hooks, is the bone closer to the head, and the pins are closer to the tail head. The angle should be almost level, with the pins being slightly lower than the hips. They should be wide apart. Also, the judges should look at the tail head, which is the very top of the tail. It should be set slightly above and evenly between the two pins. In these photos, cow B has a wide-set hip and pins, but the pins are angled way lower than what is desired. Her tail head is set slightly above the pins, compared to cow A, who has wide hips and pins, and they are almost level, with the pins being slightly lower than the hooks. Her tail head is set evenly above the pins, cow A has the better rump. A cow could also have her hips lower than her pins, and this is also undesired. When reviewing the dairy cow's front end, similar to the rear legs, judges should look for front legs that are wide apart, straight, and squarely placed. Also, the PDCA scorecard talks about how the shoulder blades and elbows should be firmly set into the chest. Cow A has forward pointed feet, set wide apart, and they're straight. This shows that she has a firmly set shoulder blade, compared to cow B, who has front feet turned out, bringing the elbows in and making the distance between her legs narrow. This could be a sign that her shoulder blades are not very strong, giving her the characteristic of a narrow chest. Thank you for watching! Be sure to check out our other livestock judging videos, as well as the Alabama Cooperative Extension YouTube channel.


Here we are zooming into the planetary nebula, NGC 7027. The nebula is about one light year across. In 2020, its central star was viewed by Hubble in near-ultraviolet light. Hubble first looked at this planetary nebula in 1998 using visible and infrared light. By comparing the old and new Hubble observations, researchers have additional opportunities to study the object as it changes over time. These observations will help reveal how much dust obscures the star and how hot the star really is.