Hello and welcome to my talk about deck-based white block cipher modes and an exposition of the blinded keyed hashing model. My name is Alder Gunsing and this is a joint work with Jan Damen and Park Manning. So a very commonly used primitive in symmetric crypto is of course the block cipher. And this encrypts some plaintext into some ciphertext under a secret key. However it has a fixed block size like 128 bits for example. And if you want to encrypt a variable sized message we need some kind of mode of operation. So for example counter mode. But these modes require a nonce which has to be stored somewhere. And very often we have some place to store it but in some situations like this encryption for example we do not really have the space to store it. So what we can also do instead is that we design a white block cipher. And the white block cipher is simply a block cipher with a variable block size. So we do not really need a nonce for this as every part of the output depends on every part of the input ideally. But if we do encrypt the same plaintext twice we do get the same ciphertext. So we do leak some information. What we can also add is a tweak to it.  And this is a normal white block cipher but it also takes a tweak as an additional input. So the tweak behaves a bit like the secret key. In that the ciphertext completely changes when we change the tweak. But in contrast to the secret key the tweak can be public. And this is useful for in for example disk encryption. Where we can use the sector number as the tweak. And this means that when we encrypt the same file multiple times on the disk, they do not get encrypted to the same ciphertext. So we do not leak the information that the same file is repeated multiple times. And what we do is that we build two tweakable white block ciphers based on two kinds of primitives. The first one is the doubly extendable cryptographic keyed function or just a deck function for short. And its inputs can be of any size and it also outputs an arbitrary long string. And the second primitive is the keyed hashes. Its input can also be of any size but its output is just a fixed size. And in contrast to the block ciphers, these primitives do not have the requirement that they have to be invertible. So this allows for a more flexible design in them and allows for faster primitives. So the first construction we have is the double decker. It is a generalization of the farfaller white block cipher by Bartoni and others. And it looks a bit complicated at first, but if you merge the left two lanes and the right two lanes together, you can actually see that this is just a four-round fashion network. But the topmost and the bottommost functions do not write to the whole lane so we do split them. And those functions are actually the keyed hash functions and the functions on the inside are deck functions hence the name. And the outer lanes we have a fixed size and the inner lanes have a variable size. And this just means that the keyed hash functions do indeed write to just a fixed size lane. It also means that the bulk of the data will be in the inner lanes. If you look closely you can actually see that those lanes are only processed three times. So it is actually more efficient than just a normal four-round fashion network because the bulk of the data is processed less. We also have the docked double decker. This is a variant of the double decker where two lanes are merged together and some input is moved around. So it actually has one lane less. And again the outer lanes here are of a fixed size and the inner lanes are variable size. So again the bulk of the data will be in the inner lane which means that it's only processed three times. But in this case what's also interesting is that the deck functions only get a fixed size input. So they actually become stream ciphers conceptually which are much more commonly used. So this is more suitable for that. So now I will talk a bit more about the secured model of the double deckers. So a very commonly used security property of keyed hash function is the notion of epsilon x-ray universality. This property means that the probability of getting a specific difference between the outputs is small. So we actually require that the probability of getting a difference y is less or equal than some small epsilon. However this property only considers the difference between a single query pair. So when we look at Q queries instead this bound simply becomes Q choose two times epsilon. However this epsilon is the worst case bound over all query pairs with some difference. And for some functions not all of these pairs do get close to the worst case bound. So this bound can actually be a very bad estimate. So instead we consider the blinded keyed hashing model or big h for short. There we want to estimate those multiple queries more precisely. So it is actually defined as the following setup. So when we have a keyed hash function h we consider it big h secure. If it is indistinguishable in the following setup. So on the left hand side we have the real world. Here we have some input x which we pass through our keyed hash function. And then we apply a difference delta to it. But instead of directly giving the output we first pass it through a random oracle. And in the ideal world we simply give the two inputs to a random oracle. But by first passing the output through a random oracle in the real world it becomes a bit interesting. Because this means that the distinguisher cannot directly see the output of the keyed hash function. And this means that it gets very little information. It actually means that it does not get any information besides that it knows whether there was a collision or not but nothing more. And a very good example of this is Zufi. So when we have a single query tuple Zufi claims to have a security bound of 200 power minus 127. And this holds in both the XOR universality model and the big h model. But if we extend it to q queries when we use the XOR universal model we can only get a bound of q choose 2 times to the power minus 127. But Zufi actually has a dedicated claim for the big h model which is much better namely one of q times to the power minus 128. And this makes a very significant difference. So when we use Zufi as an XOR universal function we only get a claim security guarantee of 64 bits. But when we use it in a big h model this claim security improves to 128 bits which is of course a very significant difference. But we cannot directly apply the big h model to our construction so we have to do a bit of work to reduce our construction to the big h model. And if we use the XOR universality definition instead this is trivial to do. This is of course also the reason why this is so commonly used. But we are able to do this to do this reduction. And we do show that the double daggers are secure when the key hash function is big h secure and also when the dag functions is prf secure. And for the more we also have another interesting security property of the double daggers. This is because we apply the tweak to the dag functions instead of the keyed hashing functions. And this means that the bound of our keyed hashing function becomes tweak separated. And because the dag functions behave independently for different tweaks we do not have to worry about collisions in the keyed hash function in in those cases when the tweaks are different. And this significantly improves our security bounds in some settings. So for now we will consider just the normal epsilon XOR universal keyed hash function h. But instead of looking at all Q queries we will separate the queries based on the tweak. So we make QW queries with some tweak W. Now we will look at the security laws on our keyed hash function in three different scenarios. To the first one we just have the general case with a general bound. But to understand it a bit better you also look at two extreme cases. First one where we just use a single tweak every time. And the other extreme where we do not repeat the tweak at all. So we use a different tweak every goal. And the naive security bound in all these three cases is just a normal Q choose two times epsilon. But this is not the case. So in general we get QW choose two times epsilon. And then we sum these terms over all tweaks. But if we use just one tweak this doesn't make any difference at all. We again just get our normal Q choose two times epsilon. But if we have no tweak repetitions at all we actually get a bound of zero in this case. So it doesn't even matter which hash function we use. And of course if we have some case in between where we have limited tweak reuse we get some bound in between those. So a good example of this is disk encryption on SSDs. So the double decker is very suitable for disk encryption. Because disks are separated in sectors and we can use the block size just equal to the size of these sectors and we can also use the physical sector number as our tweak. And the fact is that in SSDs these sectors have a limited lifetime because they get damaged every time we write some data to it. And if we look at some specific SSDs we see that it can every sector can be written to at most of around 500 times. So if we use those numbers into our previous bounds we get the following result. If we do not have any tweak separation at all this is secure when 2 to the power 74 times our epsilon is significantly smaller than 1. But if we have tweak separation this improves to 2 to the power 46 times epsilon. And that is significantly smaller than 1. So this means that we might get away with some faster key hash function if we have this tweak separation. But we have to note that we only get this guarantee when we use the physical sector number as a tweak not the logical one. So this means that it is mostly applicable when encryption is implemented directly in firmware of the SSDs. So now I want to compare our construction to a previous construction in the adiantum. The adiantum was presented here at FSE last year. And the goal for the designers was really to minimize the number of block cipher calls because those are very slow on low-end Android devices. And for this they basically used a three-round FISL network. But because that is not secure they added an extra block cipher call in between. But this block cipher calls only used applied on a very small part of the data. And the bulk of the data is on the left-hand side which doesn't has any effect of the block cipher call at all. And our docked double-decker construction is actually very similar to adiantum. So if we start at the bottom you can see that the bottom two functions are actually called exactly the same in both adiantum and the docked double-decker. But it is different for the block cipher call because the docked double-decker splits the left lane into two parts. We are able to lay the block cipher call flat. And this means that we don't need the inverse of the block cipher at all so we can actually just replace it with a deck function. And because we laid it flat the top key-dash function has to be swapped as well of course. So concluding, first of all we introduced the two double-deckers which are two tweakable white block ciphers which are based on deck functions and key-dash functions. We also introduced a new security model BKH for keyed hashes which is a generalization of the more commonly used extra universality. And then we also were able to use this model to prove better bounds for some specific keyed hashes like Zufi. And finally our usage of the tweak improves the security in some situations where the tweaks are limited to re-used. So that's the end of my talk. Thank you for your attention.


Hey guys, it's Nate, aka The Foot Account, and welcome back to the channel. TFA on the move, different setup, but still same video today. We are talking about the SBC that is maybe finally dropping in this game. We've been looking forward to it for a couple of days now. We're talking about that hero pack. Will EA drop it today? We got to look at the other content coming today as well. The mini release, more trailblazers players coming into packs. So we're going to go over all that and more in today's video. If you're excited for it, drop a thumbs up. Subscribe if you're new. Let's go over yesterday's content really fast. As always, we had a couple of different player SBCs. First of all, we had the SBC four is Malia Tsar, a great super sub item coming in at 56,000 coins and also links that Jonathan Klaus card from Road to the Knockouts. His price is going up a bit. This SBC is being very well received with the four star skills. And really, it's the pace in this card that makes it worth doing 95 acceleration, 96 sprint speed. And not bad dribbling stats either for a card that's pretty cheap to do. You take a look at footbin and it's coming in right around 50,000 coins. And it's just one squad to complete, which is just the 85 rated squad with a team of the week. So craftable, maybe a little bit expensive. Again, in this early stage of the game with how much fodder you maybe have. But that one's nice to back to back things of solid SBCs, both technically wing type players. But in my opinion, I think that's a dub for super sub reasons for sure. Now, another player SBC that dropped yesterday was again an under kind of upgraded squad foundations. This time for the WSL, we had Van de Sanden and this card doesn't look too bad. But really, as you look at the objectives that go along with this, it's just again, the same trend over and over that these squad foundations cards for all these kind of lower leagues just don't get a good enough juice to be usable for most players. Now, Liverpool links here, and especially if you go to objectives, you got some other players from these big clubs on the women's side of things. But I think there was Brighton, you have Chelsea involved in there, and Arsenal with Hurtig, Carter and Vicky Losada. So big links there, which are not too bad. But again, the stats are just not really there. And I don't think these interest as many people as we could have been interested in these because their stats are just not as great. So really bummed by those. But that's just kind of the trend that's been continuing with all of those objective cards and with the squad foundations in general. So after that yesterday's content, the market did do pretty well. We'll talk market a bit more in a second. But let's get to the big news today. We're hoping for better content today on Sunday. And last Sunday was pretty good. If you do remember, we had the David Beck MSBC, but will EA do something that they did on Sundays in years past? That is the hero upgrade pack. We're talking about that today, guys, because we thought it was dropping last week on Wednesday, the pack is in the code and we've just been waiting. And we haven't seen it yet. But maybe today is that day. Also, it'd be hilarious if they went out and did what they did last year right around this time, make that huge mistake of dropping the 25K hero pack in the store, not expecting that. But for real, it really could be a day today where we see the Max 87 hero SBC. I even think there is a leaker that tweeted out that he is expecting to see now. Again, this is one of those leak accounts that we're not 100% sure is really credible just yet, but he is saying that the Max 87 is coming today on Sunday and that does kind of fit the vibe of years past where Sundays were the icon SBC and the hero SBC days when they would drop. So if that's going to be today, that's going to shake up content a lot. I'm still watching like 85 to 87 rated fodder, guys. I think that with an SBC like this hero pack, we talked about it in a video last week, how much we think it might cost. I don't think it's going to be that expensive. It's the 84, 85, 86 and 87 rated cards that I think would move the most if that SBC would be dropping today. Honestly, a hero upgrade pack in my mind has to be cheaper than the Rodrigo SBC. Rodrigo is coming in at what, three, 400,000 coins. I know that all fodder is up right now and that's going to make this SBC probably a little more expensive than what it should be. For the cards that are in it, there's a lot of lower tier cards. Again, if we take a look at some of the list of the hero players that could potentially be in this pack, I mean, yes, you've got the 87 rated max, so Tevez, Futre, Dina, Talay, Voller are not in it at all. You've got some great players in here, but you also got some players that are not going to be as desirable. Like Nakata is going to be super packable. Rosiki, Mostavoy, Unberg, those types of players. I just can't imagine that this SBC is going to be more than like 200,000 coins to get it done. And I think that's going to make the low tier of fodder move the most and probably move the best. So I'm definitely watching out for that. And maybe today with squad battle rewards, you could go out on the market and pick up some of those, especially like the 86s that we shouted in yesterday's video, like 8K, those have started to move up in price into like 8.6 or 8.7,000 coins for that part of the market. Also, if there were to be that SBC today, there would be probably some panic selling on some of these heroes that are going to be in the pack once again. Maybe Ramirez gets panic sold a little bit, but also a card like this. Or I think we mentioned this in the other video when we were looking about looking at the hero pack would be a card like Robbie Keane. He would probably get panic sold. People would be like, oh, my goodness, the pack is out. There's panic. I got to sell cards to do the pack. But at the same time, he's not going to get packed that much, right? It's going to be the Rosiki, the Nakata, those types of players who can get packed the most. So there could be some panic and a bounce pack. And on the whole market in general, if we get that hero pack today, there's definitely going to be at least some panic just about everywhere because that is just an SBC that so many people want to do. I wouldn't think that it'd be like a crazy, crazy amount of panic today for that. But we'll talk more about Sunday market here in just a second. Other SBCs that could be today, we do still have the potential, I guess, for Lauren Blanc, an icon SBC, maybe EA scrap the hero pack today and do what they did last week, drop an icon player SBC. We had, of course, the Beckham last Sunday. Blanc is leaked. If this drops, I also think this one's going to end up being overpriced because of how expensive fodder is right now. I believe Blanc on the market is still around 400,000 coins, which this is a really good center back card, guys. And a lot of people would want to craft this SBC. He's got great play styles. He's got the jockey. He's got the anticipate plus bruiser and aerial. And he's medium, high work rates, three star weak foots, not the best, but the great France links as well. And also center attacking mid alternative position for some interesting squad building opportunities, even though the stats don't look amazing on a card like this, if the price is anywhere near doable, even with fodder at the high price that it is, this is an SBC that a lot of people would want to do just because I don't know how good he is in this year's game.  Icon just gives so much chemistry this year in squad building. I think that SBC would probably be more than what he is on the market. But that could be a potential part of content that would drop today as well. And then we can't forget about, as always on Sundays, we're looking at a mini release. And these are the players that are going to be the mini release today. We've got Henderson, Mitoma and Dante. I think Mitoma would definitely be the most hyped out of these. And we're going to keep an eye on their prices for most of the day on Sunday because some of them or probably Mitoma, depending on the stats, right? If he looks really good, could get really, really cheap and then rise up really, really high into Monday morning. We saw that last week with a couple of cards, namely Hinkapay, right? Good so went up as well. But I think Mitoma would have a lot of hype. So we've got to keep a fresh eye out for that kind of situation on the market as well as we head into like Sunday night into the evening. Now, let's talk about the market a bit more. Do you need to sell, right? I'm just looking at Rafael Verón's price and he's what, 85, 83, 84 somewhere in there? Just right around 85K where he's been, right? Yesterday, the market had a pretty nice rise, which was expected, right? Let's take a look at Verón on foot then because I've been following his price at least a little bit and knowing where he's been fluctuating. We had a nice Saturday morning rise, which is always to be expected as everybody's out playing footchamps. Verón went from 84K up to 89, dropped back down to content. The market is still feeling very safe, is I think the best way to describe it at the moment. There's not a lot of panic and I'm not expecting a lot of panic. A hero pack today would create some more and it would probably cause some dips on the market. But I don't think it would be a reason for you to have to go out and sell. Where's Rashford? That's another player that I've been keeping an eye on in prices. He's still like 170. If he's still 170, the market's still really stable. He's, OK, 160. So he's down a little bit. I don't know if it's maybe anticipation for today's content. I mean, Rashford was 177 yesterday and also we do have squad that rewards of coming. Maybe some of these prices kick back after squad that rewards. But still, overall, the market seems to be a pretty, pretty stable space.  Or is it just kind of natural fluctuation as we go throughout the weekend as people are buying and selling cards for teams and all that sort of thing? I wouldn't be too worried about the market right now. Even if we get really good content today, I think the market would bounce back really well into tomorrow and Monday, too, if there's an opportunity to get in on some really, really low prices. Now, let's talk about low prices and maybe a couple of these cards that you could see rise up this morning on Sunday with squad that rewards. If you watched this video before, then it might be a decent idea to go out and find a gold card like Rashford or maybe Varan, who's a bit low and try to pick them up and sell them after squad that rewards because the past couple of weeks, it has been a really good time to make some quick flips on the market. This week, for sure, there's going to be a lot of rewards paid out because during this last week, if you guys remember, we had the whole squad battles like glitch thing where people were playing 3v3 in squad battles because of like whatever was it like a Volta glitch or something, people were trying to get top 100 by playing 3v3 against ultimate squad battles. So there's going to be definitely some people getting rewards from that today. And I think that'll create some positive price movement on the market. I would also say for today, look for Snipes on fodder. If you're looking to do an SBC like I am for like Son or for Rodrigo, or if you think the hero packs come in today and you maybe want to get some 86s or 85s on a low price, definitely look at these prices on bid and snipe during rewards because that'll be an opportunity of pack supply where you could find some of those. So that's definitely what I would mention for the squad battle rewards market kind of thing today. And guys, also, we had to keep an eye on the SBCs. Are they going to finally drop some more supply? Are they going to try to keep these fodder prices in check or are they just going to keep dropping more player SBCs and let them keep rising? Trailblazer challenge one was dropped on Friday. I have to imagine we would get one of these either every other day or every couple of days. I was expecting one yesterday. We didn't get it, but definitely with another challenge SBC today or we could see the return of the 100 K packs in the store. They are gone now and they didn't come back yesterday. There's still 50 Ks. I would not be surprised if there was more store packs today, especially with the mini release being out. So all in all, it really just kind of comes down to does EA go for the icon SBC today with like Blanc or do they go with a big hero pack SBC hero pack would definitely create some movement on the market. There'd be great opportunities to trade with that. Focus on out of pack specials. If you're if you're looking for a safe place to make quick flips on the market, out of pack specials are always a really good place to go, whether they're expensive ones, whether they're cheaper ones, just because they don't have as much supply. They fluctuate down really fast. Like this Luis Diaz is one that every single day goes from like six hundred and sixty or six seventy all the way back to seven thirty. Oseman wrote to the knockouts. These RTTK cards from Team One are great to trade with. Early on, in forums are amazing to trade with as well. Oseman's really high right now over 600,000 coins. He was I'm pretty sure he was about five hundred and twenty K yesterday at one point. And of course, watch out for your trailblazers because these cards do fluctuate really, really well each day. I've been keeping an eye on like Jude Bellingham this evening. He was like a million coins yesterday and he was he still is eight hundred and seventy. Maybe he goes back to like nine fifty or something today after rewards. So that's the sort of thing you could watch out on for a market fluctuation today as well. But it's really going to come down to this EA want to drop a hero pack today or just an icon SPC for Blanc or maybe they just dropped Declan Rice with the mini release that comes out. The mini release is like the number one guaranteed thing today. Everything else will see what EA wants to do. But that's going to be a video for today, guys. If you did enjoy, drop a thumbs up on a common level. If you have questions and subscribe for news beneath one count. Catch you guys later. Peace out.


In module 5, we have discussed many of the materials which show interesting properties both from electrical resistivity point of view and also how some of these materials hold the key to electronic properties based on the magnetic response. So in the first few lectures, we have discussed about colossal magneto resistance. It is mainly to do with oxides where the resistivity is basically fine tuned by the magnetic transition and we have also looked at two other applications namely GMR and TMR. Those are actually not the materials intrinsic property but those are extrinsic property dependent on the interface of the multilayered structure and how this magnetic alignment of this layers across the interface can define the electrical property. And those are specially rich features because they affect the applications to a larger extent and we have also seen another extremely illustrious candidate that is a high temperature superconductor in the form of oxides. How they have shown unusual properties mainly coming from defect chemistry and the class of superconductors that we have seen are mainly highlighting the importance of what can happen within one unit cell which can affect bulk phenomena such as metallicity in metal oxides. Today I am going to attempt on a larger issue of carbon family because in the last 15 years the number of publications that has been generated because of the new adventures that have gone through in this carbon family has almost overtaken any other field and this carbon family has also is another very important interface which has brought biologists, physicists, chemists and engineers together. This is one of the another important milestone other than the high temperature superconductivity and colossal magneto resistance which has brought interdisciplinary approach into our modern research. So I would like to place all these issues on record because if we really look at some distinctive innovations or discoveries which has come which has almost shaken our research activities across the world I would say that this is the most important and third most important milestone in the last 25 years. The first slide also sums up the complexity because it is not possible to just represent one structure to define what this carbon family new carbon family is. As you would see here it is all about a black stuff that is coming and that black stuff can be anything. It could be in the form of a ball which we call it as fuller in or it could be in terms of a wire which we call it as carbon nanotube or it could be as a sheet which we call this as graphing. Now to just bring to your focus what is hidden here it is not just the shape but it is the dimension that has progressively changed and to understand all these three new allotropes of carbon is absolutely impossible to cover in just one lecture. So in this lecture I will try my best to bring essential features of each class and try to see whether we can get some comprehensive picture of all the three discoveries that has come through in the last 10 years and this is just a few milligrams of carbon which is actually carbon nanotube which a person is holding and this little amount of carbon can actually cost you several hundred thousands of rupees or dollars. So it is so expensive so important and the we will see in the next few slides what are the rich chemistry that is hidden in this compounds. Just to highlight how much we have transcended in this research in terms of dimensionality all we know is the most familiar three dimensional carbon that is graphite and diamond. Both the chemistry of it and the practical applications of it we know so I do not want to highlight dwell more into it. But after 3D we have immediately come across the zero dimension carbon that is nothing but fullerins or bucky balls they are actually in the form of a football and if you look at the symmetry if you take a Ecosahedron and then try to chop off the apical carbons then you would be able to get this bucky ball or the fullerin and therefore if you look at the this is of a higher symmetry Ecosahedron has the highest symmetry and in this symmetry you call this as a zero dimension and also the confinement of this size is very few nanometer. So, from 3D actually we have transcended to zero dimension and in terms of the history of the invention from zero dimension we have transcended to one dimension that is single wall carbon nanotube or multi wall carbon nanotube and from one dimensional carbon recent discovery holds lot of promise on that two dimensional carbon that is graphene this is realized in 2004 and now you would see on a comparative scale graphene is actually going to take over the whole industrial applications because of it is rich physical properties. Now, what we need to understand as we go from a zero dimension to two dimension these are the new manifestation of carbon until recently even in the school test books it was written as the third allotrop of carbon which is graphene. But now if somebody has to write or history makers have to re correct that we now have at least 5 manifestation of carbon including the two dimensional graphene and one dimensional carbon nanotube. But basically I want to bring another essential feature if you really look at the structure of how this fuller in or this one dimensional carbon nanotube evolves you would understand that it is basically made of the two dimensional graphene sheet.  So, when you slice these layers then you result in a graphene sheet. So, it is as simple as that but then the technology was not to its maturity that such two dimensional layers could not be achieved. But now we have a way to do that and we will also look at the chemistry begin how to make this graphene sheet. So, this is the paradigm shift that we see in this carbon research and therefore, we can very confidently call this as a new family of carbon. So, in this lecture I will highlight to you starting from a zero dimension fuller in and I will dwell little bit more on one dimensional carbon nanotube and then I will look at some of the details of two dimensional graphene. Just to highlight one more point this curve which is shooting up is actually the amount of publication that has gone through in the recent past on carbon nanotubes compared to the fuller ins the fuller ins is here and then you can see a sudden upsurge here for the graphene. Graphene is just hit the news and therefore, graphene is going to really transcend but overall the major focus among all these three has been carbon nanotubes because it has been well established now even in terms of applications. So, just to give you idea about how the global research is positioned now you have lot of activities mostly on carbon nanotubes compared to fuller ins. I cannot resist by introduce these two people who actually have been involved along with them professor Croto also is given the distinction of being one of the noble laureate but first person who really hit the news is Dr. Richard Smalley from the rice university but with profan's sadness I should also say that he succumbed to cancer few years back. So, he is no more but he was the person who really found this buck minister fuller in he isolated it along with professor Croto and this is the picture of the bucky ball that they isolated from rice university at Houston in Texas. And here is another person he is actually electron microscopy's and he was not a synthetic person though he is basically electron microscopy's all he did was a very careful investigation of the fuller in which was made and during his electron microscopy studies he found some images which became very prominent and that was the cause for the discovery. But what really brought the fuller in to focus is this simple cartoon which otherwise would have missed the whole lot of discovery I want to just emphasize the curiosity that we need to have in doing research and in this case what you see here is the mass spectra mass spectra which gives just one single m by e p ratio for this fuller in which does not come in 0 to 100 me it is beyond 500 me which usually we might be tempted to ignore specially when you talk about carbon clusters you would not like to look at a higher m by e ratio and this is m by e ratio comes beyond 500 m mass and this single peak actually brought the discovery of fuller in into focus otherwise there was no way they could map it. So, every characterization tool in my material synthesis is of a great importance and therefore I would like to stress how this discovery in the first place was made. And then because of the curiosity that was generated in fuller in chemistry the single walled carbon nanotube was found and as you see from this cartoon below that there are different layers that or different layers with different color purity you can see but each of this layer actually is a composition of carbon nanotube. But with different walled diameter so this walled diameter tells the intensity or the different carbon nanotubes that you can separate and thanks to chemistry that it is possible to really purify these different carbon nanotubes when they are suspended into a common solvent. So, this is how it is isolated and little bit more into the discovery of carbon nanotube the whole transition from fuller in to carbon nanotube came because of this microscopy as Dr. Sumio Ijima from Japan he is in the NEC center and this is how it was to be when he was studying the material deposited on cathode during the arc evaporation of synthesis of fuller in he found that the cathodic deposit contained a variety of close to graphitic structures including nanoparticles and nanotubes. So, this is a simple curiosity and this is the mapping of such discovery and what you see here these are all close walled nanotubes carbon nanotubes and they are also multi walled and this brought the curiosity about the discovery of carbon nanotubes. So, to start with make two observations because this issues need to be told that there is a role of serendipity that is sudden discoveries which has played very heavily in this new family of carbon and observation and insight along with relationship between mission oriented and curiosity driven research. So, each one is a classic example of the statements that I have made mission oriented research and being very careful when you stumble at a discovery because that might actually transcend you to another discovery. If you are only concerned about that one single peak corresponding to fuller in we could have just missed out on a whole rich chemistry of carbon nanotubes. So, this is a curiosity driven research therefore, every single image that we record every single spectra that we record is actually very very important. Now, this is a cartoon which is actually a simulation, but this shows the different polyhedra's that the carbon can generate and in this case you can see the three different polyhedra of carbon and hydrogen. One is a cuban type another one is dodecahedron and the other one is the carbon nanotube. This is exohydrogenated carbon nanotube. So, this is out of a simulation that we have developed just to show that there are three different polyhedra's that the carbon can exhibit. So, let us take for in the first place the discovery of fuller in and what it really means as I told you in the previous slides. This is a carbon with higher symmetry and therefore, we call it 0 dimension and the numbers that we need to remember here are there are 12 carbons with 5 membered ring and there are 20 carbons with 6 membered ring in this bucky ball and out of which if you look at the edge sharing between the 5 membered ring and the 6 membered ring there are 30 such edges and there are 60 such edges between a 6 membered and a 6 membered and a 30 such edges between a 5 membered and a 6 membered ring. These are the features of this carbon why I am telling that is because when we try to bring out different chemistry or some new chemistry out of this fuller in we need to understand in perspective where to attack which carbon atom to attack. Therefore, it is important for us to know some of these coordinates and this fuller in C 60 is typically of the order of 7 angstrom that is 0.7 nanometer and therefore, the volume is around 180 angstrom. So, these are the numbers that we need to have in perspective and how do we isolate because whenever a fuller in is made you actually get a range of carbon suit which can have different fragments or different C carbon clusters. So, the chief of this is nothing but C 60, but it is also observed that C 20, C 30, C 70 are all fragments that can be observed along with C 60 which is the major product or which is called as the fuller in. So, one of the useful way to identify whether you have a very clean C 60 or not is to use NMR and here is a NMR of C 13 which is recorded for fuller in that is C 60 and C 60 will actually give you only one C 13 NMR peak and that is between 140 to 145 ppm. It is a very, very characteristic peak coming from a C 13. So, if you have just one peak in C 13 that means you have got a clean C 60, but if you are going to have C 70 then you would actually have 5 peaks coming in the same range, in the same range therefore it is very easy for us to map whether we have C 60 or C 70 as a mixture and in C 70 you do not have the same sort of symmetry therefore there are 5 different carbon centers in C 70 as a result you would actually find 5 peaks in C 13 NMR. So, therefore it becomes very easy for us to map whether it is a pure compound or not and one of the best thing that can happen in this whole chemistry is the solubility because it is otherwise very difficult to isolate carbon and fortunately carbon 60 can dissolve in a variety of solvents and as you see here I have listed very few of several common solvents have been explored organic solvents, but these are some unusual solvents in which carbon 60 is soluble and therefore I have recorded it. So, in most of the common organic solvents like ethanol, methanol, dichloromethane or DMF or DMSO the solubility is very very negligible of the order of sometimes 1 gram or less than 1 milligram per ml. Therefore the most important one is 1 chlorine aptiline where up to 51 milligram you can dissolve in 1 ml and as you can see here you get a very good purplish color of solution which is devoid of any suspension therefore it is possible for us to even make a film out of it and this can be used for variety of other operations and therefore the solvents that we need to use whenever we get a carbon suit goes in this order. Naptiline based solvents or as you see here dichlorobenzene, trimethylbenzene, xylene, carbon disulfide all this shows very good solvent property for this carbon nanotube. One more thing that you need to understand in perspective is there is another cartoon which clearly gives another possibility that if you oxidize the fullerine then this can actually become if you hydrate this fullerine then it can become a hydrated fullerine as a result you can make this even water soluble. So this is an example of a hydrated fullerine which can improve on water based chemistry which is environmentally also more preferred therefore hydrated fullerines are also possible when you try to carefully hydrate this fullerine molecule. Now how does this fullerine come because when you try to synthesize fullerine as you know you try to use a arc plasma method by which you try to get a sudden deposit of carbon from graphitic rods and how it all happens the proposed mechanism is as follows cyclic polyenes what you see here they can fold on to itself so tightly that the new carbon bonds can form which is actually shown in the dotted lines. So these are all C 60 polyene actually can be bundled into this fashion where new bonds come up and they curl up to give a C 60 molecule other than that because it is such a flash process there is no way that we can generate or simulate how the bond making happens for this to happen but this is the proposed mechanism for how the new carbon bonds can be formed. Now what do we do with this fullerine and where is the chemistry lie in this bucky balls actually fullerine can be modified and that is where the chemistry comes into picture you just do not look at it and simply appreciate but then you try to put lot of molecules or take out some atoms out of it and try to create rich chemistry in that. So the substitution of this fullerines actually can be viewed in three ways one is exo hydral fullerines where you try to put atoms or molecules or complexes on the top on the surface of the bucky ball or the fullerine so you call it exo. Another thing we can do we can try to push some atoms or molecules in a preferred way which can go and they can be held through a real charge transfer process it is not simple physical existence but there is a chemical phenomena happening between the molecules which are caged inside and therefore those are called as endohedral fullerines and another thing is it is not just the fullerine playing a host lattice where it can either do exo or endoh it can also be a guest not only a host and in that case fullerine molecules can actually be pushed into carbon nanotubes so it can actually play a guest role also as much as it is a good host. So based on these three divisions several examples can be generated this cartoon gives you an idea all the fullerine reactions that are possible specially c 60 molecules undergo most of the reactions that we have listed here also c 70 to a lesser extent may undergo addition type of reactions polymerization type or substitution types of reaction specially with the boron. So just I would like to pull out few examples one is this bucky balls can be polymerized in this fashion this can become very interesting. So simple polymerization of this through extended linkages like this is possible so you make a polymer which can be dendrimeric or it can be linear therefore polymerization of this is possible and then I will take few examples to discuss it is impossible to go through all the cycle one is hydrogenation to fullerines you can completely hydrogenated because there are double bonds in it and then you can also make epoxides this is a very reactive reaction where you try to treat it with oxygen in the presence of light or we can actually do cycloaddition in this fashion or we can actually have lot of host guest complexes organometallic derivatives which can be generated on the top of the bucky ball. So several reactions are possible in this form and we will take one or few two examples to see how this can be done endofedral fullerines these are fullerine cages with encapsulated molecules which have many potential applications it is construed that scientist will be able to engage a radioactive tracer and inject that safely into human body for mapping or for any spectroscopic investigation for any radiation therapy it is possible that we can actually use radioactive tracers to be injected into human body in a very safe mode and that way fullerine is compared to be a very safe carrier because you can put that inside and you can transfer it into the body. Another thing is currently various molecules can be engaged in fullerine for example lanthanum can be put inside carbon cage which is a C 82 cage and helium which is a monatomic gas can be put inside C 60 therefore even putting preferred metal ions depends on the cage that you are looking for C for example lanthanum cannot be easily put into C 60 because of its dimension and other physical properties that may become intricate therefore it is also to some extent selective and similarly you can put scandium in C 66 cage so it is possible but in those cases the product yields are actually less than 2 percent and in endofedral fullerines there are lot of information that we can get for example metal of fullerines there is a charge transfer between the cage and the enclosed metal as in the case of scandium that is put inside C 66 so many rich chemistry can be verified as to what really is the interaction it is not just a bound pair but something unusually happens to this endofedral fullerines and for a review actually we can go through article by professor dunge these are again two examples of exohedral fullerine and this is from C 60 molecule which is actually capped to osmium metal here and this osmium metal is bound to two pyridine rings so you can actually get a exohedral fullerine using osmium and this can be put in this apical position here or we can actually use iridium metal center also and iridium carbonyl this is a carbonyl moiety and chlorine attached to it with other aromatic rings so this sort of exohedral fullerines have also been attempted and if you find out this exohedral fullerines actually has a very potential application as hydrogen carriers and therefore it is being explored very richly for application into hydrogen storage because this osmium or iridium metal centers can actually bind dihydrogen species and they have a special tendency to exchange this dihydrogen give it give up and also to retake and therefore when it becomes a reversible process then it is a very useful material for hydrogen storage and what US department of energy forecast is they just need a 9 weight percent hydrogen storage density in any material and 9 percent is enough to drive any automotive vehicles so it is found that organometallic molecules based on C60 and boron which is doped seem to have special affinity to dihydrogen species that is molecular hydrogen so you can try to take it complexes of transition metals with hydrogen they also can take only thing these transition metal complexes they actually polymerize when the dihydrogen species is removed as a result it is a irreversible one and that is not the chemistry behind hydrogen storage so if you want a hydrogen storage material then you need to be able to liberate the hydrogen and also selectively take it back otherwise this cannot be a useful candidate and in such cases scandium hydrogen species which is attached to C60 has been found to be a very good complex this leads to stable species which can reversibly absorb additional hydrogen so this is one of the candidate which is being explored for hydrogen storage applications and same I have tried to show you through this view graph you can see here scandium metal center which is able to bind a rich amount of molecular hydrogen species here and this can become reversible so we can put it and take it back doping with boron becomes very important in this case so this enhances the complex stability by increasing the binding energy and this allows the binding of an additional hydrogen molecule per scandium increasing the amount of retrievable hydrogen and this is actually a paper found in physical review letters in 2005 now the other chemistry that can happen from fluorine is that you can get into the carbon nanotubes and therefore fluorine when it is endohedral fluorine they can actually serve as a carrier which can be filled into open sided carbon nanotubes so single wall carbon nanotubes encapsulating C 60 is also there only thing achieving this is a very tricky thing although theoretical studies they show that to put fluorine into carbon nanotubes it takes only 0.37 electron volt which means it should actually happen at room temperature but so far studies have not been successful where people have tried it up to 350 degrees in vacuum so here is another example where the Russian group they have tried to attempt at room temperature only thing the yield is one less than 1 percent adding single wall carbon nanotubes to a saturated solution of fluorine has been attempted and vice versa taking fuller in into a saturated solution of single wall has been attempted and one approach which has given dividends is it is almost like a brute force where you try to use high pressure so here is supercritical carbon dioxide which is used and using this under high pressure for 10 days they were able to dope successfully fuller in into carbon nanotubes to the order of 30 percent so it appears that with the more of high pressure it is possible to do this nano peapots sort of synthesis so this has also been attempted in the recent past these are some of the examples of how different derivatized fuller in can be made and these are specially candidates for HIV properties and this has appeared in bio organic medical chemical letters chemistry letters and this has come out in the year 2005 where they have found specially the geometrical ones the trans and cis isomers they have a very selective response to HIV virus so this exohedral fuller in are specially candidates which can have specific activity and here is another example where we can try to make dendrimus out of fuller in so you have the fuller in moiety here but you can actually attach such first generation dendrimus so as a result you can actually get a very macroscopic molecule and this is specially useful because it turns out to be totally water soluble so this has specific applications therefore such molecules also have been prepared in the recent past and lastly on fuller in's I would like to mention that fuller in is not just about a substitution but fuller in's with doping with potassium ions have shown a extraordinary property of superconductivity so this is a super conducting potassium doped C 60 K 3 C 60 which actually shows a TC somewhere at 19 K but what you would see here if you try to replace this small cation potassium with rubidium or then rubidium you can put and translate it with cesium you can see that the lattice parameter of this C 60 is changing from 14.2 to 14.6 and as there is a expansion you also in the crystal lattice you also see that the TC is varying so this has been attempted and this is one of the extraordinary response of fuller in in terms of its electrical property so just carefully doped with the monovalent ion potassium rubidium cesium anything you can translate it and these are not just a fluke method it has been characterized very clearly that it seems to have a very definite dependence on carrier density so depending on the carrier density the TC can be altered so fuller in has specially hit the superconductivity map mainly because of its substitutions around the carbon cage. Apart from this phenomenon of superconductivity that is seen in fuller in another important application is also in the area of photovoltaics as you would see here this is called as PCBM which is a very well known candidate of C 60 which is nowadays used as a blend along with a fluorine of fluorine polymer this is the fluorine base with different substitution in this case it is with the Benz diethyazole and with such molecules it is possible for us to make a blend where you actually get a donor and acceptor fuller in as acceptor and the fluorine as the donor so you can actually make a hetero junction polymer and this is the view SEM view graph of how a polymer blend will look like you can see that you get a very continuous spread of a amorphous polymer film and what you can clearly see is that this is the PL this is the absorption and PL of the fluorine moiety where you can see the fluorine absorption is somewhere around 500 maximum at 500 but once you make the blend you can see that it is actually blue shifted which means it is shifted to higher energy therefore this will become a very efficient blend for photovoltaic application and this is the view graph in the inset which gives you approximate clue to how this sort of hetero junctions can behave and this is in dark and this is the IV curve in light and you can see that the open circuit voltage OC and the fill factor is quite decent here and carries a good amount of current density so the latest application of fuller in although it is not being talked about as much as carbon nanotube but it is actually playing a very very silent role in terms of becoming a very useful electron acceptor in photovoltaic devices. One last example before I finish on fuller in is the water soluble fuller in derivatives which has been found to have antiviral activity and specially in terms of treating with this sort of virus forest virus or stomatitis virus what has been found out is if these viruses are blended with water soluble fuller in and if there is a visible light illumination with respect to the illumination time you can see that the virus level is rapidly coming down and this is with addition of C 60 and without the addition of C 60 you can see the response and without light you can see the response and with the light with C 60 you can see a tremendous influence on the antiviral activity so carbon 60 or fuller in seems to have a very peculiar response to biological applications also the chemistry there is this effect is attributed to the generation of singlet oxygen which actually will impair the viral activity so it is the singlet oxygen that is generated which is responsible for this antiviral property. So in summary of C 60 we can say C 60 bucky ball was the first fuller in that is discovered and it is the third form of pure carbon which is next to graphite and diamond but this summary is inconclusive because we have the other new ones which have come into picture variations of fuller in include exohedral endohedral and nano peapods and synthesis challenges still exist for all the variations of fuller in because the mechanism of formation is still unknown and potential applications are now envisaged in the field of medicine nano electronics and in energy of which I have given a representative example. Now having said this I have to confess that this is a very limited scope in which I have tried to tell about the chemistry of fuller in but there are several literatures in the in the web sites there are several useful links which can give us tremendous information about the chemistry of fuller in which I will be listing in the slides at the end of the lecture. Therefore, I encourage that the readers can go through that now we will focus our attention on carbon nanotubes and this carbon nanotube is a one-dimension carbon nanotube and we can see how this carbon nanotubes evolve from the basic structure as you would see here there are two cartoons which I have projected here one on the left side on the top is a single wall carbon nanotube which you can easily map it around and this is just a picture of graphene which is actually rolled up. So, that is the easiest way to visualize how a carbon nanotube is evolving and then on the right side you see this is a multi-walled carbon nanotube. So, several walls are there which means one small carbon nanotube got fixed to the other and then to the other therefore, you can actually go for several walls. So, it is called multi-wall nanotubes and there can be just two there can be even seven there can be four depending on the process that you adopt to make this compounds.  So, the point is the way you try to roll up the single wall nanotube will end up in different electrical properties of the single wall nanotube which I will try to list it. Now, the way we can try to roll up this depends on the unit cell or the way we map it. For example, let us take the case of this axis if you try to draw a line and this is a C H vector now in this we can express C H as n A 1 plus m A 2 where A 1 and A 2 are unit vectors of graphene in real space. So, the way we mix this numbers n and m will matter what sort of carbon nanotubes we can get. For example, in the case of n 0 what you see here n 0 this relates to a zigzag carbon nanotube if it is going to be along n n it is called a armchair nanotube. So, what does this mean here this is going to be 1 0 and this is going to be 2 0 that is what we mean by n 0 and this is going to be 3 0 and so on. So, if your axis or your vector is going to lie on n 0 then you would actually get a zigzag nanotube and if it is going to be for example, here in this case this is 1 1 and in this case this is this case this is 2 2 and in this case this is 3 3 and here this would be somewhere around 4 4 then we are talking about a n n armchair. So, the way you roll it up matters with respect to this C H vector and that will determine what sort of nanotube you get and the corresponding electrical property and that is what we see here in this cartoon. So, if you have a armchair which is nothing but your 1 1 2 2 3 3 and so on then the alpha that you generate with respect to this alpha is going to be 30 degrees and in that case actually you would end up with your armchair configuration and if it is going to be 0 which we saw in the previous cartoon that is your 1 0 0 2 0 sorry 1 0 2 0 3 0 4 0 then you get across zigzag which is alpha is equal to 0 degree or it can be also a intermediate one where your a is not equal to b in that case the angle can vary between 0 to 30 degrees and you end up with other configuration. So, based on the way you scroll your graphene sheet you can either get a zigzag one which is metallic in its nature or it is a armchair which is semiconductor in its nature or it can be a chiral one which is semi-metal in nature. So, carbon nanotube itself brings about lot more complexity by the way it is arranged so it can result in different dimensions it can result in different configuration it can result in different property different dimension I mean it can be single volt it can be multi volt and it can it can have the diameter which is different and as you see here the way you roll it you can also expand the dia of your nanotube and this also affects the electrical conductivity. So, you can also get a metal you can also get a semiconductor depending on this so the whole issue of carbon nanotube revolves around which one you selectively get and how what is the method that you use for getting such selective ones and as you see here this is another cartoon just tells you the if you are going for a armchair then you look at the edges how they reflect and if you are going for N0 you can look at the edges how they transform to be. So, just by looking at the way it is scrolled you can decide on the configuration and depending on whether it is a zigzag or whether it is armchair it is also possible for you to get a different sort of dimension of your carbon nanotube and in this case you can see the TEM microscopy which clearly shows the TEM image shows this sort of a structure that means this is a single volt carbon nanotube which has a dia of 1.37 and here you have another one which is called a double volt this is one volt and this is the outer wall so we call this as a double wall. So, this double wall stuff is also possible or you can see this TEM image which actually has more than 4 so this is a multi-walled nanotube. So, in essence when you look at the literature you can actually see this abbreviation quite a bit SWNT or MWNT both are referred to as single wall and multi-walled nanotubes for certain applications multi-wall is more than enough, but for certain preferred applications you always desire to get a single wall nanotube which is a challenge. Just to draw your attention to the electrical properties and why so many literature outputs have come on carbon nanotubes. Let us just make a lighter comparison between the different forms of carbon then we will get to know why this research is still a very intense activity. Now if you take the property and compare with the different carbon forms you can see here specific heat this is comparable to diamond thermal conductivity if you observe the thermal conductivity of single wall is much much higher than diamond or graphite. Therefore, from thermal conductivity point of view single wall nanotubes are really most preferred. Electrical conductivity again you can see for graphite it is 900 to 1700 Siemens per centimeter whereas in the case of carbon nanotubes it is almost comparable or even double than the graphitic form. Therefore, in terms of electrical conductivity it holds a lot of promise and then the same is true for thermoelectric also you can see the thermoelectric power at 300 K is around 3.5 for graphite whereas it is 22 for single wall nanotubes. So, you name any physical property there is a very distinct difference between either graphite or carbon nanotubes or diamond with carbon nanotubes. Therefore, there seems to be in essence some curiosity on almost every property that we are looking at. Now, how do we make this carbon nanotubes three important methods are there which I would like to highlight one is arc discharge method another one is chemical vapor deposition another one is laser ablation method which is a vaporization method. So, in arc discharge you actually bring two graphitic rods you apply very high voltage and a plasma generate then all the carbon shoots are trapped in alkene and then we can try to isolate different fragments of carbon nanotubes. So, that is the way it is done and then we can actually produce single wall and multi wall carbon nanotubes with few structural defects and then tubes tend to be short with random sizes and direction which is the limitation of your arc discharge method. Whereas in chemical vapor deposition you place a substrate in oven heated to 100 degree and slowly add the carbon bearing gas usually acetylene is sent and in that case it frees up the carbon atoms which actually combine into carbon nanotubes. It is a easiest way to scale up to industrial production and the only problem with the chemical vapor deposition is it actually induces lot of defects and then we can look for the most sophisticated one that is laser ablation blast the graphite and then try to trap the carbon that is coming and there is various conditions primarily this gives selective single wall carbon nanotubes, but the problem is it is more expensive and it requires more sophisticated infrastructure. As a result people usually prefer either arc discharge or chemical vapor deposition which is much more versatile and these I have included just to give you an idea about what this arc discharges you have the two graphite rods and this is actually kept in vacuum in helium atmosphere then you get the discharge and trap the carbon suit or we can actually shine the laser to graphite rod and then we can trap the suit in a water cooled copper collector or we can actually take a silicon-silicon dioxide wafer and try to put some nickel film on that and then run it through hydrocarbon and when this is heated then this would actually decompose the hydrocarbon to carbon nanotube on the nickel metal. So these are various ways of getting this single wall carbon nanotubes or multi wall carbon nanotubes this one I have specially included just to show how people have become obsessed with the carbon nanotubes. As you can see for those who are really working on this it can become an obsession like a doll and this person here is actually holding such a three dimensional model. So you can see how it can become so close to your heart when you try to work on carbon nanotubes you can see the simulation pictures which show how this carbon nanotubes can be tagged to something and this is another view graph which shows about carbon nanotube forest look at the way laterally they are grown bundles of carbon nanotubes can be formed and these are called as carbon nano worms you know so much of chemistry which is rich and several groups are actually working into probing the interesting aspects of carbon nanotube. So I will stop here and try to deal with this in the next lecture specially on the chemical properties of graphene and also on single wall carbon nanotubes.