Welcome, everybody, to EuroCube 2021! My name is Alexei Dovenko and I'm going to present you a joint work with Alex Birikov about dummy shuffling against algebraic attacks in whitebox implementations. Enjoy! I will start with a brief introduction to whitebox cryptography, followed by greybox algebraic attacks and algebraic security, which are the main topics of this work. The main part of the talk is about shuffling and how it should or should not be used to protect against algebraic attacks. Let's start! In the whitebox model, the adversary has full access to the cryptographic implementation, typically of a symmetric key primitive. The main security goal is to prevent the key extraction. There exist possible additional requirements, such as one-wayness, incompressibility, trait at riskability and others. We focus on the most challenging direction in the whitebox cryptography, which is about implementations of existing primitives, such as the AS block cipher. This is in contrast with the idea of designing dedicated whitebox ciphers. Whitebox implementations are closely related to the more general framework of cryptographic obfuscation. Indeed, any generic whitebox technique would likely be a useful tool for general cryptographic obfuscation. There are two camps around the whitebox cryptography. Industry has a strong need for practical whitebox implementations to use it in many applications, such as DRM or Securing Mobile Payments. Industry does whitebox, but relies on secret designs. In academia, theoretical obfuscation, such as indistinguishability obfuscation, was very recently constructed on top of reasonable hardness assumptions, but it is far from being feasible to implement. There were attempts of practical designs, starting from the seminal work by a show et al. in 2002 and followed by many reparation attempts, but overbroken by very efficient attacks. Even worse, a work from chess 2016 showed that most of them are vulnerable to classic side channel attacks, which can usually be performed in an automated way. This created a new line of research aiming to develop whitebox countermeasures against very generic attacks, such as power analysis attacks or fault attacks. Power work follows this direction and dives deeper towards whitebox-specific generic attacks, more precisely algebraic attacks. I would also like to point out that obfuscation in general has much more applications than just obfuscating the AS, and looking at the whitebox techniques from this viewpoint is much more fruitful and promising. To put the work in the high-level landscape of obfuscations, consider this graph, which relates the implementation complexity with some sort of security assurance. A reference or an optimized implementation is very efficient, but provides no security against whitebox adverse areas. Classic whitebox and code obfuscation techniques can provide security against some attacks at the cost of somewhat heavier implementations. Finally, theoretical obfuscation methods such as IO are fully secure based on some reasonable hardness assumptions, but are far from being reachable. Furthermore, the chess 2016 work uncovered a barrier for practical whitebox implementations, namely the classic graybox attacks and extended attacks applicable specifically in the whitebox setting. This work is directed towards breaking this barrier at the cost of some increase in the implementation complexity. While we do not claim to fully break the barrier, we provide a tool to protect against a very powerful class of attacks, algebraic attacks, which I am going to introduce briefly. Let's start with the differential computation analysis attack, or DCA. DCA is basically an application of classic differential power analysis to whitebox implementations. What is so special in whitebox is that there is no measurement noise. All computed bits can be recorded precisely. And the authors show most existing whitebox implementations are broken fully automatically. This somewhat puts the whitebox state of the art behind the side channel state of the art. This feels wrong, and it is natural to try to apply classic graybox countermeasures to strengthen whitebox implementations. And the most popular and efficient protections against power analysis attacks are masking and shuffling. What happens if we apply them to the whitebox setting? Let's start with the masking countermeasure. Classic masking schemes are linear. Assume that we protect a sensitive function as this is performed by splitting it into a T-additive shares. For now, we focus on storing the shares and ignore how to perform operations on them. The problem with storing the linear shares in the implementation in clear is that there exists a linear combination of the intermediate values that equals to the sensitive function. Let me illustrate the attack. The adversary runs the implementation on some input and records all computed values, a computational trace. Then the process is repeated several times. At the same time, the adversary computes the sensitive function. For example, in the case of IS, it can be one output bit of an S-box in the first round, which is a classical target is inside channel setting. Typically, such a function depends only on a few key bits, which can be easily guessed. The process is repeated until a sufficient amount of traces is collected. Now, the linear masking implies that there must exist a subset of columns that add to the sensitive value. This can be expressed directly as the linear system of equations, namely a matrix vector equation. After solving it, we obtain the positions of the shares. But more importantly, also a confirmation that the sensitive value S was indeed computed in the shared form in the implementation. In the case of IS, it would confirm the right guess for the portion of the key. What are the conclusions? First of all, higher order masking would not help. The attack does not depend on the weight of the solution. Secondly, the attack is very generic and automatic. It only requires recording of the traces and solving a linear system. What do we have? We want it to protect against DCA, that is correlation attacks, by applying masking protection. But it turns out that it is completely vulnerable to this linear algebraic attack in the white box setting. In the side channel setting, this attack is prevented by the inherent measurement noise. Before going into protections against algebraic attacks, I would like first to describe a few generalizations, which we should also take care of later. The first one, naturally, is increasing the degree of the attack, aiming to break non-linear masking schemes, which I will talk about later. This can be done by expanding the set of columns by all products of pairs of initial columns. We multiply the first and the second column, then the first and the third column, and so on. Now we solve the resulting linear system and obtain the recovered non-linear masking. Here the solution has two linear components, V3 and V1, V2, which we can recall as the product of the first and the third column. This recovers the quadratic masking scheme V1 times V2 plus V3. While this attack is more about finding the locations of shares, in this case it also recovers the actual masking function. This means that the attacker does not even need to know the shape of masking, only the degree bound. It follows that the attack is very generic. Generalization to higher degrees is straightforward. Not however, that the increase in the number of columns requires to increase the number of rows, which is the number of traces. And as a result, the attack's complexity grows very fast with the growth of the degree of the attack. The takeaway is that higher degree masking schemes can be attacked, but at a higher cost. On practice, protection against degree 2 or maybe degree 3 attacks seems to be sufficient. The second generalization is about allowing some noise in the system. It is not motivated by any existing countermeasure, but rather shows a particular requirement for a good protection. The idea is that an implementation might include some noise in the computations so that the sensitive value is not always reconstructed correctly. But the errors should happen quite rarely. In this case, a simple approach would be to attempt the simple linear attack, and if it fails, to repeat with a different set of traces. To clarify, the adversary does not see the error vector e, but simply tries to repeat the attack again and again. At some point, we might get a system without any errors, and complete the attack. The problem described is an instance of the so-called learning parity with noise, or LPN, problem. And there are more advanced attack techniques than just waiting for a system without errors. The takeaway is that good low-degree approximations of the sensitive function are sufficient for attacks, so that a designer must ensure a sufficient weight of the error for all computable expressions. The third generalization highlights the role of the sensitive value and its relation to the input in the protection. Assume that an implementation computes a function f, which is a product of the sensitive function s, and some pseudo-random, unpredictable function r. The basic linear algebraic attack would fail, because when s equals to 1, the function equals to a random value, which is hard to predict. And this happens half of the time. However, we can observe that when s equals to 0, then f also equals to 0. Can we exploit it? The idea is simple. We restrict the system to the subset satisfying s equals 0. Then we solve the remaining system and find the solution. Note that this is a degree 1 attack, even though the expression is quadratic. The takeaway from this generalization is that the protection should not depend critically on sensitive functions. As we could see, the algebraic attack is very powerful, especially with all of its generalizations. Now I'm going to describe the framework of protections against algebraic attacks. The framework of algebraic security was proposed by the authors of this work at Azure Crypt three years ago. The security model is defined in a setting similar to side-channel security models, such as probing security. The implementation is allowed to use randomness, which in the white-box setting has to be replaced by pseudo-randomness, and also includes an encoding and decoding steps, which are not included in the analysis. To define the security requirement, consider any non-constant function in the linear span of the functions computed in the critical part of the implementation. These are functions of the input and randomness. It is required that each such function must have a sufficient error term on any fixed input. That is, for any fixed input, any non-constant function in the linear span must be sufficiently far from the constant functions 0 and 1. In other words, the functions should have a low bias, or apparently a large error. Of course, algebraic security of higher degrees can be defined by considering the higher degree span of the functions instead of the linear span. The main goal of the model is to achieve secure computations, given that simple encoding and decoding functions are allowed to be out of scope of the attack. In addition, in the real white-box setting, the pseudo-random generator will also be a part of the attack surface. These parts are yet to be included in the model. They cannot be simply included directly, since they contain the input and the output, which are leaking by definition. Of course, one could include full implementation in the encode part and use some encryption to pass it through the critical part. For the protection to make sense, the encode-decode parts should at least be independent from the implementation that is being protected, but depend instead on the input and output size or maybe the implementation size. Finally, I would like to know that from the theoretical point of view, this problem is not hard. For example, one can use fully homomorphic encryption as a form of masking. It would clearly avoid all low-degree algebraic attacks, and so the difficulty is to find something much more practical, of the complexity comparable to classical masking schemes. One natural countermeasure achieving algebraic security is nonlinear masking, where a sensitive failure S can be decoded from shares by a nonlinear function F. At AsiaClip 2018, we proposed a provably secure minimalist quadratic masking scheme. That is, the degree of F is 2, and it has minimal possible secure quadratic expression. This year, H.S., Zekar, Eisenbarz and Liskevich generalized the scheme in two ways. They replaced the quadratic term by a monomial of an arbitrary degree, and also split the linear term into an arbitrary number of linear shares. This allows to achieve a combination of algebraic and correlation security more efficiently than by composing their respective masking schemes. However, they only proposed concrete algorithms and a proof for a degree 3 scheme, protecting against degree 2 algebraic attacks, which is likely more than enough on practice. In these works, the security proofs are quite involved, and it seems that reaching larger security degrees is quite hard. We now move on to our contributions, applying the Schaffling countermeasure to protect against algebraic attacks. Let's start with a basic Schaffling example. Assume that an implementation computes the same function t times in parallel. A usual example is the AS-block cipher, where the same S-box is computed 16 times in parallel in each round. The idea of Schaffling is to randomize the order of computations. The goal is to introduce extra noise against correlation attacks, which would also amplify the security from linear masking schemes. On practice, it can be done in many ways, depending on the computation model. The computations can be shuffled in time or in memory. In our formulation, we consider that the inputs are shuffled, then the functions are applied in parallel to all the inputs, and then the outputs are unshuffled back. Each such application is called a slot. We focus on the core of Schaffling, evaluation slots, as the critical part in the algebraic security model. It seems that Schaffling is a complex nonlinear procedure, and so should protect against algebraic attacks. In fact, here the Schaffling information is not even included in the attack surface, and the right order of slots is not recoverable by any attacks. But is it actually secure? I will actually now show that the basic Schaffling does not provide a reasonable protection against algebraic attacks. As usual, we focus on the critical part. We ignore the initial Schaffling and the final unshuffling steps. We only look at the shuffled sensitive values. Note that there exists no function recovering a concrete single value, such as z1. Simply because the information about Schaffling indices is not included in the critical part. However, there is still an algebraic leakage. The sum of all values is independent of the Schaffling order. And it also is a linear function of the computed values. Therefore, an algebraic attack can target this sensitive function. I would like to clarify the full setting, which may be not clear from the simplified figure on the slide. Of course, one could easily break such basic Schaffling in an ad hoc way by somehow noticing that the same values are being shuffled in the same places. However, the more general setting that the actual algebraic attacks cover allows to scatter these values arbitrarily in the implementation and to mix them by an arbitrary linear function with all other values. This only somewhat exaggerates what happens in a real implementation. The shares can be hidden in different places. All sorts of linear masking schemes can be used on top of Schaffling. In this case, it is quite difficult to come up with a non-algebraic attack. So please keep this setting in mind. I will only illustrate minimal cases, but for the algebraic attacks, more countermeasures are broken for free. That's why they are so problematic for the designers. Getting back to the leakage of the sum of values. More generally, all symmetric functions are leaked, which are by definition those that do not depend on the input order. Importantly, the attack ignores the implementation of Schaffling and Un-Schaffling. But is it exploitable on practice, or is it just a theoretic attack on the model? In the IS, the sensitive value would depend on 16 key bytes, which clearly cannot be guessed. Here we show a new kind of attack, differential algebraic attack that allows to break basic Schaffling at a minimal cost, even if it is further protected by some linear masking and mixed with randomness. Consider an IS instance with 16 S-boxes, which are shuffled, and their shuffled outputs are leaked. Again, this means that their sum is leaking clear. Now we execute the implementation on a related plain text, obtained by ejecting a difference in the first byte. In the sum of values is leaked, but only one of them is different, which means that we can exclude the unknown terms by subtracting the sums. As a result, we obtain an expression that depends only on one key byte, and it can be attacked by the linear algebra attack. This attack can be simply implemented by tracing the implementation on two related plain text, sorting the respective traces and the respective sensitive values, collecting enough such traces, and running the simple linear algebraic attack. Know that we shifted from typical random plain text attack to a chosen plain text attack. But it totally makes sense in the white box setting, where the adversary can encrypt arbitrary plain texts. One might say, another generalization, how can we hope to protect against all of them? Luckily, in the paper we show that the algebraic security model already prevents differential algebraic attacks. This highlights the strength and the universality of the model. In fact, it is not difficult to see the proof. The randomness in the model should be independent across multiple executions. Therefore, when noisy functions are added, the error can only grow. And adding the traces only makes it worse for the attacker. We are now ready to define our main hero, the dummy Shuffling. Follow the basic Shuffling described before. The dummy Shuffling simply adds a new dummy inputs, which are chosen independently and uniformly at random. We call the corresponding evaluation slots as dummy slots, while the original slots are called main slots. In the algebraic security model, we consider the initial Shuffling and the dummy generation part as the encoding step. And note that it is independent of the main computation C. The parallel main computations are considered as a critical part to be secured against the algebraic attacks. The decoding step is out of scope. Again, because including it would require extending the model because otherwise the outputs Y would simply directly leak. I will now describe security of dummy Shuffling against the linear algebraic attack. Assume we are protecting an implementation C. First we have to compute its property E1, which is the minimum error of a non-constant function in the linear span of C. Then we can show that the dummy Shuffling scheme is secured against degree 1 attacks, with the error lower bounded by the parameter E1, times the ratio of dummy slots to the total number of slots. Now we have two problems. First, computing E1 can be very hard, as it is similar to computing a minimum weight of a linear code, which is a hard problem. Second, what if an implementation has a very small parameter E1? Cannot we protect it? A good protection should be applicable to any circuit. Now we show how to deal with these problems. The idea is to sort of refresh the non-linear gates, such as AND or OR in the implementation. This is done by adding a uniformly random bit in a dummy slot and adding zero in the main slot. In order to achieve this, the respective random or zero bit must be prepared in the encoding step of Shuffling and then passed as an input to the slot. Note that each gate receives a new independent random bit. In other words, a main slot would accept a real input padded with zeros, while a dummy slot would accept a random input padded with more random bits. Note that this is not a security problem, since the large number of zeros cannot be detected algebraically by a low degree function with a negligible error. And we have the following theorem. The dummy Shuffling scheme is secure against degree 1 attacks, with the error lower bound of almost 1 over 4, and we can get as close to 1 over 4 as we want by increasing the number of dummy slots. The theorem follows from the previous theorem and the fact that the refreshed circuits have this special parameter E1 lower bounded by 1 over 4. We are now ready to describe our main result. It turns out that the dummy Shuffling with refreshed implementations actually provides higher degree security. More precisely, it provides security against algebraic attacks of degree up to the number of dummy slots. Of course, for each degree, the error bound is different and gets close to 1 over 2 to the 2D, as the number of dummy slots increases. Here we only consider a single main slot, as it is simpler to analyze. This is the most generic case and is applicable to any initial implementation. We simply consider a full implementation as a single slot. A final remark is that the error bound, 1 over 2 to the 2D, is optimal heuristically, at least in the Boolean Circus Computation model. That's because the first few nonlinear gates would take uniformly random inputs and so have error 1 over 4. And taking a product of D such functions gives the error 1 over 2 to the 2D. On the other hand, this may be only a limitation of the algebraic security model, which requires all functions to have as efficient error, even those that are computed from pure randomness and are independent of the input. Whether this achieved error bound is sufficient to prevent LPN-based attacks is yet to be understood that there was no study evaluating the feasibility range of such attacks in the wild box setting. I'm going now to compare briefly the resulting protection with previous works. This slide presents a brief comparison with previous works, namely the nonlinear masking schemes. The dummy shuffling scheme significantly improves both implementation complexity and the error lower bound. More importantly, it provides protection against algebraic attacks of an arbitrary fixed degree at a very reasonable cost, which we find quite surprising because the nonlinear masking schemes induced a rather significant overhead. Nonetheless, we believe that every provable security tool enriches the designer's toolkit and is worth studying in depth. In particular, dummy shuffling itself is very vulnerable to fault attacks, while masking schemes have at least some resistance. Please find more interesting results in the paper, including an interesting proof-of-concept construction used in one of the winning challenges of the V-Box 2019 competition. Thank you for your attention.


We're here to remember your loved ones and to honor them for giving the most precious gift, the gift of life. Zan's Garden was created as a tribute to patients cared for at Jersey Shore, whose final act of kindness, the gift of organ and tissue donation, has saved the lives of countless others. The beautiful garden includes a pathway lined with red bricks imprinted with the names of organ and tissue donors, including those we are here to honor today. I walk through there pretty much every day. When I go to operate, go to meetings, I walk through, I look at the names.  To somebody like myself who was in need for tissue, it was the biggest gift that could have been given. Three days before my 50th birthday, I received that greatest gift that one could ever give, saving my life. I received the pancreas and kidney, saving my life. And if you have young kids running around, I have seven grandchildren and all I hear about are superheroes. Anybody else hear about superheroes? I want you to see the quilts and see what real superheroes are all about, because these superheroes save real lives. One sunflower seed has the potential to bloom, grow and create countless other seeds. So too does the gift of life through organic tissue donation.


OK, folks, we got prices all over the map today. Anyway, we're going to take a look at them. We had stock sharply lower. Dow was down about 300 points at one time. It's come back relatively strongly. Still down on the day a little bit, I believe, last I checked. Let's just take a quick look up here and see where we are, and we'll see here that we've got the, actually, the S&P is up, the Dow Jones is basically unchanged, and they're actually looking pretty good considering where they were. I mean, my goodness, that's a heck of a deal. We got the, what else do you see? The grains are firmed up a bit, crude oil still down a little bit on the day, but not much. It was $2, $3 a barrel lower, looks like it's turning around too. So this might be a turnaround Friday. Who knows? The chart that I think is important, I posted it here in the Tiger Den for those that belong to the wonderful Tiger Den that TFNN gives us for people that want to share information. And boy, we got some sharp people in there, folks, but I posted the chart showing you the importance of this bottom today in the stock market at 3940. We talked about that on the video that I did last night to say, watch that closely because that is an uptrend. We've had higher bottoms and higher tops ever since the 12th of March. And we're now into springtime. And so this might be a time where this major low this week, and we could accelerate to the upside, which would be good for the banking crisis, because that would tell the people they could start to buy the banks. And if they come into short covering the banks, folks, that's going to be enough to get this stuff moving because the technical part of the picture with Apple and some of these others doesn't nearly that bad. So that's what I'm paying attention to. So we're going to watch and see. Trade what you see, not what you think, because thinking gets you in trouble. But what you see is not going to get you in trouble because if there's more buyers, prices are going up. If there's more sellers, prices are going down. That's basically the bottom line of what we're watching here today. I'm going to take a little break<PHONE_NUMBER>. Stay tuned for 24 seven with myself, Larry Pesner. The reality.


Hello and welcome to the Grand Line Review, your source for everything One Piece. My name is Liam and I wish that my teapot also had testicles. And today we have a very special video because it is a review of chapter 109, which marks the 100th chapter of the Wano Arc. And let's all just, you know, take a moment to absorb that information. Wano began in July 2018 with chapter 909. And here we are now in 2021, just now getting down to business, which is pretty wild. For some other stunning statistics, we are only three chapters away from surpassing Dress Roses 102 chapter count, and thus having Wano become the longest arc in One Piece history, which it most assuredly will. And right now 100 chapters in a series with just over 1,000, while the keen mathematicians amongst you will note that roughly 10% of the entirety of One Piece has now taken place on Wano. And all of those thoughts are pretty incredibly insane. So by going to celebrate with a round of arc inquiry, a very simple minigame where I'm going to ask you a trivia question and you were going to answer it. Should you answering correctly, then your punishment will be to subscribe to the Grand Line Review, also resulting in consistent injections of One Piece culture administered straight into your YouTube feed.  But here is our trivia question. Which of the following characters did not appear in the first chapter of Wano? Is it A, Jozu, B, Vista, or C, Rakuyo? All whitebait commanders, but which one of them did not make it into the very first chapter of the Wano arc? Please do make your choice now and we shall reveal the answer in three, two, one, and bam, it was A, Jozu. The whitebait pirates appear in this like funky refresher panel, but weirdly enough, there is no Jozu.   And you know the thing to do, so please do say hi in the comments below if you are a new member of the Grand Fleet, welcome. But that's enough of that. Let's abruptly get into the chapter, kind of like how Orochi rather abruptly stumbled directly into his demise, his second demise. So whatever potential that Orochi has left in this arc, I think it's fairly safe to say I wasn't expecting most of it to completely evaporate within the first two pages here. It was pretty incredible though, especially to see the sheer bloodlust within the vassals because they didn't even need to think twice. Each and every one of them, well, not all of them, but most of them went straight in for the kill on our Hydra Lad Orochi, which is fun because looking at this panel, I can only see five of the vassals actively slicing Orochi's heads. Nekomomushi and Iso appear to have been left out of the fun. Shame for them. Still, those five plus Kaido means that so far in this arc, a grand total of six different people have taken seven different Orochi heads. Now, if my maths is accurate, then six plus one equals seven and then eight minus seven equals one, which means that you, sir, have bought one head left hiding somewhere.  So something I'd been thinking about since last week was the Yamatana Orochi legend because I was curious if the heads could regenerate or if there was any restrictions on how to, you know, like kill the thing. And while I didn't dive too deeply into it, the original mythology of the creature was less than helpful because as far as I can tell, what happened is the Orochi got drunk and was promptly killed whilst passed out. So I'd like to think that this is just Oda skipping a whole bunch of unnecessary head cutting with Orochi and get it all done in one shot, then have Orochi perhaps be a bit more conservative with his arrogance from here on out. So does anyone remember right back at the beginning of Wano before Orochi's like proper introduction where there were theories that the vassals were going to end up having this epic battle against this mythical monster? So that didn't happen. Something very interesting that happened towards the end here though, it appears to be a pairing of Raizo and Fukurokuju, which is definitely appropriate. Alquerky Ninja versus the literal head ninja. If I come to think of it, they've both got pretty big heads, don't they? Fukurokuju's is just long lost. Raizo's comes equipped with some much needed girth. Why I really like this though isn't so much because of this specific matchup, but the idea that the vassals are going to keep being split up. Like how Inarashi was left behind last chapter to face off against Jack and paired off against various opponents in the same way that the straw hats typically are. Although that shouldn't be too surprising in retrospect because there is Preston for this. Weirdly enough, the most recent conflict of this scale we can look to in the series comes courtesy of Dress Rosa, during which all of the Colosseum fighters got paired off against members of the Don Quixote Pirates, which just as a side note is another crazy thought due to the nature of what Hawcake Island was, we have not had a classic one piece mega battle since like 2015. So you know what, give me some vassal action here. Although rather worryingly, I'm not sure if there are enough opponents on the island left to Cater for all of the vassals because what remains of the Tobiropo seems to be reserved for the straw hats. And we are now starting to run quite low on relevant named villains. Oh, and one thing I did notice the lack thereof was Iso, he was quite absent from I think every panel in this chapter. Like the only panel I could make a reasonable argument for is maybe this one because that here squiggle that might be Iso, very maybe. It doesn't really matter though because I'm sure it's not some sort of grand conspiracy. I just enjoy seeing what Oda chooses to focus on because there are times where he will deliberately just not draw characters who are meant to be in a present location simply to increase the focus and effect on the ones that he wants to zero in on. To the main event though, the bulk of this chapter was dedicated to a very fun sequence of the worst generation versus the emperors. And it looks like we have finally made some sort of decent progress. Before that though, I think it's incredibly important to talk about that amazing combo attack from Big Mom and Kaido. I could be wrong, but this may very well be the single most powerful attack that has ever been featured in One Piece. I'm trying to think of others, but the only potential candidates I have that spring to mind are like Kaido's Borobreth or Elizabethos King Punch. And I don't know, maybe you could also throw in some devil fruit business from Whitebeard and Sakazuki. But still, I don't think that any of them are quite comparable to this. And one initially strikes me as the composition of the panel. It's almost underwhelmingly simple. About two thirds of it is pretty much just blank white negative space. Something that you don't often see in a big showcase panel of One Piece because Oda likes to cram as much detail into these events as possible, which is why something like this is actually quite special. Because this attack is so powerful that it is effectively erasing any semblance of detail that comes into contact with it. It's very simple, but extremely effective, especially in a series like One Piece, which is well known for cramming as much detail and texture into everything as possible. And the attack itself is obviously an homage to the Elbafian giants who performed essentially the same technique way back on Little Garden, which decimated the island eater. But as insane as this attack was, something even more wild happened, which is that it was blocked single-handedly by a green-haired swordsman. Potentially the most powerful attack in all of One Piece, blocked by three swords and a dream. I honestly feel like I'm reading Zoro fan fiction. To be fair, I do think that this is a bit overblown. It's not like he was actually capable of blocking or deflecting it. It was just a temporary stop to allow lore to move everyone to safety. So you know what?  I almost feel like we need to start keeping track of all of this with some sort of raid point system awarded to characters for just amazing crap that gets done. For example, slicing down Scratchmanapoo. That's a raid point. Casually attacking Queen and making him squeal like the rounded pygmy is. That's a raid point. Being the first character to actually make Kaido dodge an attack, ding, raid point. And now having blocked one of the greatest attacks in the history of the series, whilst the rest of the worst generation just kind of stood there and shot themselves. Yes, big raid point. So that is Zoro sitting on four raid points currently, which I do suspect is more than anyone else. With all of that said, Zoro has taken this a lot more harshly than most people seem to realize because there is a very concerning panel right at the end of the chapter with Zoro coughing up quite a bit of blood. A panel that I'm not entirely sure why exists because it has very little to do with the situation at hand. The other three surrounding panels are about lost Mac talking big mom and confirming that Zeus can't save her. But amongst all of that, we just see Zoro interrupting by coughing up some blood. So Oda clearly thinks that it is very important for us to know that Zoro is in far worse condition than the rest of the chapter would portray. So I'm not entirely sure what to make of that except that Zoro probably has quite the struggle ahead and may very well need to either take a break or even drop out entirely from this fight in the very near future. It's definitely not what I want but at the same time, I look at this panel and I go, oh, that hurts. Moving to lore though, this chapter finally answers a question that just about everyone has been asking ever since the introduction of his abilities, which is, you know, why not teleport the emperors or literally any opponent into the water and just be done with the arc? And of course the expected answer is Haki. Their Haki is simply too, too powerful, which I don't know. Oda put himself in a very tricky situation here and I mean, it does make sense but it's kind of a weak explanation, especially since Haki isn't something that is always active. So a really great strategy instead of, you know, charging head on in with the vassals, probably would have been to have lore sneak up into the festival and swap Kaito's body with someone or something or whatever. Unless we're saying that Kaito always keeps his Haki active or that Haki remains in place, sort of like a passive effect, either way, this has always been the problem of lore. His abilities are simply too strong. So situations like this where we need to explain why they can't be used just end up being kind of awkward.  You know, the one that's like an instant win condition against any opponent, because that would be really helpful right about now or better yet, even long before now. Well kid, to be honest, I just don't want to, which I find to be every bit as satisfying of an explanation as the one we got. But while Luffy does cool Luffy things, our remaining worst generation members do come up with a very cool plan to remove Big Mom from this nightmarish picture and I like it. It was the perfect use of the individual skill sets of every other combatant except for maybe Killer who just ended up like chasing a sword. And it very much reminds me of the time when the straw hat successfully repelled Big Mom downstairs. Once again, showing us that Big Mom really isn't also great without an entire empire or at least a few other figures to support her because alone, Big Mom can meet her doom by being struck with a simple rock. You know, I quite vividly remember making fun of lore when he tried to assault Kaida with rocks back in like chapter 1001. And I think I might have to eat those words now because whilst those rocks didn't work on Kaido, they most certainly did work against Big Mom. So you know what? I'm just gonna stop questioning your rock related tactics. Now in regards to Big Mom's fate, I highly doubt she's actually going to fall into the sea. Right now the worst case scenario would probably be for Kaido to swoop down and save her then emerge back on top of the roof with Big Mom riding him as much fan art has depicted. It's quite interesting though because if Big Mom does fall then I'm not entirely sure that she has any way of getting back onto Onigashima meaning that she would effectively be removed from the entire conflict. At least until she could create some sort of other flying homie to get back up. But this could very much be signaling the start of our serious battle time here with everyone just focusing on Kaido. Assumably after taking care of the rest of the beast pirates from a story perspective, I imagine. Meanwhile Kaido versus Luffy during this chapter was nothing less than exceptional. There was another fun smack talking moment where Luffy noticed that Kaido dodged his attack, which is all the fuel to the fire that Luffy needs. During the last chapter, he insisted that their attacks were having an effect against Kaido and Kaido himself has now just confirmed that. So when Luffy's deranged mind, which is probably best represented by this panel, all he has to do is keep punching and he will eventually win. What is this Luffy face? It's such an unflattering angle. But Kaido is even worse. Look at this guy. What is this? He looks like he has no idea what's going on. Like he's having a complete inner crisis and doesn't even know who he is. So there's some interesting strange Kaido art here. The Kaido does repay the shenaniganry from Luffy with what looks like a brutal clubbing from above. And looking at this panel just sends me consistent waves of pain because this one has to hurt like nothing before. From what we can see, Luffy couldn't even try to block it. It's quite the attack. And I actually think it looks much cooler than the Emperor Combo attack earlier in the chapter. Now, as is often the case, one piece was on the cover of Weekly Shonen Jump, which is nice and simple. Just a classic shot of Luffy being adorned by the atmosphere of the flower capital. There's really not too much to say about it. It's definitely not my favorite cover by a long, long stretch. It's just a little bit too basic for me, I think. The color spread on the other hand is anything but. A nice little scene of the straw hats in the snow with Tama and Ko. I love everything about it, including the ridiculously detailed jackets. It's always fun to see what Oda chooses to write on color spread clothing and stuff such as Zoro's jacket, which just says three swords. And I have to say it was quite the lucky and fate to coincidence that he managed to find a piece of clothing that said exactly that. Considering I'm pretty sure he is the only user of three swords in the entire world. So he may have started his own brand. But here's the thing that I think people are really going to jump on. Ah, Tama has the straw hat. So Tama Fanakuma confirmed. Confirmed again, I guess. Tama taking Luffy's straw hat. At face value, this is a very playful, fun thing because she is about to put it on one of the statues. But to the conspiracy theory internet, this is going to be another piece of evidence for the Tama train. Now there was already a big call for Tama for straw hat after Act One of Wano, where Tama became the only post timescape character to have worn the hat. Other than Luffy, of course, and our loyal rock friend. So this color spread can definitely be interpreted as some sort of foreshadowing because there is also precedent for that. Like when Robin stole and wore the straw hat long before she joined the crew. But I have to say I remain unconvinced. Of every possible new member from Wano, Tama feels the most unlikely, even with all of the stuff behind her. Who knows though, maybe in a year's time we'll all look back on this and go, holy crap, Oda was practically telling us right here. So keep an eye on this space. And to check out other examples of grand one piece in World Conspiracy Theories and do check out this video which dives into some of the most puzzling and disturbing background mysteries of the series.


Hello friends welcome again to another session on trigonometry and in this session. We are going to study one more Formula, which is called cosine formula in the last session You saw sign rule where a by sine a is equal to b by sine b is equal to c by sine c And that was equal to twice the circum radius of the triangle, right now in this session We are going to study one more Formula which is a square is equal to b square plus c square minus 2bc cos a and likewise for other sides as well So there are these these formulae are part of nothing something called cosine formula. Okay. Now, how do we even? Prove it. So how do we prove it? so there could be two cases guys one is when the triangle is acute angle triangle and The other one when the triangle is obtuse angle triangle So we'll try to prove this for both the cases. So let's try and first prove for case a that is it is acute angle triangle Right acute angled triangle. So if the triangle is acute angled then what happens?  So here BD is so BD is perpendicular to AC here Similarly in this case also BD is perpendicular to AC right both the cases. So let's take up the acute angle case first Now first is a square is equal to b square plus c square minus 2bc cos a now Okay, so considering triangle B DC, okay in triangle B DC We can write by Pythagoras theorem a square is equal to BD square plus DC DC square, isn't it? right BD square plus DC square by what by Pythagoras theorem very easy no problems here by Pythagoras theorem I can write this isn't it? So hence a square is BD square plus DC square therefore a square is Equal to now. Can I not write a square as or sorry BD square as C square and it will be a better idea to write it as let's say this is x so this Let's say ad is equal to x Okay, so DC will be equal to clearly ac Minus x that is B minus x Okay, so let's write a a square is equal to a BD square plus DC square right, so let's first try and Write a few more equations relations. So like c square will be equal to BD square Plus x square by same logic by Pythagoras theorem Pythagoras theorem, isn't it? Right c square is equal to these BD square plus x square, right and ad upon ad upon ab is equal to cos a Is it ad?  What do we what did we assume it to be x and a b is anyway c so c cos a x is c cos a right x is C cos a now continuing here. What do we get? So clearly? BD square is equal to c square minus x square from here BD square is c square minus x square isn't it now c square minus x square and x is c square cos square a Right here is x Isn't it? And what about So BD square is no now DC square. What is DC? DC square is clearly b minus x whole square Right B if you see DC square is B minus x whole square. So if you expand it, it will be b square plus x square minus 2 b x Correct, so let's write this so b square and x square is c square cos square a from here again And this will be minus 2 b and x is c cos a C cos a so let me write the numbers of the equation. This is equation number one This will be equation number two and this is equation number three So from one two and three guys from one two and three What do we get? We get a square is Equal to let's write BD square first. So BD square is c square minus c square cos square a Correct and let's write DC now DC square DC square is given as B square plus c square cos square a Minus 2 BC cos a Correct from equation number three. So if you see this cancels out. So hence we get the first relationship a square is equal to B square plus c square minus 2 BC cos of a Right, this is cosine formula Now you can similar by similar logic you can prove the other ones too, right? Since the choice of a and b and c is totally dependent on the user or the person who's doing it So hence irrespective of whatever a b and c you can Apply the symmetry logic and you will get that These relations the second one and third one will also hold you can try on your own and you'll see that by the same logic instead of Dropping a perpendicular from B. You have to now drop from a and then from c like that and then you can find out You know the other two relationship as well. So this will pass through the same point Yeah, so this is the cosine formula for an acute angle triangles. Now. Let us see Will it be same for the obtuse angle case? So here is the obtuse angle and now let us again do the similar exercise and What you can see BD has been dropped again BD is perpendicular to AC. So hence here I Can I should write BD perpendicular to AC? Okay, so now What is AD so if you now say see again, we can write from here also a square is equal to BD square plus CD square by Pythagoras theorem, right? BD square can be written as A BD square can be written as C square minus AD square BD square can be written as C square minus AD square and CD square can be written as AD minus AD minus B whole square Am I right AD? Minus B whole square, right? Now if you see this is C square minus AD square then plus AD square Then plus B square minus to AD into B, right? So AD square AD square goes it becomes C square plus B square minus to AD into B nobody's AD guys so if you see AD upon C is cos of A, right?  So rearranging you will get a square is equal to B square plus C square minus 2 BC cos of A correct if you see guys, this is you know Pythagoras theorem becomes a special case for all of this What happens if A is? angle A is 90 degree so if Angle A is 90 degrees And what happens we know that cos of 90 degree is equal to zero, right? So clearly if A is 90 degrees, so what will the diagram diagram will be something like that, isn't it? So A becomes 90. This is A and This is B and this is C. This is Pythagoras theorem So that means this is A. This is B. This is C So a square must be equal to B square plus C square, which is true If you deploy this back here, you will get a square is equal to B square plus C square, right? This is the Pythagoras theorem. So you can treat Pythagoras theorem as a special case of cosine formula. So please remember these three formula for problem solving in olympiads and in different exams like J and all this is a very important formula This will be used in physics as well a lot. So in vector algebra, these kind of relations are used a lot. So please Keep these three in mind, right? This is called cosine formula. In the next session, we'll see projection formula


okay James P. Madonna here Megalife 21 progressive discussions I am now headed for the the Royal Hibachi buffet it is Friday afternoon that's right root 46 West Saddlebook in Jersey I am headed for it right now I could smell the wonderful aroma of barbecued meat not to mention the great seafood that is here let's see oh he's got new plants bless their hearts look at that all right I'm now entering the building James P. Madonna is now entering the building Commodore Jeff Zambello Commodore Jeff Zambello whoever invented the low flow faucet and showerhead should be crucified like the Romans did to Jesus they should be crucified unbelievable all right now we're gonna I'm leaving them the men's room and we're gonna see what gastronomic delight we're gonna find here at the Royal Hibachi buffet okay root 46 West Saddlebook in Jersey oh look at that oh succulent duck but oh look at this a Mongolian barbecue action look at this oh my god this guy's the king look at all the shrimp and the meat and the noodles look at that look at this guy what the hell is in another dish carrots is that the Bugs Bunny look at that I don't know it's got a lot of carrots over there yes he's the king of Mongolian barbecue he cooked three eggs for somebody last week somebody wanted three eggs there were eight eggs this week there were eight I'll come back to him later I gotta go get my food oh look at this beautiful lamps beautiful lamps from Turkey the party room is open the party room was it what am I gonna have you oh oh lamb ribs oh you know how to better get Commodore Jeff Sam bellow I better get the duck oh look at the duck look at the duck I'm in luck look at the meat on it I am in luck it's roast duck and speaking of roast duck this is in honor of the Exorcist Bishop as seen on the travel channels hit show ghost adventures with Zach Bagans he was preparing a roast duck and I just want to I just want him to see this beautiful roast duck look at all that succulent meat Exorcist Bishop Brian look at that $10 all you can eat in this place and with all fresh seafood it can't be beat man it can't be beat leave it up to James P. Madonna to find the best values exorcist Bishop I mean Bishop exorcist so whatever demonology okay a little a little surf and turf do I want calamari with mussels and marinara sauce or lamb lamb ribs I think I'll take some lamb ribs can't be beat man Commodore Jeff Sam bellow I hit the jackpot this Friday I can always come back for more lamb ribs you know I know it's gonna be real greasy but you know what it's it's good grease okay let me get some cock dribble over here some nice black northern mussels okay marinara sauce Salvatore Mercurio being that I got the mussels marinara here all right Salvatore Mercurio I just want you to gaze upon this delight got scared you saw a spider I'll get out of your way no tentacles only to body unfortunately I like the tentacles but I don't see all right she's getting lamb ribs very nice oh they got covers now here at Royal Hibachi so unsanitary people don't like do anything I tell you one thing your duck is pretty good it's on steroids it's real meaty excellent what the hell is that oh brown gravy for for the mashed potato oh look at that brown gravy now featuring brown gravy isn't that something got the beautiful woman but I won't put her on YouTube don't worry I won't put you on YouTube I could but I won't chicken I see chicken at home all right so stonies stonies speaking of chicken buffalo wings outstanding botanos maduros and I always have that I don't I always see that so stonies I always see that chicken I always have that I want the expensive stuff oh look oh wow look how curly look at those curls look at those curls all right you know what I'm gonna have to come back for the lemons comment or Jeff Zamboni I mean comment or Jeff Zambolo isn't that beautiful isn't that a work of art now I get the lemons all right color coordinate color coordinate the lemons with the yellow ball the yellow with the curls on unbelievable here we go some lemons from my water and for well not not the fish because I usually put that on fillets can never have too many too many lemons all right I got to get myself a steak knife I better have steak knives where the hell's the steak oh look at this look at this only one steak knife left there's only one left Jeff Zambolo look at this only one steak knife left what the hell's going on here all right let me sit down let me sit down I'm getting nervous now I'm getting disgusted pated here's the ice cream this surf and turf muscles marinara with succulent roast duck and barbecue lamb ribs there's my lemons I'm gonna squeeze them into the water they have lamb ribs they're very good and their duck is meat usually people grab all the duck when they see it but it's real a lot of meat on the duck the duck is out of luck we're not I'm not out of luck the duck is out of sacrificial land taking a look at what's going on here with the sushi you know what that sound means we got Mongolian barbecue action there wow look at the size of those shrimp don't crimp the shrimp Commodore Jeff Zambolo look at the size of those shrimp maybe I should partake in that there you go to vapors of life we got broccoli I see mushrooms lonely noodles some chicken really big shrimp though give me an idea of the vapors of life Jeff Zambolo the vapors of life here we go more shrimp shrimp some carrots mushrooms very thick mushrooms too broccoli I love mushrooms that's why I'm a fun guy oh I smell ginger Mongolian barbecue action going on here the different man cooking it but you know it's really a no-brainer you just flip it around you know give me an idea what we got here roast beef look at that look at that no shrimp oh I knew it was gonna happen I knew it I knew it I knew all the gigantic shrimp was going to be gone no matter what do I want tilapia I don't know no potato soups peasant food peasant food no we got something Parmesan I don't know maybe the signs on the other side I don't know what the hell that is something something Parmesan but I am definitely I definitely missed out on the the jumbo shrimp this is chicken palm I don't know I don't know what it is mystery meat palm and get some oh look at that Arabic rice bless their hearts sacrificial sacrificial lamb really really tasty rice let me honest with you has slivered almonds in there chickpeas you can smell the cumin all right got lamb in there all right did I say slivered almonds everybody hoarded all the jumbo shrimp unless they bring more out the way since I I got screwed out of the jumbo shrimp I'm not there's no sense of me staying there videotaping hey the oysters they brought out the oysters check out the seafood salad a little too heavy on the peppers let me see if they got blue cheese no they do they do have blue cheese let me see where's the blue cheese now they don't have the chunky the chunky blue cheese that I like they don't have that that style blue cheese I must have the right blue cheese the curly haired one she hasn't been as friendly as normal oh my god look what they did to the apple pie they destroyed it looks like a flock of crows a flock of birds attacked it destroyed the apple pie what's this okay here here we have tray let's you a latin delight and look what I see over there I see papaya I see papaya oh last time I hesitated I got screwed out of the papaya before somebody takes all the papaya excuse me little lady people always screw me out of the papaya I blamed the curly haired girl for taking all the papaya on me no no I'm only kidding I'm only kidding look at a succulent look at that the magic melon of the tropics Jeff Sambello look at that beautiful papaya was voted the highest in nutritional value out of all the fruits of the world I think mango it made a second mango came in second look at this I'm so excited look at a papaya beautiful you too enjoy drive safe don't don't get frostbite look see all the papaya look at that oh you too you too Arabic rice was okay there we have a beautiful plate of papaya and here is Arabic rice with lamb sliver diamonds chickpeas and I don't know what this is it's something Parmesan hopefully it's not roadkill Parmesan gotta say hi to the ice cream station yeah that guy that that new the new guy that took over the Mongolian barbecue he had a puss on his face you better not give me a hard time I'll tell you that I'm in no mood for bullshit


Hello and welcome back to another episode of Physics Partner. Today we are going to talk about diodes, a fundamental component in electronics that plays a crucial role in controlling the flow of electricity. So, what exactly is a diode? In simple terms, a diode is a semiconductor device that allows current to flow in one direction only. It has a distinct structure consisting of an anode, a positive terminal and a cathode, a negative terminal that are separated by a junction. Forward bias occurs when a positive terminal of a voltage source is connected to the p-type region and negative terminal to the n-type region of a diode. Allowing current to flow through the diodes, this reduces the barrier potential at the junction, enabling the diode to conduct electricity easily. Conversely, reverse bias happens when the positive terminal is connected to the n-type region and the negative terminal to the p-type region, increasing their barrier potential and preventing current flow. In simple words, a diode behaves as a good conductor in one direction and as an insulator in the reverse direction. Now let's discuss how diodes are manufactured. Arzanic and indium are added to silicon during diode preparation as dopants to create n-type and p-type semiconductor regions. Respectively, Arzanic introduces extra electrons making the material n-type while indium introduces deficiency of electrons creating a p-type region. When combined in a single crystal, these regions form a p-in junction allowing the diode to control the flow of electric current in one direction while blocking it in the other, enabling its function as a semiconductor device. One of the key advantages of using diodes is their efficiency in converting alternating current to direct current, which is vital for a smooth operation of electronic devices. They also provide protection against voltage spikes and prevent reverse current flow that could damage sensitive components. In real life, diodes can be found in a variety of applications such as LED lighting, computer power supplies, solar panels and automative electronics. For example, LED lights use diodes to emit light when electricity passes through them in one direction, making them energy efficient and long lasting. In conclusion, diodes are indispensable components in electronics that play a significant role in regulating current flow and ensuring the proper functioning of electronic devices.