Hello and welcome to this session in which we will discuss the audit of a group financial statements. What is the big idea of a group financial statement? Let's assume I own an audit firm in New York City, United States. Now I ordered a company called Adam Shipping Inc. It's a U.S. company but this U.S. company will have a foreign subsidiary. Now the subsidiary does not have to be foreign. I'm creating this example to make it more realistic or easier to kind of relate to. Now ASI, which is Adam Shipping Services, they own a subsidiary which is what we're going to be calling a component in Beirut, Lebanon, which is in the Middle East called Lebanese Shipping Inc. LSI. Now since I am the auditor of Adam Shipping Company, I am the auditor of the parent company and LSI is part of ASI. Therefore, when I have to audit, I have to audit the whole group. I have to audit ASI. They might even have another subsidiaries in Dubai, another subsidiaries in Egypt. It doesn't matter. I have to audit all of them but I happen not to have an office in Beirut, Lebanon where that location is being audited. So what do I do under those circumstances? Well, I am the principal. I am the main. I am the group engagement partner. I'm the principal partner. So I'm responsible for all these companies, not only ASI, ASI and its component. So the group engagement partner, which is Farhat Accounting and Other Services, is responsible for the group engagement, its performance and the report on the group financial statements. Now what is the group financial statements? I'm going to show you the definition in a moment but think of it as the consolidated financial statement. So when you audit a company, a parent at the subsidiaries, you are auditing everything, the group financial statement. This is what we mean by the group financial statement. I'm responsible for establishing the audit strategy, evaluating the evidence in order to draw a proper conclusion because I have to assure an opinion on the group financial statement. I have the final say. So there is a lot of responsibilities on this group engagement partner. For public companies, they call it the principal partner. The main idea in this situation, Farhat Accounting and Other Services is the group engagement partner. Now what is a group financial statement? Again, as I told you, think of them as the consolidated. Refer to the financial statement that present the financial information of multiple component. Now ASI could have again multiple component. It doesn't have to be one component. I'm going to keep it with one component to make the illustration simple. Before we proceed any further, I have a public announcement about my company, farhatlectures.com. Farhat Accounting Lectures is a supplemental educational tool that's going to help you with your CPA exam preparation as well as your accounting courses. My CPA material is aligned with your CPA review course such as Becker, Roger, Wiley, Gleam, Miles. My accounting courses are aligned with your accounting courses broken down by chapter and topics. My resources consist of lectures, multiple choice questions, true-false questions, as well as exercises. Go ahead, start your free trial today. No obligation, no credit card required. Now we need to learn a few definitions. One, we already kind of covered it briefly. A component, what is a component in this recording? What is the component in this explanation? Lebanese shipping ink, which is this subsidiary. It could be a subsidiary, a joint venture, an equity method of investee for which the group or component management prepare financial statement to be included, consolidated in the group financial statement as required by the framework. So any company, a subsidiary, a joint venture that we need to include is called a component. Now we're going to learn about what's a significant component. Now it's not only a component, it's a significant component. A significant component should be audited by the group engagement or the component auditor. Don't worry, we're going to define component auditor in a moment. The significant component is identified by the group engagement team as an entity or a business that is either. So how can you be a significant component, an important component, either financially, you have plenty of assets, plenty of revenue, financially significant to the group, or it doesn't have to be financially significant, have the potential to contain significant risk of material in the statement. So either, either to dollar amount, it represents a large dollar amount relative to the total company, either an assets or revenue, or the risk that it involved, it's significant to the group of financial statement. Either of these will qualify the component as a significant component. Once it's a significant component, it has to be audited by either the group engagement or which is ASI, the company in New York, or some other auditor, a component auditor. Now, if the component is not significant, simply put the component is very small, then under those circumstances, analytical procedures, conducting analytical procedures will suffice as far as the auditing procedure. Now, what is a component auditor? I just mentioned that a significant component must be audited by the main auditor or a component auditor. What is a component auditor? It's that audit firm that I'm going to be contacting in Lebanon and asking them to audit this company. Well, in this situation, we're going to call it Lebanese auditing services. So I call this office, I say, okay, I don't call them randomly, you're going to say, I'm going to have to do some work before I call them, is an auditor who perform work on the financial information of the component, which will be used as an evidence in the group audit. So I'm going to be relying on these, on this group, Lebanese auditing services. So guess what? I'm going to be, I'm going to have to do a lot of work in terms of this audit firm, LAS, LAS. A lot of acronyms, just to make the point because there's a lot of definitions, that's why I'm trying to make it a realistic scenario. A component auditor may be part of the group engagement partner firm. For example, PWC would have an office in Lebanon, it could be a network affiliated firm, they could have a network, or it could be unrelated firm. So on this example, I'm going to assume this LAS, it's an unrelated firm to me, just totally unrelated. I just, you know what? I went to the website, I looked up a few companies, I said, I like these guys, let me call them, and let me do some search about them. They're unrelated to me. Okay? Obviously, if I know someone, it's even better, but I'm just going to make up the example. Now, what is my responsibility since I selected this group? What is my responsibility as a group engagement partner and the team? And the team means the team of the group engagement partner. Well, I should understand the LAS independence and professional competence. Are they independent of this shipping company? Are they professionally competent? That's my responsibility because you're going to see later, I'm going to have to assume their work in one way or another. If they're not independent, I have to determine whether I should use them or not. Better not use them, but I have to make that determination. I also have to understand the extent in which they will be involved in the work of the component auditor, like how much work they are going to be doing. What's the extent of the work? Whether they will be able to obtain information necessary for the consolidated process. I'm going to have to understand, look, tell me, are you going to obtain enough information for me where I can draw a proper conclusion? And I have to understand what type of regulatory environment the component auditor is operating under. Are they using IFRS? Is the auditing standard in Lebanon highly regulated? So on and so forth. I have to understand this. Also, what am I responsible for? I am responsible for overseeing and performing the group audit engagement at accordance with the professional standard and regulatory requirement. So although they're doing the work, I'm responsible for their work and for determining whether the auditor's report is appropriate and the given circumstances. So I'm basically, at the end of the day, I'm responsible for everything as the engagement partner. The group engagement team should have a thorough understanding of the group, the component and their environment in order to identify significant component. It's my job to determine whether that component is a significant component. I need to gather sufficient appropriate audit evidence, including the work of the component auditor to support the audit group of the financial statement. All we're saying here is as an engagement partner, my responsibility of a group engagement partner is basically the box stops with me. So I have to do all this work. Now, if sufficient appropriate evidence cannot be obtained, cannot be obtained, the auditor should either decline to take on the new engagement or withdraw from a current engagement. Unless withdrawal is not possible, you would issue a disclaimer if that's the case, if you cannot gather enough. What type of documentation do you have to have? Well, the group engagement team should document at least the following. An analysis of component, whatever team could be more than one component, identifying which one are significant and the type of work performed on them. What type of work did we perform on them? Two, any written communication between the group engagement team and the component auditor. Remember, my office in New York and I am working with a Lebanese auditing firm. All the communication regarding the engagement team requirement has to be documented. A list of component for which the component auditor's report were referenced in the auditor's report. I need to take a look at the report. Also, the financial statement of the component and the report of the component auditor for the component reference and the auditor's report on the group financial statement. Simply put, I want a list of the financial statements, a list of the financial reports, of course, a list of all the paperwork. Simply put, this is what I would keep. Now, would I reference the component auditor or would I not reference them? I have two options. Option one, no reference. Simply put, this is called I am assuming responsibility, no reference. In other words, I am accepting their work and I'm not mentioning their name and their report whatsoever. So if you look at the report, you're not aware that there's a company in Lebanon called Lebanese auditing services that any work. So you don't mention anything about them in the report. That's one option. Now, if you have to do that, if the auditor assume responsibility, well, they must be involved in that work to the extent that it relates to expressing an opinion on the group financial statement. So if you don't say anything, you have to be involved. You have to know what's going on because you are taking basically full responsibility. The involvement may include performing risk assessment procedure. You might have to do that. You might have to perform additional procedures. They did the work. You might want to maybe send the team just to do a little bit of work, review their documentation, review the components auditor documentation, review their audit program. So you have to do a little bit more work because what you are doing here is you are assuming responsibility because you are not mentioning them. You are not referencing anything in the report that you had another auditor work help you or you can reference them. Here you are not assuming responsibility alone. You are dividing responsibility. Now, you mentioned them. When do you divide the responsibility? Two conditions has to exist. The component auditor that Lebanese auditing firm followed GAAS or the PCAOB. If they did not follow them, mentioned the additional procedures to compensate in order to meet the relevant requirement. If I'm following GAAS or PCAOB and they're not following GAAS or the PCAOB, they could be following international auditing standards. That's fine. That's acceptable to them. But since I am accepting the work, I have to make sure the amount of work needs the GAAS and the PCAOB. Two, the component audit auditory report is not restricted. Simply put, they have to give me that report. And if somebody asks for it, I have to be able to furnish it because you're going to see in the audit report, I will show you shortly, it says we rely on the report, which was furnished to us. If you want to see it, we can also show it to you. It's not restricted. So the report cannot be restricted and they have to do enough work that's comparable to the US standards, whether it's a private or a public company. Now, the report should include in the opinion section and the basis of opinion, depending what type of report we're looking at, we'll look at both. Because sometimes it's only in the opinion, then we have in other reports, it's the opinion and the basis. If it's a PCAOB, we'll look at a report, don't worry about this. The component was audited by the component auditor. We have to mention this clearly. You're going to see it in the report. The magnitude, how much were they responsible for the magnitude, the size of the financial statement audited by the component, percentage of revenue, percentage of assets, which framework they used, IFRS or whatever framework they use. And the group auditor is responsible for making any necessary adjustment for the framework. In other words, they used IFRS because that's the standard that they use in that country. We in the US, we use GAP. I am the auditor. I'm responsible to make the appropriate adjustment, if any, to convert them from IFRS standard framework to GAP standards. Now what happened if the component auditor opinion is not clean? So they gave an opinion, it could be a modified or they included an explanatory paragraph. What should I do as a group engagement partner, as the main auditor? Well, I have to determine whether I should modify the opinion for the group financial statement or simply put add an emphasis of a matter or other explanatory paragraph to explain the issue. So now it depends on the situation itself. So it's a judgment. That's all what you need to know for now. Let's take a look at a component auditor's report, AI CPA. And obviously we're going to be looking at report that reference the component auditor. Otherwise, if they don't reference the component auditor, it's just a regular report, which we cover in a separate session. So this is the AI CPA standard. And it's called an opinion. We have audited the financial statement of Adam company in its subsidiary, which compromise of the balance sheet, we named the financial statement in our opinion based on our audit notice and notice here and the report of other auditors. We don't mention their names, other auditors. The company consolidated financial statement present fairly in order to your respect and its subsidiaries and the result of their operation basically standard language. We did not audit the financial statement of the company. So this is the subsidiary of the parent company of Adam company, a wholly owned subsidiary, which statement reflect total asset and constituting 18% of the asset and 16% of the revenue of the whole company. These statements were audited by other auditors whose report has been furnished to us. And as in our opinion and so far it relates to the amount included in B is based solely on the report of the auditor and our opinion is based on their auditors. So now we reference them. We said we did our work. They did their work. We looked at the report. This is what we're telling you. Now if we're looking at a component auditor under a PCAOB. The PCAOB we're going to have an opinion and the basis for the opinion. Let's take a look at the language. Again, we have audited the financial statements of Adam company, blah, blah, blah. So we did not audit the financial statement of the company, the wholly owned subsidiaries. Same language. We just want to let you know that we did not audit that company. Those statements were audited by other auditors whose report has been furnished to us and in our opinion it looks good. Now in the basis of the financial statement we believe that our audit and the report of the other auditor provide a reasonable basis for our opinion. Notice we are relying on their. We are dividing the responsibility between us and them, the other auditor. What should you do now? Go to far hat lectures and look at additional MCQs. True, false, additional resources. That's going to help you if you're studying for the CPA exam. Those questions, they should be easy, easy questions if you understand the topic. Don't take any chances, invest in yourself, invest in your career. Good luck and stay safe.


I don't need it. I have it already, yeah. So the second talk of the session is Indistinguishability of Fuscation from Constant Degree, Gradient Encoding by Yujia Lin. Thank you for the introduction. Can you hear me well? Seems like I can't shout. All right. OK. So today we're going to talk about circuit of fuscation. This is a primitive that aims to compile a circuit into one that preserves the functionality, meaning that the compiled circuit should produce the same outputs on every input and becomes unintelligible. Intuitively means that it resists any reverse engineering trying to figure out what is some valuable information embedded in the original circuit. We recall such a compiler and a fuscator. And in particular, the notions in the literature have been trying to formalize what exactly this unintelligible mean, and they capture different levels of security. What we look at here today is really the weakest notion called indistinguishability of fuscation or simply IEL. IEL tries to hide just one bit of information. That is, which one of the two equivalent circuits, C1 and C2, is being fuscated here? By equivalence, we mean that those two circuits really have the same identical size as well as the same truth table. And for such two circuits, we require that the IEL-fuscated compiled circuits to have computationally indistinguishable distributions. As you can observe here that IEL is trivial to construct if we're not concerned about efficiency. How? Given a circuit C, just try to find the canonical circuit using unbounded time that is equivalent to the circuiting question. So the real quest here is finding such a compiler that is actually efficient. So for a long time, there was no progress on constructions of IEL. Until 2013, there came a box parachuted down into our community. We open the box and we find the first IEL by garg at all. And since then, three years after in 2016, we have, first of all, many more IEL constructions. And moreover, through this boat of IEL, we have managed to sail from what we know and love as the crypto proper land to this crypto wonderland. And in this land, many talks that we didn't know how to achieve before, for example, multi-party and non-interactive key exchange are primitives that we didn't imagine before. For example, gobbling for tooling machine or RAM computations in time independent of the time complexity now become suddenly possible. And the list of new feasibility data that has been established in the past three years is actually way more than what I could put on the slide. And additionally, IEL also implies many primitives in the crypto proper lands. So it seems that it seems to be charting a much broader map of cryptography for us. Or does it actually? It turns out that all IEL construction today are only candidates, roughly meaning that we don't have a high confidence in their security. And they're built upon this structure called graded encodings. And in the past three years, graded encodings have been going through this continual cycle of proposals of construction and attacks. And very recently, there's even an attack that directly attacked the very first IEL construction by Garga and all when instantiated with graded encodings. Most of the known IEL constructions are not directly broken. I think it is fair to summarize that the state of the affair has been balancing at the border of security and insecurity. Therefore today, does IEL exist? The answer to this question is still uncertain. But if the answer is yes, this amazing land is the world that we live in. And we should just continue to expand the limit of crypto. And if IEL does not exist, then the map reverberate back to before, and all those new primitive we constructed will fall back into a limbo. But then at the very least, we should go primitive by primitive to figure out what is the exact border of feasibility. So answering this question is important. Of course, there are many ways one can imagine to go to make progress towards answering this question. In particular, there will be continuous research on constructions of graded encodings and attacks on them. But that is not the focus of this talk. In this talk, we're going to look at the reduction from IEL to graded encoding because we love reductions. For stronger the reduction, the simpler the graded encoding we need, either to construct them and maybe in the distant future, we can, one day, eliminate its use. In particular, our known IEL candidates rely on polynomial degree graded encodings. And here, a degree D graded encoding can help us to do two things. One is a homophic evaluation of any degree D polynomial. And the second is to zero test its output. And this work, I show that, in fact, constant degree graded encoding suffices for constructing IEL. And therefore, we simplify the functionality of the graded encodings needed for constructing IEL. To really understand this simplification, let me next now look more closely to what graded encodings are and what their degrees mean. So graded encodings generalize this primitive called a multilinear map. Multilinear map allows us to encode a ring element in some group indexed by a label L by putting it in the exponent. And for consistency of notation, I'm gonna use this bracket notation shown in the slide to represent the encoding with the index of the group in the lower right corner. Such a encoding naturally supports a homomorphic addition in the same group as well as testing whether encoding encodes zero or not if we have identity elements. The magic of multilinear map is really at the fact that it allows us to homomorphically multiply multiple encodings in different groups and the producing encoding of the product in some target group. And the degree of such a map is simply how many numbers of encodings that we can multiply together. And when this degree is two, we get bilinear map. Graded encoding generalize multilinear map in the following sense. First, we no longer think about the encodings as being associated with groups, we just think about the mess generic ways of encode some ring element with some label. In particular, the encodings can be noisy. And because the encodings can be noisy, we no longer have zero testing for free and we can only do so for encodings with some special label, we call the zero testing label. Moreover, multiplications can now be done in an incremental way. And the price starts, the output encoding will have a label that grows to the sum of the two input labels. These three capabilities together. Graded encoding schemes or JAS allow us basically to homomorphically evaluate the polynomial and then testing whether the output is zero or not. As long as this polynomial satisfies all the label constraint, by that I mean the fact that addition only operates over encodings with the same label and multiplication as the label up. So the degree of a JAS is simply the maximum degree of all the polynomials that could be homomorphically evaluated and then zero tested. It's easy to observe that the degree must be upper bounded by the norm of this special zero testing label because every multiplication with every multiplication, the label grows. But it's really a separate parameter. In fact, it could be much smaller than the norm of the label because for example, that the noise may grow too big that overwhelm the signal and prevents decoding anymore. In summary, when comparing with polynomial degree JAS, constant degree JAS really supports a much simpler functionality in the sense that only allow us to evaluate the very low degree polynomials. And in fact, in the ideal or generic group model, their powers are strictly separated away. Why? Because ideal polynomial degree JAS is so powerful that it actually implies a VBB of fascination which is known to be impossible in the plain model. Whereas there has been work showing that there's no VBB of fascination from ideal constant degree JAS. And furthermore, the same line of work essentially showed that constant degree JAS cannot be helpful for building black box construction of IEL in the sense that if such a construction exists, then we can generically remove this constant degree JAS and obtaining an IEL without it. In this work, we show that constant degree JAS does help however, non-black box construction of IEL. We show such a construction exists assuming sub-exponential semantic security of JAS, sub-exponential security is a computational assumption over JAS formulated by pas, selan, and tan. The purpose of this talk, what exactly this assumption is, is not going to be important. We also rely on two other assumptions. One is sub-exponential WE and the sub-exponentially secure PRG in NC0. And because all the underlying primitives are sub-exponentially secure, the resulting IO is also sub-exponentially secure. So we do note that our assumption on the PRG is strong. In particular, we require it to have polynomial stretch. And one candidate is Golrak's proposal that essentially is evaluating a system of random KCSP with respect to some primitive Q. And so far there has not been any successful attacks as long as Q is chosen carefully in a non-degenerative way. Though the assumption is quite strong, our theorem can actually be generalized as a generic way to trade the complexity of PRG for the complexity of JAS. And because all the primitives we consider are sub-exponentially secure, in the rest of the talk, I'm gonna omit mentioning it explicitly. All right, so how can we go from constant-degree JAS to IO? We'll do so by going through this intermediate step of building IO for a small subclass S of constant-degree computation. Here by constant-degree computation, we mean the following. We'll say that a Boolean function F has degree D if it is computable by a degree D polynomial. And the punchline is over n-ary. Meaning that no matter in which ring you evaluate this polynomial, it will always agree with the Boolean function F on every possible input in the domain. Constant-degree function, you should think of it as being implemented using lots of additions, but only a few layers of multiplication. As you can imagine, such functions are very weak, complexity-wise. In particular, if this function is total, meaning that its domain contains all the binary string of certain lengths, then shown by Nesha and the shagady, Nesha and the shagady, that such function is contained in NC0. However, if the function is possibly partial, then it could be outside NC0, but still contained in AC0. In other words, our first step is a stronger bootstrapping theorem that goes from IO for a subclass of constant-degree computation all the way to IO for P. In contrast, previous bootstrappings always start from IO for NC1, much stronger. It seems that given this stronger bootstrapping theorem, it is only natural to expect that now to construct an IO for subclass of constant-degree computation should be easy to just apply known IO schemes to this subclass, and by the fact that it has constant-degree, it should follow that constant-degree jazz suffice. It turns out that this expectation is just false. Even though the circuits have constant-degree, it will still require polynomial-degree jazz in particular, the degree will be in proportion to the input length of those sophisticated circuits. Therefore, to actually enable the entire construction, we need to provide a new IO construction that not only rely on the fact that this class has constant-degree, but also the fact that it has certain special structure that we formalize as having constant-type degree. And for any such class of circuits, we show that IO exists using only constant-degree jazz. So for the rest of the talk, I won't have time to go into this new IO construction, or just try to give you some high-level idea of how the bootstrapping theorem works. Okay. So the starting point of our bootstrapping theorem is the recent transformation from functional encryption, or FE, to IO. Unfortunately, so far, we don't have construction of FE from any standard assumption. The best we know how to do is this weaker version called the Boolean FE from the assumption of learning with errors. So Boolean FE, as the name suggests, handles only Boolean circuits. In contrast, the full-fledged FE also handles those multi-bit output circuits. Therefore, the natural question is, can we upgrade? Can we go from the bottom to top? And we show that upgrading is possible if we have IO for a class of circuits that has only constant-degree, assuming PRG and C0. Before going into details of the upgrading, let me first tell you quickly what functional encryptions are. They're basically public-key encryption with partial-decryption keys. Like a public-key encryption, we can generate public-key and secret-key pairs, and we can use the public-key to encrypt messages, which will produce a ciphertext. But with the new capability that we can generate those partial-decryption keys associated with some circuit C. And this partial-decryption key itself could also be viewed as a circuit in general. And with such a partial-decryption key at a decryption time, we could evaluate this circuit on a ciphertext, and that would produce the outputs of the circuit C evaluated on the message M in the clear. So efficiency of functional encryption in particular requires that the encryption time should be polynomial in the length of the public key and the length of the message. In particular, it should be independent of any parameter of the circuit C that you will generate a partial-decryption key for later. The security follows from standard semantic security for public-key encryption. We require that encryption of message one and another are indistinguishable even with access to some partial-decryption key as long as the circuit does not separate those two messages. When we consider the special case of a Boolean functional encryption, we simply mean that this is a scheme that handles only Boolean functions in key gem. So we're gonna denote a Boolean scheme always with the B ahead of the algorithm name. So now comes the interesting part. How can we upgrade a Boolean functional encryption to FE for, say, L-bit output circuits? Our first idea is very natural. Just generate the public key and secret key using the Boolean scheme. And in the key gem, when you're given with a circuit that has, say, L-bit outputs, we're gonna try to first Booleanize this circuit by creating a circuit that outputs the output of C one bit at a time. How? Think about this B that takes two inputs. One is the message, the other is the index of an output bit ranging from one to L. And this circuit will simply output the I-bit in the output YI of C evaluated on M. Play use this scheme, the Boolean scheme to create a secret key for it. How do we encrypt? Well, in order to eventually produce all output bits, what we want is to encrypt every possible pair MI with I ranging from one to L and just publish this whole list of L ciphertext. And with this list of ciphertext at decryption time, we can evaluate the secret key for the Boolean circuit B on every ciphertext and producing every bit in output. Great. It's easy to see that semantic security of this scheme follows from the semantic security of the Boolean scheme. Problem that this scheme is not compact. In particular, the size of the ciphertext scales linearly with the number of output bits, but it really should be independent of any parameter of the circuit C. Idea to get around is to use IO to compress this list of ciphertext. How? We're gonna view this list of ciphertext as the output or as the truth table of a certain circuit E How does it look like? It's gonna have the public and the message hardware E and the input only the index I, it will produce the I ciphertext by encrypting the pair MI using the Boolean scheme. And additionally, it will generate the randomness needed for the encryption by evaluating a PRF. Now, instead of trying to publish this whole list of ciphertext, which is very long, let's just a fast gate this circuit E, which can then allow us to reproduce every ciphertext we need. Now, compactness is restored immediately. Why? Because the circuit E has a compact size and therefore it's a fast gated version and hence the ciphertext. Security is less obvious to see, but using known techniques, we can show that it follows from the security of IO, PRF and the Boolean function encryption. Great. So far, we get that if we have IO for all the circuits that look like E, then we can go from Boolean to FE and eventually to IO. But how about the promise to constant degree? Is this circuit E having constant degree? Absolutely not. In fact, it's a very deep circuit in NC1. So first observation is that the encryption algorithm could be made into NC0 by using randomized encoding. So that's not a problem. The problem is that PRF simply cannot have constant degree because such functions are learnable. And there are other problems that the circuit E is actually more complicated in order for the proof to go through. In particular, it will require us to have a puncturable PRF as opposed to normal PRF. But let's ignore all the additional problems for now and just try to handle the problem of constant degree PRF. So how can we get around that? Well, our idea is to construct a special purpose one that has constant degree just for E. So what is the property of E that we can leverage then? The property is that it only applies to PRF on a polynomial-sized domain. So the hope is that since the domain is polynomial, if we have a constant degree PRG, then we can build a constant degree PRF for a polynomial domain. How? By using the GGM-PRF tree. Remember that the GGM-PRF tree uses a length doubling PRG to create this binary tree that have depth exactly log L, where L is exactly the size of the domain. And each of the pseudo-random block in one of the leaf can be evaluated in D iterations. In each iteration, we expand the PRG once and then choose the right block to be expanded in the next iteration using the corresponding bits in the input. If this function has a high degree, why its degree is at least the number of iterations? And even if the domain is polynomial, this is not good enough for us. So our first idea is to squash the PRF using high fanouts. We're gonna use a quadratic stretch in PRG and this naturally give us a fanout N tree with constant depth. Great. Now this means that we get a PRF that has only constant number of iterations. However, it creates the problem that in order to choose the right block for the next iteration, this choosing procedure where we call the one out of M MOOCs has a high degree. Only a restriction when the choosing index is represented in binary. So the next idea is why don't we just represent it as a unit factor that has exactly one in the right position, then choosing simply corresponding to computing in the product and can be done simply in degree one. And this give us eventually a PRF with very special input representation that has D unit factors inside. And by plugging this PRF into our circuit E that we saw before, we get a class of circuits that have constant degree and that will enable the stronger bootstrapping theorem. In summary, in this work, we simplify the need of jazz from polynomial degree to constant degree for IO. And I believe that this is only the beginning of simplifying jazz. The ideal and ultimate but still very distant goal is of course that we can simplify so much that one day we don't need it anymore. That is of course very far from where we are now but still continually in this direction further simplifying jazz I think is a meaningful interesting question. Okay, thank you. We have time for one question. So you mentioned you also had to modify the IO construction to have to, so that if you want to do IO for constant degree functions, if you use constant degree multilinear maps, can you say a little about what they, you know? You mean a general connection between PRG and the, so the degree, so the reason we use PRG and C0 is because it has constant degree and then they're equivalent. If you have a PRG of any degree D, then you will need a jazz of degree polynomial in D. So there is a polynomial relation between a degree of PRG and the degree of the jazz you need. Okay, so let's find the speaker again.


So my career in computer science was launched one day when I'm sitting in the fraternity and a friend of mine a guy named George Ernst, he's older, a couple of years older than me came in and he said he said I'm taking this course from this crazy professor strange-looking guy But he said if you want to get an A in in my class Just write it on the blue book and the final exam and I'll give you that grade He said whatever grade you want. Just write it on the blue book. So I said that that sounds interesting Said what is that class for taking and it was a class in computer programming being taught by the world famous Alan Perlis I used to say well back in those days. It was like Building a log cabin with an axe you had an axe and a bunch of trees And it was up to you to figure out the architecture of the log cabin and all the techniques of building and just had to Do it so it was that was great fun and adventures even though it was extremely inefficient Nowadays you can get anything any program that you feel like writing you don't need to write You just need to find it on github and you can write it But then getting the damn thing to work still is a lot of a hassle, but now it's it's it's a big pain so anyway, but I found that so I just found that that world of programming was easy and I guess to say Perlis and the other professors were so enthusiastic about Computing that that it just drew me away from my interest in physics So I started working at Xerox this guy Bob Taylor who was my boss at Xerox had gone off and hired The most brilliant computer scientists he could find from all over the country because he'd been funding them when he'd worked for DARPA Taylor is an interesting character. He He was a anyway He was a DARPA program manager who initiated the funding for the internet among other things But he knew all these people so he knew Butler Lampson as a brilliant Computer designer. He knew a guy named Alan Kay who was World had been famous at the age of four or something for being on the original quiz kids There was a guy another guy from Berkeley named Peter Deutsch Who was described as being the world's greatest programmer and he he was working at Park so so I went to work this place and that was That was a fantastic atmosphere of brilliant computer innovation Oh, there was an article about Rolling Stone about Xerox Park before I got there and in that article Alan Kay is quoted as saying The people here are amazing. They all have amazing track recorders of technology And they're used to dealing lightning with both hands Whatever whatever that means, but the implication was these were God-like geniuses of computing and indeed they were they were I mean they were every bit as smart as in their own way as my colleagues have been at Berkeley or Carnegie Mellon We're building a personal computer system called the Alto which History showed was sort of the precursor for the Macintosh, which is the precursor for Windows-based personal computing everywhere along with networking along with laser printing along with all the innovations You can imagine we're essentially produced by a small Club of people in Silicon Valley during that time We went to lunch and that Alan said that he wanted me He was wanted to know if I'd be interested in coming to Carnegie Mellon to run this project that was going to build this computer system It's got to start with an innovative and strategic thinker. He said basically the IBM Okay, we're going to create a bunch of software for the campus But you you will be able to sell this at all the campuses of the world And so we're going to so even though we're creating the software you're going to own it And in return for that owning it you're going to play it pay us 75% overhead on our costs So this was from Cyrus point of view. This was a sweetheart deal if you know anything about Carnegie Mellon, you know The Carnegie Mellon is it's always cash flow oriented We in fact sired actually wrote an editorial saying Universities getting patents on their research is a waste of time Universities want to get the grants up front and let the research be in the public domain. So that was his philosophy about University research it wasn't that the university should try to hang on to the hang on to the intellectual property So he just made this deal with IBM without thinking about it He said I'm and I don't he says he and me doesn't have any money to fund this ourselves So you're going to fund the whole thing you're we're going to make a 75% profit on it and And then you'll own the software and I met this guy named JCR Licklider who invented a good deal He he basically made DARPA create computer science at Carnegie Mellon I mean he was he was a seminal character that not many people know about today. I met him I was on an elevator with him. I said, well, are you are you still working at DARPA? Are you know? He said no, I said I'm back at MIT now, but I've been at IBM and so forth I've died. I was only at DARPA for a few years and he said I I've decided I like to repot myself every five years. I Said oh Well, that's an interesting thought So anyway after five so I've been trying to figure out what happened with my life I said, oh, well, apparently that had a big impression on me because after I'd worked on this Andrew project for five or six years I said, no one I don't want to do that anymore in the summer of I don't know 93 or something Alan Newell announced that he was dying and it was it was like a horrible Development for all of us and I and I I felt terrible about it I was never really a close confidant of Alan's but I was the huge admirer of his I called him So I called him up one day. I said I'm sort of embarrassed. I said, I'm sorry I'm really sorry. This is happening to you and he said well, you're not as sorry as I am It was such a cool guy What I perceived to be one of Alan Newell's dying wishes was that we would be doing research in human computer interaction In the computer science department He'd had a bunch of meetings about this and we were all supposed to rally around and create a an effort in Human computer interaction, which was a combination of psychology and computer science with the goal of making computers usable and You know using scientific principles to make computers usable by people Sort of a new sort of a new academic discipline or an amalgam of academic disciplines Newell had tried to start that but he wasn't willing to do the administrative stuff to do it and nobody else was I Was off starting my company. That's all it was all happening in that period But when I got back I said okay To honor the memory of Alan Newell and to do this thing which needs to be done We're going to start that effort and so while I was supposed to be the nominal I was the head of the computer science department. I was trying to start that I saw I said we're gonna we're gonna go hire some Psychologists and we're gonna we're gonna study the way people use computers So and I went there I talked to a famous PR guy there named Regis McKenna who happens to be a native of Pittsburgh And he said and he'd been the guy who put Apple on the map as a as their PR guy And he said if you don't have presence here, you're not here and this was 2000. This was the year 2000 or 1999 and at that point Silicon Valley, you know people used to say silicon people in New York think they're the center of the universe People in Silicon Valley think they are the universe like the people in Silicon Valley said if you're not here, you're nobody so Basically, I talked the university into starting a branch campus and then through clever Negotiations and manipulations with NASA and Raj Reddy and a brilliant guy named Dwayne Adams We got this campus started on the West Coast


okay not part of today's plans but I cannot resist to have a little go up man versus golf hole challenge and I'm still at Cardin Park week later I'm on the Cheshire course sun is shining absolutely gorgeous I'm here filming a couple of videos for well a tailor-made two iron and tailor made high toe wedge so make sure you're keeping eye out for those but like I said with the sun shining I can't resist I've got to have a go at this so par five I'm on the 13th it is stroke index seven five hundred and one yards into the wind I'm going with G 400 max driver and after running get a tee because I wasn't prepared for this wait one second right I'm back let's see if we can get the drone going up this week I can't believe there's any reason why we couldn't so what you should be able to see right now is the fairway two trees on the left hand side is what we need to avoid anyway right are there long par five into the wind I can't get up into it'll be about being right of those trees and then we'll pick it up from there and see what club we decided to guide our way through I think there's a few bunkers that lie waiting we'll take that certainly stay away from the trees a little bit leaked out to the right and in the roof about five yards off the fairway let's go and pick it up from there and see if I can get myself into position for the third shot into the green right first of all ball is there no not too bad of a lie to be fair only five yards off the fairway but you can see the bunkers down on the left hand side of your picture I'm going to play about 150 yards down there so that's down the left hand side trying to avoid the bunkers I'm going to zoom in and hopefully through there you can see the flag so it slightly weaves its way back to the right hand side but anything I think we can get a 150 shot in I'll have a nice angle into this flag okay so I'm going to play seven I think I need a bit of loft to get it out of this roof and I think although it is into the wind anything around 140 150 clear that bunker so straight over this bunker pop bunker right in front of us that's what I'm trying to do we'll take that it was probably five yards further left than I wanted it to be and for a minute there I thought was going to go and fly into the bunkers on the far left but I'm above ground I've got a little bit longer than you'd want on this par five into the flag but I'm still in regulation at the moment okay so so far so good at least like I said a little bit further out than I want to be but partly down to the poor dry I've got 130 into the flag that is took left of the green so down the center 131 99 a smooth nine I'm into wind so fingers crossed short that was I was really happy with that I thought it was going to be close for birdie putt but I've landed just short in the in the fringe that wind did held it hold it up I went too easy on it so it's going to need that 64 degree wedge now and see if I can get up and down put practice into reality and the line we were at that was right down the neck of it and I was really thought was going to do well there as it happens nestle down a bit I'm going to go to this height or wedges 64 wedges I'm just reviewing at the moment I'm really liking this but can I execute a shot certainly take that I've got a putt for par on a shot don't forget we could get this off to a winning start decent strike of a putt really never in doubt so we start this one one off okay so next hole on this channel is going to play 15 rather it's stroking next 15 to no shot it's only 287 yards a real short par 4 but it's got lots of trouble very very tiny green lots of bunkers water on the left so it's all about finding a fair with a first shot I'm going to go 5 iron and see what I can leave myself in after that like I said hopefully for something short into a very tiny green once again down that left hand side good 20 30 yards off where I need to be which is obviously centre of the fairway and I'm in the rough which is not going to help me but I shouldn't have too much in hand but like I said coming out the rough that was not a good tee shot okay not a bad lie centre of the fairway like I said about 20 yards right and there's also a big massive bunker which I was clearly trying to avoid and just took this one a little bit down the left lie is okay but what it does do this green is very very small and it's got a lot of bunkers surrounding the flag and what I've managed to do I've got 93 into the pin but that bunker that I'm looking at is 88 yards to the face so there's literally five yards over the top of that bunker we're playing into the wind so hopefully I might just hold this one a little I'm going to play pitching wedge and hopefully somewhere on that dance floor well hopefully we picked that one up on shot trading and I'm absolutely chuffed I'll be honest with you because that's a good shot I can't say any more than that it's I'm really pleased with what's happening with a camera on this morning not greatest tee shot but that was yardage bang on and I've got a chance of birdie certainly take that and especially you haven't seen where the pin is and now it's literally only it's minimal sort of four yards on so to get the ball where it did really really pleased with that and probably slightly surprised as well because that was yes top draw that shot was chuffed with it like I said it's hard to be I film these videos and if I hit those shots every week I'd maybe a bit more it wouldn't be quite so surprised but with the camera switched on I'm actually when I pull off a good one and that was a good shot but didn't manage to get the birdie but never mind I'm still one awkward one to play so I can't lose okay so I have featured this hole on an old man versus golf hole challenge and I didn't necessarily want to include this one again but it's hard not to it such a great hole it's a 17 317 yards it's very much a dog leg right to left because between here and the pin is all water and you can take that on it's 268 yards is what I've got as a carry and it's all carry and I can't reach that it's into the wind it's not even worth me attempting it I'm all for a bit of excitement on these videos but I seriously I can't reach that so I want to be a bit boring I want to go across the corner of the water with a bit of a cut back in and hopefully leave a shortish iron into the green but it's a great golf hole this one I'm apologising as well because the drone is doing my editing I'm having all kinds of problems with it not connecting to the app at the moment so I can't record the drone footage either I may be able to dig some old stuff up from this hole though absolutely delighted with that it's been a decent morning to be fair like I said I played pretty poor last week in a private game without the camera on so these three holes that I've stuck on a video I'm absolutely delighted with that drive again gone pretty much where I was aiming we'll go and see from up there what we've got into the flag but that's a pretty decent position again I'm sounding a bit bemused because I was expecting to play pretty poorly here this morning we've got some tough pins cut here today at the park and that one's again just on the front edge so you couldn't afford to be sure again the Haito wedge full shot that was sort of 70 yards I played that and I'm really happy so a great result for me there personally but I hope you enjoyed the course as well because it was a little insight to just how good the Nicholas course is this year first time I played it for a few years and I've got to say the overall condition was brilliant greens were really really quick and true so really impressed with that and thanks again to card and part for having the average golfer here to film a man versus golf all challenge but also a couple of other product videos that may have been released already I'm not sure of the sequence of how these come out so it's another win for the average golfer I struggled all last year on these man versus golf all challenges and now one two on a bounce so I must hope I keep that going hope you enjoyed it don't forget comments down below any ideas if you've got you want me to feature on these videos that I'm not trying to cover already trying to do as much I can drone footage I think we've got a bit drone footage up at the end there for you as well on that whole but yeah hope you enjoyed it as much as I did and I'll see you soon for another man versus golf all challenge


Hi, this is Mitch Mitchell. Now just so you know, it is not my intention to turn this into a review stuff kind of channel. It really isn't. But after doing those socks that I did with the last video, I'm gonna do another one because this is something kind of different. You may have saw in the thumbnail, but Hydrox cookies are back, kinda. You may not remember Hydrox cookies. They were kind of the competitor of Oreo cookies way back in the day. It was made by the Sunshine Company and you know what? They were really good. They were different than the Oreos, but they were really good. And at one point, they used to be the cookie that was in the Ben and Jerry's mint ice cream with cookies. They were Hydrox cookies, and then they went off the market. They were actually bought by I think Nabisco. Then they were gone for a while. Then there was an anniversary. They brought them out for a few months, and then they took them out again back in 2009. So it was bought by a new company, and this company is called Leaf. I've never heard of Leaf before. I haven't. But you know, I'm looking at this thing here, and it says that they bought it in 2013, decided to bring it back using their original formula, which includes less sugar, but no hydrogenated What to say here, without trans fat or high fructose corn syrup. So they're using real sugar, which you don't usually see as much in the cookie these days. So I wanted to see can they actually make something that tastes as good as it used to, or is this going to be kind of a pretend thing that It's just not going to taste the same. A lot of you may be too young to remember this. I remembered it. I liked it. So I'm going to try it now, and we're going to see what this tastes like, and please be good. You know, it only cost $2.99, but still, you know, you don't want to pay $2.99 for something that's got a whole lot of it, and then bring it home and find out it's nasty, and you really don't want it. So anyway, that's what it looks like. As you can see, it looks just like an Oreo, only it's a Hydrox. I already see trouble coming because it doesn't smell like the old Hydrox used to smell. And, okay, that doesn't taste like the old Hydrox without the frosting or the cinder. Let's see what it tastes like. What's a cinder? You know what? It's passable, so I'm going to eat them, but they do not taste as good as the old Hydrox. Maybe we're just not used to sugar. Maybe I'm used to the high fructose corn syrup and everything else now. I don't know, but I have to admit, it's a little bit disappointing, but I wanted to try it because, had I liked it, well, this would have been a wonderful thing. I'm still going to eat them now. So anyway, that's all this is, just a little short video about Hydrox cookies. I guess you really can't go back to the old days, can you? Let me know your thoughts. I wonder if any of you have tried this and what you think of it. Let me know. Y'all take care.


as a schedule one deduction. Possibly that's a different issue. We're talking here though about the schedule A where you can't deduct those items. So our customs duties cannot deduct federal, estate and gift taxes. So remember the estate is a whole kind of different animal meaning we typically have an income tax. We don't tax people's assets. We tax them as they are earning the money that are accumulating the assets. And then when someone dies, however, we kind of switch that up and we say, now we're gonna tax their balance sheet basically.  So that becomes a tricky business in and of itself where it kind of has implications on the federal income tax, but it also has a different kind of impact because it's gonna be a state tax. Gift tax are tied into the estate tax and you could have these on the federal level as well as the state level. So typically not deductible. However, C line 16 later, if you had income and respect to a decedent. So certain state and local taxes including tax on gasoline, car inspection fee, assessments for sidewalks and other improvements to your property tax you paid for someone else and license fees. So let's take a look at these. These are state and local taxes. So you might be saying, these can get a little bit more confusing. So certain state and local taxes including tax on gasoline, when you buy gas, there's typically a tax on the gas and the idea of the tax on the gas is the people that actually use more gas are gonna be using the roads which were community property and therefore they should be paying for more of the roads. So that would be quite tedious if we tried to calculate that and figure out how much of the gas would be taxed and no car inspection fees, assessment for sidewalks and other improvements to your property tax you paid for someone else. You can't deduct someone else's tax and license fees. For example, marriage drivers and pets. So if you have a marriage license and so on can't typically deduct those. Foreign personal or real property taxes. So we're talking state and local taxes, not foreign taxes. If you have foreign income, you have a whole another world of things to be looking into that's a specialty area in and of itself which will be dependent in part on whether we have like tax treaties and whatnot with the other people, with the other countries so that you can avoid hopefully some kind of double taxation situation. So line five, the deduction for state and local taxes is generally limited to $10,000, $5,000 if filing, married filing separately. This was put in place a few years ago and it was actually an attempt to, I think simplify the code and be a little bit more fair and I'm someone that lives in California so I'm actually being hurt by this rule but I think some states have kind of been taking advantage of the tax and being subsidizing through the tax because obviously if you have a high income individual then they're gonna have high state taxes in places especially with a high cost of living like California and New York for example and it seems that that's kind of subsidizing the cost of living to go up and so on in those areas. So they actually capped it at the 10,000 so you can't take more than the 10,000 that was a controversial issue. It's clearly seems pretty clear to me that that's going to be beneficial or that that's gonna hurt more wealthy individuals and it's possibly be beneficial to or not hurt at least less wealthy individuals you would think but in any case, it's also a state thing so the states that have high cost of living areas obviously would argue against that.