 First of all, I will take one small minute from my presentation to deeply thank to the organizers of this conference. So Katrin, Christof and Matthew and all the team that is here. So I'd like to tell you that the local organization is just perfect. It's like for a real conference. So we have, I don't know if you see my real badges. We have signs all over the campus. So a real registration, not a virtual registration. So just perfect. And it is not finished. So as you may see the hybrid version of the conference is going very well. I'd like also to thank Emmanuel and Kanta for the selection of the, for running the committee for the computer science part. And again, again, Katrin, Matthew and Christof for running the local organization and the selection of papers for the economical part and to all the team that is here in the room. You don't see them. So I will not touch the camera, but at some point we'll turn the camera to them and ask them to, to come here and to have your, your, your, your clip. And I also would like to thank all the people that join us. So as far as I understood we are 143. And this morning we are more than 70 people registered to, to zoom. I will, I will start my talk now so, so please count the minutes that I speak on the on my talk. So my talk is on fairness in committee based the blockchain and actually all the credit goes to Yacoli and this is the, the big part of his, his thesis. And this is a joint work with the panel at El Pozzo from CIA and Sarah to see Pierre Giovanni from CIA list as well. So, I will start my talk, telling you what the users imagine about the blockchain. So they imagine that I have distributed ledger. There is no central authority. The distributed ledger is secure. This means that actually the written information is not erased. The information is available and the most important thing that the privacy is preserved. So what clients imagine about the blockchain is that I have a unique chain of blocks. What happens in the, in the reality is that you may not have a unique chain like in the Bitcoin or Ethereum, or even worse, in IOTA, there is no chain at all. There is a tag of transactions and transactions are added to, to, to this tag and at the, let's say at the end of the day so it's evolving, evolving, direct, directed a cyclic graph. Let's take a close look to Bitcoin. So I will follow the, the line of talks that presented before. So in Bitcoin you have clients that send transaction to some bakers. Bakers will solve some proof of work and the one that solved the proof of work will, will generate a new block and the new block is propagating in the network and all the bakers that are connected to the network will add this, this new red block to the longest chain. So they view of the, of the, of the blockchain. So what are the guarantees that Bitcoin offers in terms of consistency is the fact that we'll have an agreement on the common prefix, not the whole blockchain. And actually what we have proof, proved in a previous work published last year with Emmanuel Romaric, Antonella and Sarah is the fact that the consensus abstraction is necessary in order to ensure a strong consistent blockchain, meaning to have a new unique chain. That is a unique view on a unique chain that is viewed by all the, all the participants in the network. And here comes again the presentation of this consensus abstraction that is a very, very, it's a fundamental abstraction in distributed systems. So consensus is defined by four properties agreement. So, meaning that if, if, if a correct baker or, or minor decides a block B, then eventually all correct miners will decide the same block validity a decided block satisfies some validity predicate so it is well chained with the previous block integrity that means that no correct baker decides twice and termination means that every correct baker eventually decides so will not have papers that forget to decide. So only if all these four condition are satisfied. By an abstraction that implement this, this consensus we can say that we are sure that each produce block will be correctly added to the existing blockchain. Okay. So, there is a problem so the problems come from some impossibility results that have been. So there are common knowledge in distributed systems, meaning that it is impossible to solve consensus in asynchronous environments, even if there is only one faulty process process that crushes. Here I cited Fisher Lynch and Patterson result. The journal version that has been published in 85. So, very well known result. So this brings us into almost that lock because that point meaning, okay, consensus is impossible. But what is important to notice here is that there are some conditions in this result the first the first condition is the fact that the system is asynchronous so you cannot put bounds in the communication delays. So the second point that that comes into the mind to the people that construct the blockchain based on this consensus obstruction is the fact that the participant to the consensus. They have to be known, which is not the case for all the block chains but the ones that are based on the on the committees use this, this, this assumption so the participants to the to the committee, the committee that will generate a block are known, and do not change with the time do not change during the, the consensus run the consensus process. Okay, which is a small problem in the blockchain as we'll see a little bit later. Okay, so in order to fix the, the impossibility result that we so previously, there were some. Some people invented consensus protocols under the under the restriction on the execution environment so instead of considering asynchronous environments. We consider slightly weaker environment like synchronous or pseudo synchronous, or people went to probabilistic guarantees. Okay. So in order to fix the, the, the second problem that that I walked previously. People considered fixed committees for each block. The fixed committee will introduce some problems. And actually, the problems come from another obstruction that is implemented. So this is an underlying obstruction on the off the block committee based blockchain, which is called repeated consensus. So in repeated consensus what we try to do is to characterize, characterize actually the properties that we want from, from the whole chain of blocks. What what the repeated consensus. Save that. First of all, we have to guarantee that every obedient participant at the ukulele already defined the notion of obedient participant has an infinite output, so does not stop in the middle of the competition. So this is the agreement, meaning that if I take, if I analyze the the blockchain of each, the output of each participant, and if I take the output is output of one obedient participant. So this output should be equal to the output of another obedient participant. And finally the validity is the same as the in the consensus abstraction, meaning that each block that is in the blockchain of any obedient participant has to satisfy satisfy validity predicate. Okay, so Well, there are some problems with the committee based blockchain that have to be solved. So committee based blockchain are so the fact that we use consensus or repeated consensus that were problems that have been already covered by 20 years of research in the in distributed system does not solve the technical problems in in blockchain. So one of the problems that comes with the blockchain area is is the fact that we have to be very careful in the way we select committees in order to avoid the oligarchy problems. So, the idea is that I select the committee, the way I select this committee if the committee that introduced blocks in the blockchain will be the same. The same people will be rewarded the same people will will influence the way the blockchain is constructed. So it's a hard problem to solve. Another point is is the rewarding the committee rewarding how to reward the committee and when to to reward the committee. And again, this is a hard problem to to solve in blockchain and most of the committee based block chains. Evoke to these problems, but do not propose. How to say standalone solution for none of these these problems so so But we wanted to study is the fact that. Okay. We have these two mechanisms so we identified these two mechanisms selection and and and rewarding. And now in order to avoid the problems that that arrays from selection and rewarding we, we think that actually these problems can be solved by studying the fairness in the committee based block chains. And intuitively the fairness in blockchain can be so the common, let's say the common knowledge, the common. Yeah, the, the, the, the, the, I would say a definition from the, from the literature, or fairness with with with a doctor to the blockchain will will state that any obedient participant, having a fraction alpha of the total merit in the system gets at least a fraction alpha of the total reward so this would be a very common sense definition. Well, if I if I look now to the way that the furnace have has been considered in blockchain so the, the, the, the work that was closest to to analyzing the the furnace in the way we we felt that it should be summarized is the work of Gary in his Bitcoin backbone protocol and he introduced the notion of of chain quality. But this notion of chain quality was very, very proper to the way Bitcoin is is functioning. And because it considers the number of block a participant will add to the blockchain. This comes with with two problems in in the, if we want to apply exactly the same analysis to the committee based blockchain. So, first of all, the idea of characterizing the blockchain does not does not cover the way the committees are selected in the committee based blockchain, and the second problem is the fact that producing a block in the committee based is a cooperative work while in Bitcoin is a more standalone process so I solve my proof of work, and then I introduced my block in the blockchain while in the committee based blockchain. We agree, we are a committee we agree on the way that the block will be added to the to the blockchain. So, now because we are told, all of us convinced that we have to to to to to deal with two different mechanism in the committee based blockchain the selection mechanism and the rewarding mechanism. So what we wanted to do is to have an analysis to propose actually definition for the fairness in the way that the committee selection is done, and the fairness in the way the, the, the participants are rewarded. So, intuitively, a committee selection mechanism is said to be fair, if each participant becomes member proportional to its merit so I will not formalize the merit and right now, so assume that there is some indicator that gives for each participant, but in the system, a numerical value that corresponds to corresponds to the merit. And in terms of fairness of the rewarding mechanism what intuitively what we would like to have is that, if I, if I analyze my blockchain for each level for each height in the in the blockchain. The obedient committee members will be rewarded, meaning only those that actively participated to the, to the, to the generation of a block for a particular height will be rewarded. So, please make a sign. Okay, if, if. So if I have one minute left. Yes, you can. Yes, you have five, five minutes more. Okay, thank you. Thank you very much. So, for the fairness of the committee selection, actually, we came out with two properties. Well, the first property says that each participant with a positive merit should become a committee member infinitely often so the keyword here is the infinitely often. The second common sense properties the fact that the participant that has no merit should not be selected, more often than a participant with a higher merit. Okay, and if we analyze three different types of selection mechanism. So that we can find. We can think of. If I take, if I select participants in the system that have a higher stake, then we can prove that this mechanism is not fair and actually this brings me to the oligarchy problems that I have previously. If I select people that have lower stake in the system that and I reward them. This mechanism will be will verify the fairness definition that I give previously, and again another simple mechanism that is used generally in the distributed system in general the round robin mechanism is again fair so meaning that I will select each people in the system in a round robin way. Okay, so in terms of rewarding. We came out with with inspired by previous work in in failure detectors. We came out with with the characterization of rewarding parameter for process for a participant for a specific level in the in the blockchain and we say that this rewarding parameter has to have three properties. So it's a precision age being the height that I am focused on. Yeah, so it says that if a process is not a committee member for this height. This is the word has to be zero. This is a completeness, meaning that if I is a committee member for a for the height age and I is obedient then it's rewarding has to be one and the third property that is accuracy says that if a process is a committee member for high and it's not does not follow his protocol that the agreement protocol, then his word has to be zero. Okay. And now the fairness of rewarding mechanism. So we we came out with two definition of the fairness. And the definition that said that we say that rewarding mechanism is fair if for all levels, age levels. Yeah, so the mechanism satisfies for each, each participant age precision completeness and accuracy the three properties that I announced earlier. So what we saw is that if we apply this definition. Actually, we came quickly with with impossibility results. So we weaker the definition. So we came out with eventually fairness that says that there exists a level high. Age zero such that for all the levels that are greater than ages the zero. If the mechanism is if the mechanism satisfies the three condition precision completeness and accuracy then the mechanism is is fair. Now, some results. So I mark as theorem the formalization is in the paper and the accolades here to give you the proof on the blackboard. So we have a whiteboard here. So the term says that there is a fair reward mechanism in committee based blockchain if and only if the system is synchronous. So meaning that I have a non bounded delay on the message propagation. Another results that says that there exists an eventually fair reward mechanism in the committee based blockchain if and only if the system is synchronous or eventually synchronous and the Byzantine participants so those that are allowed to not follow the protocol to send messages, different messages to different participants. So if this Byzantine nodes are detectable, which is a very hard problem in distributed system. And a quick case study tendermint. So for the rewarding in in in tendermint. So why tendermint because it's the only one that evoked in the white papers. The fact that we can think to a way of selecting committees in order to construct the blockchain. So in tendermint. What happens is that once a new block is decided for a specific height of the of the blockchain. So the participant will the participants will collect the decision of the other participants of the committee members. For that particular height and will construct a set that is called the set to to be rewarded. During the consensus process for a specific height. So processes will also the committee members will also propose to to reward the members of the committee that constructed the block for the height age minus one. Okay, so what we prove is that in an eventual synchronous system, the reward mechanism of tendermint as it was proposed by tendermint is is not even eventually fair, which is weaker than than fair. And actually by modifying slightly the tendermint mechanism. Introducing module level time out and time out and the detection of Byzantine participants, then we come with an eventual fair rewarding mechanism. So this work opens a lot a lot of research directions more than we could have solved. And as you could see for the selection mechanism practically we don't have any specific result. So we focused only on the rewarding so this has to has to be done. And another important research direction would be the analysis of fairness of different other blockchains like Algorand Uroboros, which are not committee based or Iota which is not committee based so our analysis does not fit with this kind of blockchains. And maybe for people that are in distributed system so one big problem that is still has still to be solved here is how to detect Byzantine behavior in in blockchain so we don't know how to do it, but by using the past of the past exchange in between notes to the the history of messages exchange. So maybe we'll be able to come out with with nice Byzantine behavior detectors. So this closes my talk. So I will be happy to answer to your questions.