 Hello everybody, so SOK stands for Systematization of Knowledge and we thought it was a good time to gather our thoughts and try to classify what's the situation with this problem, consensus problem that has gained a renewed interest with the advent of blockchain protocols, Bitcoin and so forth and that's what we're doing this work. This consensus basically is somewhat ancient problem as this slide that I found where you can see impossibility results for solving this problem, in this case, be something in general's problem as a lamp or it all formulated it in the early 80s so it has been around for a while and this thing that I show you is like the broadcast version of the problem where there's a single source and all the parties have to agree on what the result is through a protocol. And the consensus problem is actually the version where everybody has an input and everybody is supposed to have an output, satisfying these basic properties, everybody has to agree and it's all start with the same value, that has to be the outcome and that's the validity or non-trivality condition and of course this thing has to terminate. So this somewhat is classical stuff and so this stuff as I mentioned earlier is one of the important problems in the area of distributed computing, it's an important instance, basic instance of secure multipartic computation, building block in cryptographic protocols and so forth and has renewed interest recently with the advent of blockchain protocols, more interest from wider research community and in fact new ways of approaching this problem as suggested by Nakamoto in this email trail where he suggests that blockchain and proofs of words can be used to solve what he calls the business in general which is in fact the business in agreement problem where everybody contributes an input. This was a very informal suggestion which doesn't work because it doesn't satisfy this non-trivality condition but it's one way he was suggesting to do this. Okay, so what we do in this work is we try to systematize what's going on in the ecosystem landscape and classify it according to what was done classically and what is done in the blockchain space and this is one way we classify, we just look at assumptions or resources that the protocols make use of from a network point of view, you have a communication, what kind of communication primitives like point-to-point as a classical approach versus peer-to-peer diffusion, that's the blockchain approach. We look at what kind of setup these protocols have to have, no setup, public state setup or private state setup, the LRS what we call a PKI for example, public infrastructure, the public state setup would be a CRS, the Genesis block type setup and computational which means what kind of security guarantees that we have information theoretic and if computational what kind of things we use like one way functions proofs of work, random molecules and so forth. Okay, and I won't mention this last stuff. This classification kind of looks like, oh, and before I do that, so one observation is in the cryptographic computational setting you need the honest majority to solve this problem consensus, which is not sometimes universally known, but this is the case regardless of what resources you use. So we get a picture like this that don't bother reading all everything but on the left what we have is the classical world and on the right we have the new world, the proof of work blockchain world and the layers are network layer where we do point or what kind of communication primitive peer to peer, what kind of setup the protocol makes use of, computational functions can have information theoretic signatures and ground complexity which is not that important right now. Okay, so we do this classification and we point out some of the apparent contrast. For example, know that in the cryptographic setting with private setup that means a PKI, if you follow the blue line, we know how to achieve consensus in you know, tolerating a majority of corruptions. Okay, that's sort of a classical result. What is less known is if there's no setup, I mean you're using signatures, you're using cryptography but there's no setup, you cannot get this a half bound but you cannot do better than a third bound. Okay, because signatures are no use, you don't have a consistent PKI. Okay, now the contrast comes up next or not yet. So what we did in this paper with Aguilos and Leonardo's is we show how to do this approach, solve this problem using a new approach using a public setup that will be a genesis block using powers around the molecules to get the one half. Okay, so it's somewhat consistency, setup in both cases, try to set up in both cases and the one half corruption tolerance and this is an interesting thing that's quite in green where we also show this PKC paper where we show that you actually don't need a genesis block to you know, achieve consensus using a blockchain protocol based on proof of work. And this is an apparent contrast because here we know that using no setup you cannot do better than one third, here we have one half and it's an apparent contradiction because we show in an upcoming paper we model how to do this and how research constrained, you know, we have a new term called resource constrained crypto that explains how these two worlds collapse. All right, so that was the consensus taxonomy. What is relevant in the blockchain, Bitcoin and so forth is this version of consensus sometimes called lack of consensus or ledger consensus which in the traditional distributed computing literature has been called state machine replication where you actually have a ledger and transactions are added to the ledger in such a way that there's a consistency property, everybody sees the same thing and there's a likeness property that says, you know, this thing evolves, makes progress and new transactions are added. Okay, so we have a classification for this according to the state of the art and it kind of looks like this where if I point into our same paper again you can get this ledger consensus using a genesis block, you know, powers producer work and achieve one half and without no setup or modification of the previous protocol you can achieve this without trying to set up and there are more references here including I go around which is on the right side. Okay, that's what we do. This stuff is in the e-print and of course it's not exhaustive, you're probably missing a lot of things so send us comments. Thanks.