 So hello everybody This is about proofs of work for blockchain protocols. Oh So my name is Juan Graham in the process of moving to Texas A&M And this is John work with Aguilos Kiyas and your ghost by nacho tacos So I mentioned I'm moving to Texas And it turns out that your girls is from Sparta in case you didn't Know so don't mess with us Except except that Aguilos is originally from Athens Where all the you know artists? Philosophers sculptors Are but that's okay all right, so We're talking about proofs of work It's a very powerful notion introduced by Dorgna or a while back and It's been also called moderately hard functions cryptographic puzzles, but it can be formalized as a Predicate to argue and pray to or more argument predicate one of which is the useful stuff Come on Okay, there's a useful stuff that you would like to prove something about and the second one is a You know witness, which typically will take a long time to find Okay, so this search is takes a long time. It's exhaustive search for example and Verification is easy. So that's an abstract view of proofs of work And it turns out that it's being used in the original formulation by no for spam mitigation There's also an important formulation again for again civil attacks. That's a civil up there and this is important in my From my point of view because this is one of the first. This is pre Bitcoin one of the first solutions That's suggested to use proofs of work to tame the computational power of the adversary Okay, and some other applications But arguably the most impactful current application is in the design of blockchain protocols such as Bitcoin Also after actually represented like this where the proof of work is a tool to chain You know blocks and here you have a condensed history some new stuff Some witness and you have to hash all this To make it smaller than some target difficulty value Okay, and in Bitcoin this works something like this all right, so as It was mentioned by Christian before there's a fundamental tool in what is called permission less Blockchain protocols and the intuition is that this tool, you know slows down everybody gives a chance to everybody to you know Install useful stuff in the ledger in the blockchain Okay, this has been formalized This is this has been analyzed by a few works Except that the proofs were done in the you know random oracle model in a direct way what we do in this work is Formulate this power primitive that implies, you know the security of Bitcoin in the standard model and This is a little bit of a too much but essentially we have you know In some sense is primitive resembles and non-interactive proof system and also a signature and you have some Prover and a prove and a verify algorithm Notice that the prove it works on a message the stuff you want to prove something about and some randomness some key Okay, and you you have the expected properties that you might have like completeness and T Verifiability meaning that can be verified in short in a short time But these other mouthful properties have to do with Okay, I'm more to such a resistance meaning that you have a bunch of proof that should not help the other side to produce produce faster And also what you need for blockchains is some rate of success by honest parties and then store All right, so we do that and then we show that Bitcoin implementation You know Realizes this definition and we show another you know the bit going back on protocol with the security reduces to power And this is in the imprint