 Hi, my name is Shruti Nastar, and today I will be talking about succinct interactive oracle proofs, applications and limitations. This is a joint work with Ron Rothblum. So let's start by breaking down the title. What are interactive oracle proofs or IOPs in short? Well, IOPs are a new type of proof system that generalizes both traditional interactive proofs and PCPs. How does it work? Well, we can think of it as an interactive proof where the verifier only gets oracle access to the prover messages rather than the full access that it gets in a traditional interactive proof. Alternatively, we can think of it as an interactive analog of a PCP. So a PCP is basically a half-around IOP. So what are IOPs good for? Well, IOPs have numerous applications from constructing succinct arguments to delegation of computation, and even more recently, they've been used for achieving hardness of approximation results. So IOPs are useful. They have many applications. But let's go back to the first word that I had in the title, which is succinct. What do we mean by succinct? Well, a succinct proof is essentially a short proof. Namely, when we're talking about NP relations, a succinct proof is a proof whose length is polynomial and the witness length rather than in the instance length. Why do we care about that? Well, for general NP relations, usually the instance is much larger than the witness. So if you have a succinct proof, this means that we have a short proof. Kalaian Dras asked whether there exists a succinct PCP for all of NP. Fortnum and Santana basically gave a negative answer for that question because they showed that under a standard complexity assumption, there is no succinct PCP for SAT. However, we know that there exists a succinct IOP for SAT. In fact, we know a couple of constructions. So this creates this sort of separation between IOPs and PCPs. And IOP can do something that we believe a PCP cannot. Now, let's go back to the succinct IOP for SAT. Does that imply that there's a succinct IOP for all of NP? After all, SAT is an NP complete relation. However, this is not the case. And this is because reductions from NP relations to SAT do not necessarily preserve the witness length. So this question remains open whether there exists a succinct IOP for all of NP. Now, one might ask, why do we care about that? Why do we care about succinct IOPs? And as a first result, we show an application of succinct IOPs. We show a compiler that takes a succinct IOP and produces a succinct zero knowledge proof. And I want to emphasize that we're talking about proofs here. So we have statistical soundness. So soundness holds even against an unbounded cheating prover. This is not an argument. And this compiler requires only the minimal assumption of one-way functions. So we take this compiler and we apply it to the succinct IOP of Ronci and Rotbloom and we get the shortest known zero knowledge proofs for bounded space NP relations under the minimal assumption of one-way functions. Namely, the zero knowledge proof that we get has communication complexity to a proof length which approaches the original witness length. Now, this is cool. Succinct IOPs imply succinct zero knowledge proofs. So can we get the succinct IOP for all of NP? So we're revisiting the question that we asked earlier. And as a second result, we show that under NU but reasonable complexity conjecture, there is no succinct IOP for all of NP. How do we do that? Well, at the first step, we show a compiler that takes a succinct IOP and produces a special sort of algorithm which is a small space algorithm with polynomial time preprocessing. And we conjecture that circuit SAT cannot be solved in small space with polynomial time preprocessing. Now, circuit SAT is the Boolean satisfiability problem of circuits rather than just specific formulas. So combining the conjecture with the compiler, we get that under this conjecture, there is no succinct IOP for C SAT or more generally, there is no succinct IOP for all of NP. For more details, you are more than welcome to attend the talk that I will be giving at the conference. Thank you.