 Hi, I'm Viktor Korobov, and today I'm going to talk to you about programmable distributed point functions. This is a joint work with a lead boil, NIVGilboa and Ivalishi. So first the point functions are just functions which can be non-zero on only one special point and zero everywhere else. And the DPF allows the secret share of point function between two servers in a way that allows for the servers to perform distributed evaluation such that it is possible to add the output shares of the servers to recover the evaluation of the point function. Now this primitive can be trivially achieved with linear key size by just secret sharing the truth table of the point function and assuming one-way functions, this can be dramatically improved using a GGM like reconstruction yielding a scheme with logarithmic key length. And actually this construction is also tied in the sense that DPF to server DPF implies one-way functions. Now solutions to some problems that DPF solves in the two-server setting seem to require a public key photography in the one-server setting, and this is something which we wanted to avoid in this work. So, hence we consider the next best alternative, which is a form of 1.5 server DPF, which would refer to as very old DPF or PDPF for short. And it is essentially the same as a DPF except that the first key, which we refer to also as the offline key is just a short random seed, and hence can be generated independently of the point function. In fact, this notion implies a little stronger notion of reusable DPF, where the offline key of this short random seed will be used over multiple instances. And as with DPF, PDPFs also admit a trivial solution with linear key size by just having the open key be a PRF key and having the online key correct that. Now, regarding PDPF applications, PDPFs imply privately-functionable PRFs over a small domain, and this where privately-functional PRFs were previously constructed only from demographic assumptions, but here adding the small domain assumptions, assumption gives us a contraction from one way function. PDPFs are also useful in the 1.5 server setting where a single message is sent from the client to one of the servers. And they are also useful for compressing DPF correlations, which are useful for communication efficient MPC. This is in the so-called trusted offline setting where I secret shares that secret between yourself and Bob, and then forgets about it. In this way, PDPFs gives a way to compress many DPF correlations, instead of having to distribute the key generation protocol of DPF. Our construction is inspired by the patchable set sets due to the work of Cori and Gibson Corgan. So suppose we throw balls into bits and there are n bits, the same as the domain size, and we count how many balls we have in each bin. This gives us a histogram and this histogram corresponds to the truth table of the offline function share. This we give to Alice to the first party. To generate the online key, we remove one ball from one of the bins, the bin with index alpha, and give this histogram to the second party. Now note that the difference between these two histograms gives us a DPF over the integers. And this work will show that these histograms can be compressed using privately punctured graph. This is, in some sense, in similar manner to how cultural sets can be compressed using punctured graphs. Moving on to our results. Assuming the one way functions, there is a PDPF of sublinear key size, such as the running time of gen and deval all which is evaluation over the entire domain is polynomial in the domain size. Noted we do not get an evaluation algorithm for a single point directly only to evolve all, but for many applications such as PR, private writing and PCG is sufficient. In addition to an application we construct a standard or not for the normal DPM with constant round the distributed gen protocol which only makes black box use the property. And this improves over the O log n round protocol of donor and slot. And now in the full version of the talk with also discuss the privacy amplification for one of the political mutual in more detail. So this is the end protocol and the efficiency of our construction and optimizations. So this is all.