 Hello, everyone. So I'm Dario Fiorre from there. I'd like to advertise our work on additive homomorphic functional commitments and applications for morphic signatures, which is joint work with Dario Gattarano and Ida Tucker. So this is about functional commitments, which is a notion proposed in 2016 by Lieberman and Jung, and he was proposed as a generalization of the more popular notions of vector commitments and polynomial commitments. So the idea of functional commitments is that we have two parties, a sender and the receiver. And we think of the sender as a big party that can hold a large vector x, and the receiver is with little resources. And the idea is that the sender wants to commit to this vector x, give this commitment to the receiver, and then at later points in time, he wants to compute some function on the committed data, give the result to the receiver but also give some opening So the opening proof should convince the receiver that the result y is actually obtained by all, you know, what opens the commitment. So the property that makes functional commitments and interesting and non-trivial primitive is succinctness. And this informally says that the size of openings and commitments should be short with respect to the input sites, and ideally should be constant. And the security property of functional commitments is evolution binding, which informally says you cannot have a malicious sender that with computationally speaking can open a commitment to two different outputs for the same function. So, and so in this sense functional commitments if you look at the functionality are like a weaker version of committed proof snarks, in which the strong notion of a son is snarks that is about producing one single proof for a full statement is replaced with this evolution binding which that versus should produce two proofs for disagreeing statements. Now, given this observation it is an interesting question that of whether like, we can replace not to functional commitments in some applications with the benefit of having a notion with is falsifiable and potentially realizable from falsifiable assumptions. So in this work we actually start from this question and we ask in which applications evaluation binding is sufficient, and we observe that, you know, our very first result is this observation that if you sign a functional commitment this is a very basic notion of a more fixed While we push this idea, even farther and observe that if the functional commitment is additive or more thick then we use multi input or fixed signatures by pairing it with the linearly or more fixed signature and interestingly, like, this gives a new paradigm for building the omorphic signatures because the omorphic signature would support the same class of functions supported by the functional commitment. And also we, you know, if a commitment is additive or more thick it's also obtainable and this is other applications. So the next question is whether there exists or can we construct additive or more thick functional commitments. Unfortunately, if we look at the state of the art, only the skins for linear functions are additive or more thick so our main results are the first additive or more thick functional commitments for functions beyond linear. And we have one scheme for constant degree polynomials and another scheme for circuits in the class NC one. And these schemes have also implications to new omorphic signatures based on balance. And I will not tell you more than this in this talk. I really invite you to come and listen to our talks at Asia.