 Hi, my name is John Thompson and a crypto I'll be presenting the work formalizing delayed adaptive corruptions and the security of flooding networks. This is joint work with Christian Matt and my supervisor Jesper Buchs-Nielsen. I'd like to motivate this work using the example of Nakamoto-style blockchains. This is the type of protocol where a group of parties, which you see on the right, participate in a lottery, which you see on the left, in order to be allowed to extend the current base chain with a new block. So in this case, where P1 wins, you now like to disseminate this block to all other parties in the protocol. The way this works is that P1 chooses a random neighborhood and then forwards the block only to this neighborhood. The neighbors will then again forward the block to their neighbors and so on and so forth, until all parties have received the block. This works very well for a static adversary, however as we are about to see this doesn't work when we consider an adaptive adversary. Let's try to analyze this flooding procedure with an adaptive adversary. Here we have two options, either to consider a non-atomic or atomic message set. So if you first assume non-atomic message send, then the adversary has the possibility at the moment P1 wins and tries to send out the block, then the adversary will learn that P1 is sending out the block and can now corrupt him. Furthermore, once he corrupts him, he can actually retract the message and thereby prevent the delivery of the block to all other honest parties. Therefore this doesn't work. If we instead consider atomic message send, then the adversary does not have the possibility to corrupt the center of the block and thereby retract the block. However what the adversary can do is to corrupt the neighborhood of the center and thereby prevent the delivery of the message to the remaining parties in the protocol. So again this doesn't work. Of course what you can do is to send to all parties. Then the adversary cannot prevent the delivery, but this leaves us with quite a heavy workload for each individual party as they have to send to all other parties themselves. In this work we consider a delta-delayed adversary, where once the adversary decides to corrupt a party, it takes a certain time until the corruption actually becomes effective. So let us now try to analyze the flooding procedure against such a delayed adversary that is the date for the time it takes to send, plus the time it takes to recent the message. So as before, party 1 sends out the message to his neighborhood, but now of course the adversary can try to corrupt, but as the corruption doesn't become effective until the neighborhood has already started to forward the message, then it's too late for the adversary once the corruption actually becomes effective and all parties will anyway learn the message. Our work has two main contributions. First we provide a formal model for the semantics of delta-delayed adversaries within UC. This is both useful for flooding, but also for protocols with long-lived committees. For example, Parson-Chich used an informal model that was similar to this in 2017. Secondly, we provide two implementations of flooding networks within this model that is secure against an adaptive adversary delayed for the time it takes to send, plus the time it takes to recent. The first implementation has a constant neighborhood with a logarithmic diameter, whereas the second implementation has a square root number of neighbors with a constant diameter. Thank you for your attention.