 Hello, I'm here to encourage you to come and see my talk on threshold delineary homomorphic encryption on Z over 2 to the kz. So this is joint work with Guillem Guestagnos and Fabien Lagume. So in this work, as suggests the title, we provide the first threshold delineary homomorphic encryption scheme whose message space is Z over 2 to the kz for any positive integral k. Now, a threshold public key encryption protocol is a public key system where the private key is distributed among n different servers. It offers high security since no single server is interested to perform the decryption in its entirety. And it's also the core component of many multi-party computation protocols which involve mutually distrusting parties with common goals. So thresholds public key encryption protocols are even more useful when they are homomorphic. This means that public operations on ciphertexts translate to operations on the underlying plaintexts. In particular, at EuroCrypt 2001, Kramer, Damgard, and Nielsen provided a new approach to multi-party computation from linearly homomorphic threshold encryption schemes. In parallel, there's also been a recent interest in developing multi-party computations modulo 2 to the k for a certain integral k. This choice is driven by the fact that modern CPU computations are performed in such a ring. Hence, if the multi-party computation protocol performs computations modulo 2 to the k, protocol designers can directly apply optimizations that are often expensive to emulate if a different modulus is used. So multi-party computation would benefit from an encryption scheme with such a message space that supports distributed decryption. And this is exactly what we have developed in this work. A threshold linearly homomorphic encryption scheme whose message space is z over 2 to the kz for any k. Our construction uses class groups of imaginary quadratic fields, like the encryption schemes modulo an odd prime q of Guestagnos and Legumi from CTRSA 2015. However, as is often the case in number theory, moving from an odd prime q to 2 or to 2 to the k is not an easy task. And as we'll see in my talk, plugging the modulus to be 2 to the k in their framework doesn't work. And so if you come to my talk, you will find out how we overcome this challenge, how we managed to realize for the first time a public key encryption scheme with all three of these properties. I hope to see you next Tuesday. Goodbye.