Fully device independent Conference Key Agreement

We present the first security analysis of conference key agreement (CKA) in the most adversarial model of device independence (DI). Our protocol can be implemented {by any experimental setup} that is capable of performing Bell tests (specifically, we introduce the "Parity-CHSH" inequality), and security can in principle be obtained for any violation of the Parity-CHSH inequality. We use a direct connection between the $N$-partite Parity-CHSH inequality and the CHSH inequality. Namely, the Parity-CHSH inequality can be considered as a CHSH inequality or another CHSH inequality (equivalent up to relabelling) depending on the parity of the output of $N-2$ of the parties. We compare the asymptotic key rate for DICKA to the case where the parties use $N-1$ DIQKD protocols in order to generate a common key. We show that for some regime of noise the DICKA protocol leads to better rates.