We consider a Gaussian multiple access channel with $K$ transmitters, a (intended) receiver and an external eavesdropper. The transmitters wish to reliably communicate with the receiver while concealing their messages from the eavesdropper. This scen
ario has been investigated in prior works using two different coding techniques; the random i.i.d. Gaussian coding and the signal alignment coding. Although, the latter offers promising results in a very high SNR regime, extending these results to the finite SNR regime is a challenging task. In this paper, we propose a new lattice alignment scheme based on the compute-and-forward framework which works at any finite SNR. We show that our achievable secure sum rate scales with $log(mathrm{SNR})$ and hence, in most SNR regimes, our scheme outperforms the random coding scheme in which the secure sum rate does not grow with power. Furthermore, we show that our result matches the prior work in the infinite SNR regime. Additionally, we analyze our result numerically.
A new scenario for generating a secret key and two private keys among three Terminals in the presence of an external eavesdropper is considered. Terminals 1, 2 and 3 intend to share a common secret key concealed from the external eavesdropper (Termin
al 4) and simultaneously, each of Terminals 1 and 2 intends to share a private key with Terminal 3 while keeping it concealed from each other and from Terminal 4. All four Terminals observe i.i.d. outputs of correlated sources and there is a public channel from Terminal 3 to Terminals 1 and 2. An inner bound of the secret key-private keys capacity region is derived and the single letter capacity regions are obtained for some special cases.
