Compute-and-Forward Can Buy Secrecy Cheap

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 scenario 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.Comment: Accepted to ISIT 2015, 5 pages, 3 figure

The CEO Problem with Secrecy Constraints

We study a lossy source coding problem with secrecy constraints in which a remote information source should be transmitted to a single destination via multiple agents in the presence of a passive eavesdropper. The agents observe noisy versions of the source and independently encode and transmit their observations to the destination via noiseless rate-limited links. The destination should estimate the remote source based on the information received from the agents within a certain mean distortion threshold. The eavesdropper, with access to side information correlated to the source, is able to listen in on one of the links from the agents to the destination in order to obtain as much information as possible about the source. This problem can be viewed as the so-called CEO problem with additional secrecy constraints. We establish inner and outer bounds on the rate-distortion-equivocation region of this problem. We also obtain the region in special cases where the bounds are tight. Furthermore, we study the quadratic Gaussian case and provide the optimal rate-distortion-equivocation region when the eavesdropper has no side information and an achievable region for a more general setup with side information at the eavesdropper.Comment: Accepted for publication in IEEE Transactions on Information Forensics and Security, 17 pages, 4 figure

Secure Partial Repair in Wireless Caching Networks with Broadcast Channels

We study security in partial repair in wireless caching networks where parts of the stored packets in the caching nodes are susceptible to be erased. Let us denote a caching node that has lost parts of its stored packets as a sick caching node and a caching node that has not lost any packet as a healthy caching node. In partial repair, a set of caching nodes (among sick and healthy caching nodes) broadcast information to other sick caching nodes to recover the erased packets. The broadcast information from a caching node is assumed to be received without any error by all other caching nodes. All the sick caching nodes then are able to recover their erased packets, while using the broadcast information and the nonerased packets in their storage as side information. In this setting, if an eavesdropper overhears the broadcast channels, it might obtain some information about the stored file. We thus study secure partial repair in the senses of information-theoretically strong and weak security. In both senses, we investigate the secrecy caching capacity, namely, the maximum amount of information which can be stored in the caching network such that there is no leakage of information during a partial repair process. We then deduce the strong and weak secrecy caching capacities, and also derive the sufficient finite field sizes for achieving the capacities. Finally, we propose optimal secure codes for exact partial repair, in which the recovered packets are exactly the same as erased packets.Comment: To Appear in IEEE Conference on Communication and Network Security (CNS