We consider a cascade network where a sequence of nodes each send a message to their downstream neighbor to enable coordination, the first node having access to an information signal. An adversary also receives all the communication as well as additional side-information. The performance of the system is measured by a payoff function over all actions produced by the nodes as well as the adversary. The challenge is to maintain secrecy from the adversary in order thwart his attempt to reduce the payoff. We obtain inner and outer bounds on performance, and give examples where they are tight. From these bounds, we also derive the optimal equivocation that can be achieved in this setting, as a special case.
We consider a cascade network where a sequence of nodes each send a message to their downstream neighbor to enable coordination, the first node having access to an information signal. An adversary also receives all the communication as well as additional side-information. The performance of the system is measured by a payoff function over all actions produced by the nodes as well as the adversary. The challenge is to maintain secrecy from the adversary in order thwart his attempt to reduce the payoff. We obtain inner and outer bounds on performance, and give examples where they are tight. From these bounds, we also derive the optimal equivocation that can be achieved in this setting, as a special case.
We consider a cascade network where a sequence of nodes each send a message to their downstream neighbor to enable coordination, the first node having access to an information signal. An adversary also receives all of the communication as well as additional side-information. The performance of the system is measured by a payoff function evaluated on actions produced at each of the nodes, including the adversary. The challenge is to effectively use a secret key to infuse some level of privacy into the encoding, in order thwart the adversary's attempt to reduce the payoff. We obtain information-theoretic inner and outer bounds on performance, and give examples where they are tight. From these bounds, we also derive the optimal equivocation for this setting as a special case.
Secrecy in communication systems is measured herein by the distortion that an adversary incurs. The transmitter and receiver share secret key, which they use to encrypt communication and ensure distortion at an adversary. A model is considered in which an adversary not only intercepts the communication from the transmitter to the receiver, but also potentially has side information. In particular, the adversary may have causal or noncausal access to a signal that is correlated with the source sequence or the receiver's reconstruction sequence. The main contribution is the characterization of the optimal tradeoff among communication rate, secret key rate, distortion at the adversary, and distortion at the legitimate receiver. It is demonstrated that causal side information at the adversary plays a pivotal role in this tradeoff. It is also shown that measures of secrecy based on normalized equivocation are a special case of the framework.
We consider theoretical limits of partial secrecy in a setting where an eavesdropper attempts to causally reconstruct an information sequence with low distortion based on an intercepted transmission and the past of the sequence. The transmitter and receiver have limited secret key at their disposal but not enough to establish perfect secrecy with a one-time pad. From another viewpoint, the eavesdropper is acting as an adversary, competing in a zero-sum repeated game against the sender and receiver of the secrecy system. In this case, the information sequence represents a sequence of actions, and the distortion function captures the payoff of the game. We give an information theoretic region expressing the tradeoff between secret key rate and max-min distortion for the eavesdropper. We also simplify this characterization to a linear program. As an example, we discuss how to optimally use secret key to hide Bernoulli-p bits from an eavesdropper so that they incur maximal Hamming distortion.
We study secret communication for broadcast channels with two legitimate receivers and one eavesdropper. The transmitter sends two independent confidential messages to the legitimate receivers which have to be kept secret from the eavesdropper. Here, each legitimate receiver is interested in one confidential message having the other one already as side information available. This problem arises for example in the broadcast phase in a bidirectional relay network, where a relay node establishes a bidirectional communication between two nodes while keeping the communication secure from an eavesdropper outside the network. We provide achievable rate regions and an outer bound on the secrecy capacity region.
In this paper, the problem of function computation with privacy and secrecy constraints is considered. The considered model consists of three legitimate nodes (i.e., two transmitters, Alice and Bob, and a fusion center that acts as the receiver) that observe correlated sources and are connected by noiseless public channels, and an eavesdropper Eve who has full access to the public channels and also has its own source observations. The fusion center would like to compute a function of the distributed sources within a prefixed distortion level under a certain distortion metric. To facilitate the function computation, Alice and Bob will send messages to the fusion center. Different from the existing setups in function computation, we assume that there is a privacy constraint on the sources at Alice and Bob. In particular, Alice and Bob would like to enable the fusion center to compute the function, but at same time, they do not want the fusion center to learn too much information about the source observations. We introduce a quantity to precisely measure the privacy leakage to the fusion center. In addition to this privacy constraint, we also have a secrecy constraint to Eve and use equivocation of sources to measure this quantity. Under this model, we study the tradeoffs among message rates, private information leakage, equivocation, and distortion. We first consider a scenario that has only one transmitter, i.e., the source at Bob is empty, and fully single-letter characterize the corresponding regions. Then, we consider the more general case and provide both outer and inner bounds on the corresponding regions.
In this work, secrecy in communication systems is measured by the distortion incurred by the worst-case adversary. The transmitter and receiver share secret key, which they use to encrypt communication and cause distortion at an adversary. In our model, we assume that an adversary not only intercepts the communication between the transmitter and receiver, but also may have access to noisy observations of the system. For example, the adversary may have causal access to a signal that is correlated with the source sequence or with the output of the receiver. Our main contribution is the solution of the optimal tradeoff among communication rate, secret key rate, distortion at the adversary, and distortion at the legitimate receiver. We demonstrate that side information at the adversary plays a pivotal role, and provide a number of examples that motivate and give insight into our results.