When is a function securely computable?

Abstract

Abstract-A subset of a set of terminals that observe correlated signals seek to compute a function of the signals using public communication. It is required that the value of the function be concealed from an eavesdropper with access to the communication. We show that the function is securely computable if and only if its entropy is less than the capacity of a new secrecy generation model, for which a single-letter characterization is provided.

Multivariate Dependence beyond Shannon Information

“…Though only one of them-the Gács-Körner common information K [•] [57,58], involving the construction of the largest "subrandom variable" common to the variables-discerns that the two distributions are not equivalent because the triadic distribution contains the subrandom variable X 1 = Y 1 = Z 1 common to all three variables.…”

Thermodynamics of Large-Scale Heterogeneous Wireless Networks

“…In such networks, it also is often desirable that the computed value of the function be kept secret from an eavesdropper. In [5], we introduced a Shannon-theoretic formulation to characterize a set of necessary and sufficient conditions for secure computability. Drawing on innate connections to the problem of secret-key generation using public communication, we showed that a function is securely computable if and only if its entropy is less than the "aided" secret-key capacity, for which we obtained a single-letter characterization.…”

From secret key agreement to matroidal undirected network

“…It turns out that the secret key agreement problem can be further generalized to secure source coding in [17], [18], where the goal is to compute a secret source as securely as possible instead of agreeing on a secret key. It is natural to think that the results there can also be translated into solutions of certain undirected network problem.…”

“…In addition to studying the problem of multicasting independent messages in the previous work, we will also consider multicasting a distributed source or function of the source just like [15], [16] for the directed network. By relating the problem to the secure source coding problem in [17], [18], polynomial-time solutions or partial solutions can be obtained by exploiting the underlying matroidal structure. The concept can also be extended to a network with its direction partially fixed, with some directed and undirected links.…”