Robust secret key capacity for the MIMO induced source model

Abstract

This paper considers the problem of distilling a secret key in a Gaussian multiple-input multiple-output (MIMO) scenario with two legitimate nodes and an eavesdropper. Focusing on the realistic case without perfect knowledge of the eavesdropper channel, and following a conservative practical approach based on the maximization of the worst case secret key capacity (SKC), the problem of designing the optimal transmit covariance matrix is reformulated as a convex optimization problem. In the limiting case in which the eavesdropper channel can not be estimated, or when the estimate is highly unreliable, the optimal covariance matrix can be obtained by means of waterfilling or matched filtering like algorithms. Additionally, we illustrate the benefits of allowing time sharing between transmissions of the two legitimate nodes, and provide an efficient algorithm for obtaining the optimal transmit covariance matrices and time-sharing factor.