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In this paper, we study the problem of distributed multi-user secret sharing, including a trusted master node, $Nin mathbb{N}$ storage nodes, and $K$ users, where each user has access to the contents of a subset of storage nodes. Each user has an independent secret message with certain rate, defined as the size of the message normalized by the size of a storage node. Having access to the secret messages, the trusted master node places encoded shares in the storage nodes, such that (i) each user can recover its own message from the content of the storage nodes that it has access to, (ii) each user cannot gain any information about the message of any other user. We characterize the capacity region of the distributed multi-user secret sharing, defined as the set of all achievable rate tuples, subject to the correctness and privacy constraints. In the achievable scheme, for each user, the master node forms a polynomial with the degree equal to the number of its accessible storage nodes minus one, where the value of this polynomial at certain points are stored as the encoded shares. The message of that user is embedded in some of the coefficients of the polynomial. The remaining coefficients are determined such that the content of each storage node serves as the encoded shares for all users that have access to that storage node.
We consider an extension of Masseys construction of secret sharing schemes using linear codes. We describe the access structure of the scheme and show its connection to the dual code. We use the $g$-fold weight enumerator and invariant theory to study the access structure.
Intelligent reflecting surface (IRS) is a new promising technology that is able to reconfigure the wireless propagation channel via smart and passive signal reflection. In this paper, we investigate the capacity region of a two-user communication net
Wireless communication is susceptible to eavesdropping attacks because of its broadcast nature. This paper illustrates how interference can be used to counter eavesdropping and assist secrecy. In particular, a wire-tap channel with a helping interfer
Wireless communication is susceptible to adversarial eavesdropping due to the broadcast nature of the wireless medium. In this paper it is shown how eavesdropping can be alleviated by exploiting the superposition property of the wireless medium. A wi
This paper investigates the secret key authentication capacity region. Specifically, the focus is on a model where a source must transmit information over an adversary controlled channel where the adversary, prior to the sources transmission, decides