Computationally efficient matrix multiplication is a fundamental requirement in various fields, including and particularly in data analytics. To do so, the computation task of large-scale matrix multiplication is typically outsourced to multiple servers. However, due to data misusage at the servers, security is typical of concern. In this paper, we first study the two-sided secure matrix multiplication problem, where a user is interested in the matrix product AB of two finite field private matrices A and B from an information-theoretic perspective. In this problem, the user exploits the computational resources of N servers to compute the matrix product but simultaneously tries to conceal the private matrices from the servers. Our goal is twofold: (i) to maximize the downlink communication rate, and (ii) to minimize the effective number of server observations needed to determine AB, while preserving security, where we allow for up to ≤ N servers to collude. To this end, we propose two schemes -an aligned secret sharing scheme (A3S) and a secure cross subspace alignment (SCSA) scheme. For A3S, we optimize the partitioning of matrices A and B in order to either optimize objective (i) or (ii) as a function of the system parameters (e.g., N and ). A proposed inductive approach gives us analytical, close-to-optimal solutions for both (i) and (ii). The SCSA, on the other hand, is shown to be (rate) capacity-optimal for the general J -sided distributed secure matrix multiplication problem J j=1 M j . We show this by developing a recursive information-theoretic upper bound (converse) on the downlink rate for the J -sided secure matrix multiplication problem. With respect to (i), both A3S and SCSA, significantly outperform the state-of-the-art in terms of (a) communication rate, (b) maximum tolerable number of colluding servers, and (c) computational complexity. Overall SCSA (A3S) is the preferred choice when the focus is on the downlink (uplink).
Computationally efficient matrix multiplication is a fundamental requirement in various fields, including and particularly in data analytics. To do so, the computation task of a large-scale matrix multiplication is typically outsourced to multiple servers. However, due to data misusage at the servers, security is typically of concern. In this paper, we study the two-sided secure matrix multiplication problem, where a user is interested in the matrix product AB of two finite field private matrices A and B from an information-theoretic perspective. In this problem, the user exploits the computational resources of N servers to compute the matrix product, but simultaneously tries to conceal the private matrices from the servers. Our goal is twofold:(i) to maximize the communication rate, and, (ii) to minimize the effective number of server observations needed to determine AB, while preserving security, where we allow for up to ℓ ≤ N servers to collude. To this end, we propose a general aligned secret sharing scheme for which we optimize the matrix partition of matrices A and B in order to either optimize objective (i) or (ii) as a function of the system parameters (e.g., N and ℓ). A proposed inductive approach gives us analytical, close-to-optimal solutions for both (i) and (ii). With respect to (i), our scheme significantly outperforms the existing scheme of Chang and Tandon in terms of (a) communication rate, (b) maximum tolerable number of colluding servers and (c) computational complexity.
The application domains of civilian unmanned aerial systems (UASs) include agriculture, exploration, transportation, and entertainment. The expected growth of the UAS industry brings along new challenges: Unmanned aerial vehicle (UAV) flight control signaling requires low throughput, but extremely high reliability, whereas the data rate for payload data can be significant. This paper develops UAV number projections and concludes that small and micro UAVs will dominate the US airspace with accelerated growth between 2028 and 2032. We analyze the orthogonal frequency division multiplexing (OFDM) waveform because it can provide the much needed flexibility, spectral efficiency, and, potentially, reliability and derive suitable OFDM waveform parameters as a function of UAV flight characteristics. OFDM also lends itself to agile spectrum access. Based on our UAV growth predictions, we conclude that dynamic spectrum access is needed and discuss the applicability of spectrum sharing techniques for future UAS communications.
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