Jihad Fahs

Anthony Ayli, Khalil Harris, Jihad Fahs et al.

Homomorphic encryption (HE) enables privacy-preserving aggregation in federated learning (FL) by allowing the server to operate on encrypted data without decryption. Existing HE-over-the-air methods mainly rely on single-key HE schemes and require channel estimation or pre-equalization to compensate for wireless fading. However, single-key HE remains vulnerable to honest-but-curious clients sharing the same secret key. In addition, compromising a single client may compromise the security of the entire network, while multi-key HE schemes provide stronger client-level security by assigning each device its own secret key. We propose a four-phase protocol that enables xMK-CKKS, a famous multi-key HE scheme, aggregation over a shared wireless channel without channel estimation. The protocol retransmits partial public keys and ciphertexts through the same channel realization, so that the dominant large-modulus encryption terms cancel algebraically during decryption. We integrate this protocol with zero-order FL over slowly varying LoS-dominant channels, where each device transmits a single encrypted scalar per round and the communication/encryption overhead is independent of the model dimension. We prove that the decoded encryption noise preserves the \(O(1/\sqrt{K})\) convergence rate up to a negligible noise floor. The protocol is secure against an honest-but-curious server colluding with up to \(N-1\) clients, and numerical results on MNIST validate the analysis.

Mario Sayde, Christopher Khater, Jihad Fahs et al.

Principal Component Analysis (PCA) is a cornerstone of dimensionality reduction, yet its classical formulation relies critically on second-order moments and is therefore fragile in the presence of heavy-tailed data and impulsive noise. While numerous robust PCA variants have been proposed, most either assume finite variance, rely on sparsity-driven decompositions, or address robustness through surrogate loss functions without a unified treatment of infinite-variance models. In this paper, we study PCA for high-dimensional data generated according to a superstatistical dependent model of the form $\mathbf{X} = A^{1/2}\mathbf{G}$, where $A$ is a positive random scalar and $\mathbf{G}$ is a Gaussian vector. This framework captures a wide class of heavy-tailed distributions, including multivariate $t$ and sub-Gaussian $α$-stable laws. We formulate PCA under a logarithmic loss, which remains well defined even when moments do not exist. Our main theoretical result shows that, under this loss, the principal components of the heavy-tailed observations coincide with those obtained by applying standard PCA to the covariance matrix of the underlying Gaussian generator. Building on this insight, we propose robust estimators for this covariance matrix directly from heavy-tailed data and compare them with the empirical covariance and Tyler's scatter estimator. Extensive experiments, including background denoising tasks, demonstrate that the proposed approach reliably recovers principal directions and significantly outperforms classical PCA in the presence of heavy-tailed and impulsive noise, while remaining competitive under Gaussian noise.