In this paper, we study the fundamental problems of maintaining the diameter and a $k$-center clustering of a dynamic point set $P \subset \mathbb{R}^d$, where points may be inserted or deleted over time and the ambient dimension $d$ is not constant and may be high. Our focus is on designing algorithms that remain effective even in the presence of an \emph{adaptive adversary}--an adversary that, at any time $t$, knows the entire history of the algorithm's outputs as well as all the random bits used by the algorithm up to that point. We present a fully dynamic algorithm that maintains a $2$-approximate diameter with a \emph{worst-case} update time of $poly(d, \log n)$, where $n$ is the length of the stream. Our result is achieved by identifying a robust representative of the dataset that requires infrequent updates, combined with a careful deamortization. To the best of our knowledge, this is the first efficient fully-dynamic algorithm for diameter in high dimensions that \emph{simultaneously} achieves a $2$-approximation guarantee and robustness against an adaptive adversary. We also give an improved dynamic $(4+\epsilon)$-approximation algorithm for the $k$-center problem, also resilient to an adaptive adversary. Our clustering algorithm achieves an amortized update time of $k^{2.5}

In this paper, we study robust algorithms for the experts problem under memory constraints.

We consider the problem of online classification under a privacy constraint.

Federated Learning (FL) has recently emerged as a promising paradigm for privacy-preserving, distributed machine learning. However, FL systems face significant security threats, particularly from adaptive adversaries capable of modifying their attack strategies to evade detection. One such threat is the presence of Reconnecting Malicious Clients (RMCs), which exploit FLs open connectivity by reconnecting to the system with modified attack strategies. To address this vulnerability, we propose integration of Identity-Based Identification (IBI) as a security measure within FL environments. By leveraging IBI, we enable FL systems to authenticate clients based on cryptographic identity schemes, effectively preventing previously disconnected malicious clients from re-entering the system. Our approach is implemented using the TNC-IBI (Tan-Ng-Chin) scheme over elliptic curves to ensure computational efficiency, particularly in resource-constrained environments like Internet of Things (IoT). Experimental results demonstrate that integrating IBI with secure aggregation algorithms, such as Krum and Trimmed Mean, significantly improves FL robustness by mitigating the impact of RMCs. We further discuss the broader implications of IBI in FL security, highlighting research directions for adaptive adversary detection, reputation-based mechanisms, and the applicability of identity-based cryptographic frameworks in decentralized FL architectures. Our findings advocate for a holistic approach to FL security, emphasizing the necessity of proactive defence strategies against evolving adaptive adversarial threats.