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Motivated by the application of Reed-Solomon codes to recently emerging decentralized storage systems such as Storj and Filebase/Sia, we study the problem of designing compact repair groups for recovering multiple failures in a decentralized manner. Here, compactness means that the corresponding trace repair schemes of these groups of helpers can be generated from a single or a few seed repair schemes, thus saving the time and space required for finding and storing them. The goal is to design compact repair groups that can tolerate as many failures as possible. It turns out that the maximum number of failures a collection of repair groups can tolerate equals the size of a minimum hitting set of a collection of subsets of the finite field {\mathbb{F}_{q^{\ell}}} minus one. When the repair groups for each symbol are generated from a single subspace, we establish a pair of asymptotically tight lower bound and upper bound on the size of such a minimum hitting set. Using Burnside's Lemma and the M\"{o}bius inversion formula, we determine a number of subspaces that together attain the upper bound on the minimum hitting set size when the repair groups are generated from multiple subspaces.

While most security projects have focused on fending off attacks coming from outside the organizational boundaries, a real threat has arisen from the people who are inside those perimeter protections. Insider threats have shown their power by hugely affecting national security, financial stability, and the privacy of many thousands of people. What is in the news is the tip of the iceberg, with much more going on under the radar, and some threats never being detected. We propose a hybrid framework based on graphical analysis and anomaly detection approaches, to combat this severe cybersecurity threat. Our framework analyzes heterogeneous data in isolating possible malicious users hiding behind others. Empirical results reveal this framework to be effective in distinguishing the majority of users who demonstrate typical behavior from the minority of users who show suspicious behavior.

Anomalous user behavior detection is the core component of many information security systems, such as intrusion detection, insider threat detection and authentication systems. Anomalous behavior will raise an alarm to the system administrator and can be further combined with other information to determine whether it constitutes an unauthorised or malicious use of a resource. This paper presents an anomalous user behaviour detection framework that applies an extended version of Isolation Forest algorithm. Our method is fast and scalable and does not require example anomalies in the training data set. We apply our method to an enterprise dataset. The experimental results show that the system is able to isolate anomalous instances from the baseline user model using a single feature or combined features.

We generalize Sudan's list decoding algorithm without multiplicity to evaluation codes coming from arbitrary order domains. The number of correctable errors by the proposed method is larger than the original list decoding without multiplicity.