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Expanding the scientific tools available to protect computer networks can be aided by a deeper understanding of the underlying statistical distributions of network traffic and their potential geometric interpretations. Analyses of large scale network observations provide a unique window into studying those underlying statistics. Newly developed GraphBLAS hypersparse matrices and D4M associative array technologies enable the efficient anonymized analysis of network traffic on the scale of trillions of events. This work analyzes over 100,000,000,000 anonymized packets from the largest Internet telescope (CAIDA) and over 10,000,000 anonymized sources from the largest commercial honeyfarm (GreyNoise). Neither CAIDA nor GreyNoise actively emit Internet traffic and provide distinct observations of unsolicited Internet traffic (primarily botnets and scanners). Analysis of these observations confirms the previously observed Cauchy-like distributions describing temporal correlations between Internet sources. The Gull lighthouse problem is a well-known geometric characterization of the standard Cauchy distribution and motivates a potential geometric interpretation for Internet observations. This work generalizes the Gull lighthouse problem to accommodate larger classes of coastlines, deriving a closed-form solution for the resulting probability distributions, stating and examining the inverse problem of identifying an appropriate coastline given a continuous probability distribution, identifying a geometric heuristic for solving this problem computationally, and applying that heuristic to examine the temporal geometry of different subsets of network observations. Application of this method to the CAIDA and GreyNoise data reveals a several orders of magnitude difference between known benign and other traffic which can lead to potentially novel ways to protect networks., Comment: 9 pages, 7 figures, IEEE HPEC 2023 (accepted)

Defending community-owned cyber space requires community-based efforts. Large-scale network observations that uphold the highest regard for privacy are key to protecting our shared cyberspace. Deployment of the necessary network sensors requires careful sensor placement, focusing, and calibration with significant volumes of network observations. This paper demonstrates novel focusing and calibration procedures on a multi-billion packet dataset using high-performance GraphBLAS anonymized hypersparse matrices. The run-time performance on a real-world data set confirms previously observed real-time processing rates for high-bandwidth links while achieving significant data compression. The output of the analysis demonstrates the effectiveness of these procedures at focusing the traffic matrix and revealing the underlying stable heavy-tail statistical distributions that are necessary for anomaly detection. A simple model of the corresponding probability of detection ($p_{\rm d}$) and probability of false alarm ($p_{\rm fa}$) for these distributions highlights the criticality of network sensor focusing and calibration. Once a sensor is properly focused and calibrated it is then in a position to carry out two of the central tenets of good cybersecurity: (1) continuous observation of the network and (2) minimizing unbrokered network connections., Comment: Accepted to IEEE HPEC, 9 pages, 12 figures, 1 table, 63 references, 2 appendices

Internet analysis is a major challenge due to the volume and rate of network traffic. In lieu of analyzing traffic as raw packets, network analysts often rely on compressed network flows (netflows) that contain the start time, stop time, source, destination, and number of packets in each direction. However, many traffic analyses benefit from temporal aggregation of multiple simultaneous netflows, which can be computationally challenging. To alleviate this concern, a novel netflow compression and resampling method has been developed leveraging GraphBLAS hyperspace traffic matrices that preserve anonymization while enabling subrange analysis. Standard multitemporal spatial analyses are then performed on each subrange to generate detailed statistical aggregates of the source packets, source fan-out, unique links, destination fan-in, and destination packets of each subrange which can then be used for background modeling and anomaly detection. A simple file format based on GraphBLAS sparse matrices is developed for storing these statistical aggregates. This method is scale tested on the MIT SuperCloud using a 50 trillion packet netflow corpus from several hundred sites collected over several months. The resulting compression achieved is significant (<0.1 bit per packet) enabling extremely large netflow analyses to be stored and transported. The single node parallel performance is analyzed in terms of both processors and threads showing that a single node can perform hundreds of simultaneous analyses at over a million packets/sec (roughly equivalent to a 10 Gigabit link)., Comment: arXiv admin note: text overlap with arXiv:2203.13934, arXiv:2108.06653, arXiv:2008.00307