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AGU Abstract #1983654 

Emerging satellite networks integrated with terrestrial and aerial systems form a key part of next-generation infrastructures supporting the Internet of Everything (IoE). This chapter outlines the current status of PQC-based authentication in integrated Space-Aerial-Terrestrial Networks (SATIN), highlighting the technical challenges in achieving quantum-resilient security within constrained and complex environments. While quantum computing necessitates migration to post-quantum cryptography (PQC), existing standards often demand resources that are unsuited for SATIN’s limited hardware and fragile links. We analyze leading NIST PQC signature and key encapsulation schemes in the SATIN context, evaluating trade-offs in computational cost, signature size, and protocol compatibility. Emerging directions, including broader algorithm evaluations, advanced protocol integrations (e.g., EMSS and NIST-PQC with terrestrial backbone, PQ group key management), and some alternative PQ technologies are discussed. Addressing these challenges requires advanced simulation and experimental frameworks to enable scalable, practical, and quantum-resilient secure communications in future integrated networks. 

Erd\H{o}s and Pomerance have shown that $$\varphi(n)$$ typically has about $$\frac{1}{2}(\log\log{n})^2$$ distinct prime factors. More precisely, $$\omega(\varphi(n))$$ has normal order $$\frac{1}{2}(\log\log{n})^2$$. Since $$\varphi(n)$$ is the size of the multiplicative group $$(\Z/n\Z)^{\times}$$, this result also gives the normal number of Sylow subgroups of $$(\Z/n\Z)^{\times}$$. Recently, Pollack considered specifically noncyclic Sylow subgroups of $$(\Z/n\Z)^{\times}$$, showing that the count of those has normal order $$\log\log{n}/\log\log\log{n}$$. We prove that the count of noncyclic Sylow subgroups that are elementary abelian of a fixed rank $$k\ge 2$$ has normal order $$\frac{1}{k(k-1)} \log\log{n}/\log\log\log{n}$$. So for example, (typically) among the primes $$p$$ for which the $$p$$-primary component of $$(\Z/n\Z)^{\times}$$ is noncyclic, this component is $$\Z/p\Z \oplus \Z/p\Z$$ about half the time. Additionally, we show that the count of $$p$$ for which the $$p$$-Sylow subgroup of $$(\Z/n\Z)^{\times}$$ is not elementary abelian has normal order $$2\sqrt{\pi} \sqrt{\log\log{n}}/\log\log\log{n}$$. 

Accepted for publication 12/26/2025 

Urban expansion and the increasing frequency and intensity of extreme precipitation events bring new challenges to stormwater collection systems. One underrecognized issue is the occurrence of transient flow conditions that lead to adverse multiphase flow interactions (AMFI): essentially, the formation, collapse, and uncontrolled release of air pockets within stormwater system flows. While the fundamental physics of AMFI have been evaluated in laboratory experiments and idealized modeling studies, much less is known about their development in real or simulated stormwater networks, and about the roles played by rainfall and network properties. A necessary precursor to AMFI is the development of pressurized flow conditions within a network. The goal of this study is to understand how spatiotemporal rainfall variability affects the occurrence of pressurized conditions in a stormwater drainage network in the Richmond district of San Francisco, California. High-resolution bias-corrected radar rainfall fields for 24 recent storms were used as the independent variable of EPA-SWMM simulations. Model analyses indicate that the incidence of pressurized flow increases with storm intensity and is more sensitive to rainfall temporal variability than spatial variability. This research provides a reference for analyzing AMFI precursors in other networks and may have important implications for the improvement of stormwater infrastructures.