This paper proposes a second-order pedestrian model that comprises two types of equations: continuity equation and a set of transport equations. To complete the model, we develop Eikonal equations to explicitly consider the effects of the collective decisions of individuals and crowd pressure on pedestrian dynamics. Then, the crowd movement is simulated using a set of partial differential equations under appropriate initial and boundary conditions. Based on the stability requirements derived by performing a standard linear stability analysis, suitable parameters are selected to test the model in a numerical example. The proposed second-order system is then solved using the characteristic-wise third-order weighted essentially non-oscillatory (WENO3) scheme, and the Eikonal equations are solved using the fast sweeping method. The numerical results indicate the effectiveness of the model because the derived local flow-density relationship produces a second peak in the high-density region, which is consistent with previous empirical studies. Besides, the applicability of the model to an unstable condition is verified through the simulation of complex phenomena such as stop-and-go waves. Furthermore, the estimate of crowd pressure in the simulation results can be used as a risk-level indicator for crowd management and control.

Research on key mismatch attacks against lattice-based KEMs is an important part of the cryptographic assessment of the ongoing NIST standardization of post-quantum cryptography. There have been a number of these attacks to date. However, a unified method to evaluate these KEMs’ resilience under key mismatch attacks is still missing. Since the key index of efficiency is the number of queries needed to successfully mount such an attack, in this paper, we propose and develop a systematic approach to find lower bounds on the minimum average number of queries needed for such attacks. Our basic idea is to transform the problem of finding the lower bound of queries into finding an optimal binary recovery tree (BRT), where the computations of the lower bounds become essentially the computations of a certain Shannon entropy. The optimal BRT approach also enables us to understand why, for some lattice-based NIST candidate KEMs, there is a big gap between the theoretical bounds and bounds observed in practical attacks, in terms of the number of queries needed. This further leads us to propose a generic improvement method for these existing attacks, which are confirmed by our experiments. Moreover, our proposed method could be directly used to improve the side-channel attacks against CCA-secure NIST candidate KEMs.

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For an integral domain$R$and a non-zero non-unit$a$ε$R$we consider the number of distinct factorizations of$a$^{$n$}into irreducible elements of$R$for large$n$. Precise results are obtained for Krull domains and certain noetherian domains. In fact, we prove results valid for certain classes of monoids which then apply to the above-mentioned classes of domains.

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