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.

In this paper we generalize a new type of limiters based on the weighted essentially non-oscillatory (WENO) finite volume methodology for the Runge-Kutta discontinuous Galerkin (RKDG) methods solving nonlinear hyperbolic conservation laws, which were recently developed for structured meshes, to two-dimensional unstructured triangular meshes. The key idea of such limiters is to use the entire polynomials of the DG solutions from the troubled cell and its immediate neighboring cells, and then apply the classical WENO procedure to form a convex combination of these polynomials based on smoothness indicators and nonlinear weights, with suitable adjustments to guarantee conservation. The main advantage of this new limiter is its simplicity in implementation, especially for the unstructured meshes considered in this paper, as only information from immediate neighbors is needed and the usage of complicated geometric information of the meshes is largely avoided. Numerical results for both scalar equations and Euler systems of compressible gas dynamics are provided to illustrate the good performance of this procedure.

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