Two post-quantum password-based authenticated key exchange (PAKE) protocols were proposed at CTRSA 2017. Following this work, we give much more efficient and portable C++ implementation of these two protocols. We also choose more compact parameters providing 200-bit security. Compared with original implementation, we achieve 21.5x and 18.5x speedup for RLWE-PAK and RLWE-PPK respectively. Compare with quantum-vulnerable J-PAKE protocol, we achieve nearly 8x speedup. We also integrate RLWE-PPK into TLS to construct a post-quantum TLS ciphersuite. This allows simpler key management, mutual authentication and resistant to phishing attack. Benchmark shows that our ciphersuite is indeed practical

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Averages over smooth measures on smooth compact hypersurfaces in$R$^{$n$}are studied. With assumptions on the decay of the Fourier transform of the measure we obtain mixed norm estimates for these means, for example$L$^{$p$}estimates of multiparameter maximal functions over compact hypersurfaces.

We obtain the generalized codimension-$p$Cauchy–Kovalevsky extension of the exponential function $e^{i\langle\underline{y},\underline{t}\rangle}$ in R^{$m$}=R^{$p$}⊕R^{$q$}, where$p$>1, $\underline{y},\underline{t}\in\mathbf{R}^{q}$ , and prove the corresponding codimension-$p$Paley–Wiener theorems.