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Anonymous veto networks (AV-nets), originally proposed by Hao and Zielinski (2006), are particularly lightweight protocols for evaluating a veto function in a peer-to-peer network such that anonymity of all protocol participants is preserved. Prior to this work, anonymity in all AV-nets from the literature relied on the decisional Diffie-Hellman (DDH) assumption and can thus be broken by (scalable) quantum computers. In order to defend against this threat, we propose two practical and completely lattice-based AV-nets. The first one is secure against passive and the second one is secure against active adversaries. We prove that anonymity of our AV-nets reduces to the ring learning with errors (RLWE) assumption. As such, our AV-nets are the first ones with post-quantum anonymity. We also provide performance benchmarks to demonstrate their practicality.

This paper studies Banach space valued Hausdorff-Young inequalities. The largest part considers ways of changing the underlying group. In particular the possibility to deduce the inequality for open subgroups as well as for quotient groups arising from compact subgroups is secured. A large body of results concerns the classical groups$T$^{$n$},$R$^{$n$}and$Z$_{$k$}. Notions of Fourier type are introduced and they are shown to be equivalent to properties expressed by finite groups alone.

We show that proving the conjectured sharp constant in a theorem of Dennis Sullivan concerning convex sets in hyperbolic 3-space would imply the Brennan conjecture. We also prove that any conformal map$f$:$D$→Ω can be factored as a$K$-quasiconformal self-map of the disk (with$K$independent of Ω) and a map$g$:$D$→Ω with derivative bounded away from zero. In particular, there is always a Lipschitz homeomorphism from any simply connected Ω (with its internal path metric) to the unit disk.