Application of automorphic forms to lattice problems (Q2154470)

The paper under review is motivated by the work of de Boer, Ducas, Pellet-Mary, and Wesolowski on self-reducibility of ideal-SVP via Arakelov random walks [\textit{D. Micciancio} (ed.) and \textit{T. Ristenpart} (ed.), Advances in cryptology -- CRYPTO 2020. 40th annual international cryptology conference, CRYPTO 2020. Proceedings. Part II. Cham: Springer. 243--273 (2020; Zbl 1498.94005)]. More preceisely, the authors show a worst-case to average-case reduction for ideal lattices and explain their approach how the steps are reproduced for module lattices of a fixed rank over some number field. Two major distinctions in their approach are that for higher rank module lattices, the notion of Arakelov divisors is replaced by adèles and Fourier analysis is substituted by the notion of automorphic forms. Note that subject to the Riemann hypothesis, the worst-case to average-case convergence is analyzed in terms of the Fourier series. Thereafter, the worst-case shortest vector problem is as hard as the averagecase shortest vector problem.