Automorphisms and isogeny graphs of abelian varieties, with applications to the superspecial Richelot isogeny graph

We investigate special structures due to automorphisms in isogeny graphs of principally polarized abelian varieties, and surfaces particular. give theoretical experimental results on the spectral statistical properties ( 2 , stretchy="false">) (2,2) -isogeny superspecial surfaces, including stationary distributions for random walks, bounds eigenvalues diameters, a proof connectivity Jacobian subgraph graph. Our improve our understanding performance security some recently-proposed cryptosystems, are also concrete step towards better general arbitrary dimension.