Approx-SVP in multiquadratic ideal lattices

Multiquadratic fields are exceptional objects in computational number theory. Many hard computational problems are significantly simpler there. This includes unit/class group and discrete logarithm computations, as well as computing short generators of principal ideals. However, there are still many open questions in the area. In this talk, I describe recent progress towards the next milestone -- the approximate shortest vector problem in non-principal ideal lattices. In particular, I present an algorithm for a central subroutine -- the discrete logarithm computation based on reduction of the problem to subfields