We prove a worst-case to average-case reduction for Hermite-SVP on ideal lattices by using random-walk techniques over the Arakelov class group. This group can be seen as the group of all ideal lattices associated to a fixed number field, up to isometry.
We rigorously prove and bound the complexity of (a variant of) the quantum algorithm solving the Continuous Hidden Subgroup Problem by Eisenträger et al.
We introduce and analyze a Meet-in-the-Middle (quantum) attack on the AJPS cryptosystem of Aggarwal et al., based on Mersenne numbers. Next to that we elaborately analyze another attack, proposed by Beunardeau et al., on the same cryptosystem.
We show that computations within the unit group of local fields leads to two new algorithms in number theory. One of them is an algorithm computing 'ibeta', an object characterizing local fields. The other one is an algorithm computing the power residue symbol.