In security proofs of lattice based cryptography, to bound the closeness of two probability
distributions is an important procedure. To measure the closeness, the Rényi divergence
has been used instead of the classical statistical distance. Recent results have shown that
the Rényi divergence offers security reductions with better parameters, eg smaller deviations
for discrete Gaussian distributions. However, since previous analyses used a fixed order
Rényi divergence, ie, order two, they lost tightness of reductions. To overcome the …

… • In the security reduction of lattice cryptography, the closeness of two probability
distributions should be measured. To bound the closeness via the Rényi divergence, we
adaptively optimize the order. • Applications of our approach are – Sampling discrete
Gaussian over the integers with smaller precomputed tables – Tighter LWE to k-LWE
reduction – Tighter SIS to k-SIS reduction …