Quantum Algorithms for Variants of Average-Case Lattice Problems via Filtering

We show polynomial-time quantum algorithms for the following problems: The SIS, LWE, and EDCP problems in their standard forms are as hard solving lattice worst case. However, variants that we can solve not parameter regimes known to be worst-case problems. Still, no classical or were of SIS LWE consider. For EDCP, our algorithm slightly extends result Ivanyos et al. (2018). Our use existing reductions from those more precisely, problem given LWE-like states. main contribution is states with interesting parameters using a filtering technique.