Lattice-based cryptography began in 1996 from a seminal work by Ajtai who presented a family of one-way functions based on SIS problem. He showed that it is secure in an average case if the shortest vector problem $$\operatorname{SVP}_\gamma$$ (where $$\gamma = n^c$$ for some constant $$c > 0$$ is hard in a worst-case scenario.