$q$-ary Lattices
In this post, we discuss an important class of algebraic structures known as $q$-ary lattices that are central to lattice-based cryptographic primitives. Hardness of problems Computational hardness usually revolves around problems with worst-case hardness guarantees since we want to design algorithms that run efficiently even on the worst possible input. On the other hand, cryptographic schemes require security guarantees for random keys. Therefore, cryptographic applications require problems with average-case hardness guarantees....