The Ring Learning with Errors (RLWE) problem is widely believed to be computationally hard and underpins many modern cryptographic constructions. Its security is supported by a reduction from worst-case problems on ideal lattices to average-case instances of RLWE.
We introduce ideal lattices arising from cyclotomic fields and explain the RLWE problem. We then explore methods to find mildly short vectors in ideal lattices, emphasizing the role of the plus and the minus class groups. We consider the growth of class numbers and Iwasawa $\lambda$-invariants. Then we discuss different parameter choices for RLWE that can influence the hardness of the underlying approximate shortest vector problem.
