Paper 2020/1007

Attacks on Integer-RLWE

Alessandro Budroni, Benjamin Chetioui, and Ermes Franch

Abstract

In 2019, Gu Chunsheng introduced Integer-RLWE, a variant of RLWE devoid of some of its efficiency flaws. Most notably, he proposes a setting where $n$ can be an arbitrary positive integer, contrarily to the typical construction $n = 2^k$. In this paper, we analyze the new problem and implement the classical meet-in-the-middle and lattice-based attacks. We then use the peculiarity of the construction of $n$ to build an improved lattice-based attack in cases where $n$ is composite with an odd divisor. For example, for parameters $n = 2000$ and $q = 2^{33}$, we reduce the estimated complexity of the attack from $2^{288}$ to $2^{164}$. We also present reproducible experiments confirming our theoretical results.