Security considerations for Galois non-dual RLWE families
This work addresses security vulnerabilities in lattice-based cryptography, particularly for cryptosystems relying on Ring-LWE, but it is incremental as it builds on existing attacks and theoretical results.
The paper investigates the hardness of the non-dual Ring-LWE problem for different number rings, presenting improved attacks for specific rings and identifying a new vulnerable family, while using Gauss sums to suggest these attacks likely fail for 2-power cyclotomic rings with unramified moduli.
We explore further the hardness of the non-dual discrete variant of the Ring-LWE problem for various number rings, give improved attacks for certain rings satisfying some additional assumptions, construct a new family of vulnerable Galois number fields, and apply some number theoretic results on Gauss sums to deduce the likely failure of these attacks for 2-power cyclotomic rings and unramified moduli.