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intelligence_src_e53adb99e40ae66258
observed · 2026-10-12 16:25:04 UTC
ePrint Report: Average-Case Hardness of Lattice Problems in Special Genera of Fixed Rank Koen de Boer, Maxime Bombar, Aurel Page, Wessel van Woerden The distinguishing variant $\Delta$LIP of the Lattice Isomorphism Problem underlies the security proofs of a growing family of lattice-based schemes. As the special genus is the strongest efficiently computable invariant of a lattice, such a proof may replace the lattice used by the scheme with a random lattice of the same genus. This raises the question of how hard lattice problems actually are on such random lattices. We answer it, under GRH, with a worst-case to average-case reduction inside any special genus $\mathcal{G}$ of Hermitian lattices of fixed rank $r \geq 2$ over a cyclotomic field $K$ of degree $d$: for each of $\mathrm{(H)SVP}$, $\mathrm{HCVP}$, $(\Delta)\mathrm{BDD}$, $\mathrm{DSP}$ and $\mathrm{DGS}$, solving the problem on a random class of $\mathcal{G}$, drawn from its natural distribution, is as hard as solving it on the worst-case lattice of $\mathcal{G}$, at the cost of a factor $p = \mathrm{poly}(d) \cdot {\det}_{\mathbb{Q}}(\Lambda)^{
Fingerprint: dfb4a3e624314201b6270700e9f32c1ad0c51b0b2e4fb11ac2215073e051607f
intelligence_src_e53adb99e40ae66258
observed · 2026-10-12 16:25:03 UTC
available
Fingerprint: 366cb966e32414edc1db353849a1ee8d6b8462b83786e04001881ba6594765ad