A Torus-Structured Generalisation of NTRU: the NTC Assumption, its Cryptanalysis, and a Compact KEM

We introduce Noisy Torus Conjugation (NTC), a lattice assumption in which a short secret is confined to a non-split maximal torus of $GL_k(R_q)$ and acts by conjugation on a uniform matrix, the result being masked by a short additive error. NTRU is the $k=1$ member of the family.