let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

We propose the signature scheme Hawk, a concrete instantiation of proposals to use Lattice Isomorphism Problem (LIP) as foundation for cryptography that focuses on simplicity. This simplicity stems from LIP, which allows lattices such $$\mathbb Z^n$$ , leading algorithms with no floats, rejection sampling, and compact precomputed distributions. Such design features are desirable constrained dev...