Hawk: Module LIP Makes Lattice Signatures Fast, Compact and Simple

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 devices, when computing signatures inside FHE or MPC. The most significant change recent LIP is module lattices, reusing ideas NTRUSign Falcon. Its makes Hawk competitive. provide cryptanalysis experimental evidence implement two parameter sets, Hawk-512 Hawk-1024. Signing using Hawk-1024 four times faster than Falcon x86 architectures, produces about 15% more compact, slightly secure against forgeries by lattice reduction attacks. When floating-points unavailable, signs 15 worst case average LIP. For certain parametrisations this applies secret key recovery we reduce forgery in random oracle model new problem called one short vector problem.