Flood and Submerse: Distributed Key Generation and Robust Threshold Signature from Lattices

We propose a new framework based on random submersions-that is projection over a random subspace blinded by a small Gaussian noise-for constructing verifiable short secret sharing and showcase it to construct efficient threshold lattice-based signatures in the hash-and-sign paradigm, when based on noise flooding. This is, to our knowledge, the first hash-and-sign lattice-based threshold signature. Our threshold signature enjoys the very desirable property of robustness, including at key generation. In practice, we are able to construct a robust hash-and-sign threshold signature for threshold and provide a typical parameter set for threshold T " 16 and signature size 13kB. Our constructions are provably secure under standard MLWE assumption in the ROM and only require basic primitives as building blocks. In particular, we do not rely on FHE-type schemes.