Threshold Signatures as-a-Service: Achieving Threshold ML-DSA in One Online Round

We formally define Threshold Signatures as-a-Service (TSaaS), in which the honest parties performing the threshold signature respond only to the signing requests of a designated client. This model captures the mainstream industrial use case of threshold signatures which is to implement Wallets as-a-Service. This new model allows for optimizations of existing threshold signature schemes, in particular in the lattice setting. As a particularly relevant case study, we describe a TSaaS variant of t