An academic analysis of the mathematical breakthroughs required to construct efficient threshold signature schemes from the Learning with Errors problem.
While threshold schemes for discrete-log algorithms (like Shamir's Secret Sharing on ECDSA) are mathematically straightforward because group operations are linear, lattice-based signatures involve discrete Gaussian rejection sampling and centered binomial noise distributions, which do not distribute linearly across multiple participants.
We review state-of-the-art protocols from leading cryptographers that resolve the noise accumulation challenge: utilizing distributed rejection sampling and homomorphic secret sharing to construct efficient t-of-n ML-DSA signatures with minimal communication rounds.
Empirical measurements of communication overhead, round complexity, and computational latency across distributed nodes separated by global internet latencies.