Multi-party random number generation (MP-RNG) is fundamental to distributed systems, enabling fair leader election, Byzantine consensus, and secure protocols. We present a novel MP-RNG algorithm exploiting a previously unexplored connection: the fractional part of a consensus-computed average yields uniform randomness. This connection enables distributed randomness through a simple modular arithmetic operation. Our key insight is that taking the fractional part of the consensus value preserves uniformity even when Byzantine agents inject arbitrary non-uniform values, chosen independently of the honest agents’ samples. We prove that uniformity is maintained with fI<n non-uniform initial values and, under a standard hypothesis-testing fault model, with up to fB<n/2 Byzantine faults. We introduce a precision parameter to ensure finite-time convergence. We integrate network augmentation techniques to provide information-theoretic privacy against passive adversaries without cryptography, preventing agents from learning each other’s random inputs. The resulting protocol offers Byzantine resilience and privacy comparable to cryptographic methods while avoiding their computational overhead. The core fractional-part mechanism scales to arbitrary network sizes; when combined with hypothesis-testing for Byzantine resilience, the method is best suited for small-to-medium networks, though alternative Byzantine-resilient consensus algorithms can be substituted for larger deployments. We demonstrate the algorithm’s effectiveness through theoretical analysis and numerical simulations.
We address the problem of safety control for nonlinear systems with input delay within the framework of Control Barrier Functions. In contrast to what is already reported in the literature, we approach the problem under the observer-predictor scheme, which avoids the implementation of distributed terms in the controller. We lay the foundations for guaranteeing the safety of the closed-loop system when there are perturbations and the delay is known. The presented results are illustrated and discussed by numerical simulations.
