A Resilient Convex Combination for consensus-based distributed algorithms
It addresses the problem of Byzantine resilience in distributed consensus algorithms, offering a computationally cheaper alternative for practitioners.
This paper proposes a method for achieving a resilient convex combination of normal vectors in the presence of malicious vectors, with lower computational complexity than existing Tverberg-based approaches. Simulations show its effectiveness for resilient consensus-based distributed algorithms against Byzantine attacks.
Consider a set of vectors in $\mathbb{R}^n$, partitioned into two classes: normal vectors and malicious vectors. The number of malicious vectors is bounded but their identities are unknown. The paper provides a way for achieving a resilient convex combination, which is a convex combination of only normal vectors. Compared with existing approaches based on Tverberg points, the proposed method based on the intersection of convex hulls has lower computational complexity. Simulations suggest that the proposed method can be applied to resilience for consensus-based distributed algorithms against Byzantine attacks.