k-Set agreement is a central problem of fault-tolerant distibuted computing. Considering a set of n processes, where up to t may commit failures, let us assume that each process proposes a value. The problem consists in defining an algorithm such that each non-faulty process decides a value, at most k dfferent values are decided, and the decided values satisfy some context-depending validity condition. Synchronous message-passing algorithms solving k-set agreement have been proposed for different failure models (mainly process crashes, and process Byzantine failures). Differently, k-set agreement cannot be solved in failure-prone asynchronous message-passing systems when t ≥ k. To circumvent this impossibility an asynchronous system must be enriched with additional computational power. Assuming t ≥ k, this paper presents a distributed algorithm that solves k-set agreement in an asynchronous message-passing system wher up to t processes may commit Byzantine failures. To that end, each process is enriched with randomization power. While randomized k-set agreement algorithms exist for the asynchronous process crash failure model where t ≥ k, to our knowledge the proposed algorithm is the first that solves k-set agreement in the presence of up to t ≥ k Byzantine processes. Interestingly, this algorithm is signature-free, and ensures that no value proposed only by Byzantine processes can be decided by a non-faulty process. Its design is based on a modular construction which rests on a "no-duplicity" one-to-all broadcast abstraction, and two all-to-all communication abstractions.