Consider an asynchronous network in a shared-memory environment consisting of n nodes. Assume that up to f of the nodes might be Byzantine (n > 12f), where the adversary is full-information and dynamic (sometimes called adaptive). In addition, the non-Byzantine nodes may undergo transient failures. Nodes advance in atomic steps, which consist of reading all registers, performing some calculation and writing to all registers. This paper contains three main contributions. First, the clock-function problem is defined, which is a generalization of the clock synchronization problem. This generalization encapsulates previous clock synchronization problem definitions while extending them to the current paper's model. Second, a randomized asynchronous self-stabilizing Byzantine tolerant clock synchronization algorithm is presented. In the construction of the clock synchronization algorithm, a building block that ensures different nodes advance at similar rates is developed. This feature is the third contribution of the paper. It is self-stabilizing and Byzantine tolerant and can be used as a building block for different algorithms that operate in an asynchronous self-stabilizing Byzantine model. The convergence time of the presented algorithm is exponential. Observe that in the asynchronous setting the best known full-information dynamic Byzantine agreement also has expected exponential convergence time, even though currently there is no known reduction between the two.