You may have seen your boot soles develop a white waxy film on them. First thing's first, don't panic. This is what's known as "wax bloom." Wax bloom can occur in many different rubber products and even, believe it or not, in chocolate! What is happening here is some of the wax (or in chocolate's case fat) used in the production of the rubber is rising to the surface. If you are interested in the science behind this phenomenon check out the scientific journal I've attached to this article.
For demonstration purposes look at this pair of rubber rain boots. The right boot has been cleaned
This bloom isn't harmful to the rubber, and is easily dealt with. In light amounts it can be cleaned pretty simply with a damp cloth. If you find that it persists a specialized clean like Mother's Back-to-Black
will make short work of it.