Right now Edge and Safari are the only two browsers that do not support WebCrypto properly. With the depreciation of <KeyGen> and ActiveX the this is even more important than before. You can see : http://pkijs.org/ as an example of how this can be used to enable many of the same scenarios without the need for plug-ins. This is a great site to see what support looks like in each browser - https://diafygi.github.io/webcrypto-examples/
It has been supported since IE 11. IE was actually one of the first browsers to implement it. The spec changed, and in Edge, the implementation was updated to the current spec.