var MyStore = new ActiveXObject("CAPICOM.Store");
var oCertificates = new ActiveXObject("CAPICOM.Certificates");
// attempt to open the personal certificate store
MyStore.Open(CAPICOM_CURRENT_USER_STORE, "My", CAPICOM_STORE_OPEN_READ_ONLY);
In general, currently is not possible due to lack of support of browsers to Java or silverlight.
Chrome has dropped support to NPAPI plugins. Firefox has announced it will discontinue it in 2017, Edge has no support. Microsoft has deprecated Silverlight and Oracle has also announced the deprecation of the Java browser plug-in. Only old versions of IE could be used.
Alternatives (Not very encouraging):