Safari and Smart Card access to websites

I need to access secure websites for work with my smart card. It worked before, but now it isn't and I am not sure what I need to change regarding settings . . . I am using Thursby and a smart card reader. I am suspicious of it having to do with the recent Java update, but I am not smart enough on this to know what is causing the issue. The message I get in Safari is "Safari can't open the page "https:// . .. . ." because Safari can't establish a secure connection to the server".

I have tried resetting Safari and I have made sure my software is up to date - not sure what I am missing.