SSL on SharePoint

I am facing some problems on SharePoint. I've got a SharePoint site (let's say HTTP : //intranet.domain.be) We wanted to use this intranet from outside. So we decided to set an Extranet (HTTPS : //intranet.domain.be) To do so, we installed a SSL certificate. Everything is going well but one thing. on HTTP, i can check out, open, edit a document like a word document. on HTTPS, i try to open the same file but when i do so, a pop up appears and ask to select a certificate. None of them doesn't allow me to open the file :s Does Anyone have any idea what's going on? I checked the SSL implementation, the SP config, but everything seems to be ok... Let me know if you have an idea.