As far as I remember you have to install the certificate of twitter on your JVM.
First you should download the certificate of twitter. Use browser to go to twitter. Then it depends on your browser. For example in Chrome click on lock icon left to the https:...
, choose Connection tab, then click "Certificate information", choose "Details" tab and press "Export" button.
Once you have the certificate you should install it on your jvm using keytool
: http://docs.oracle.com/javaee/1.4/tutorial/doc/Security6.html
I hope this will help you.