When making a purchase over the Internet make sure that the order page URL starts with https:// and that there is a small padlock symbol like or in the bottom right hand corner of the browser window. This means that the data you enter on the page will be secure from any hackers and your credit/debit card information will not be in jeopardy.
One extra measure you can take when buying a diamond over the internet is to get the merchant to send your stone to an independent appraiser of your choice as discussed in section/article Getting an Appraisal. The appraiser ccan then make sure that the diamond matches its Laboratory Certificate. The appraiser will confirm the authenticity to you and then you can arrange payment to the merchant. Once payment is
confirmed, the appraiser can then send the diamond on to you.
You could also get an insurance appraisal done by that appraiser and kill two birds with one stone.