My tutor had some knowledge and experience regarding the credit card security issue. She is one of my EC tutor and she teaches in many countries like Hong Kong or Singapore. Last time she explained to us how online payment works. She said after you enter your credit card details and submit them to the shopping website, they will go to the third party, which is an creditable organisation that certify your credibility. After it approves your account, your details (but not your credit card number) will send to the shopping website. That means your credit card number will not be stored in its database, which is quite safe.
However, she never uses credit card in restaurant. Why? It's because some restaurants just copy your credit card details, and then throw away after they use it. The problem is maybe a guy will pick the paper in the bin and you'll never know your credit card number has been stolen.
Actually I don't have a credit card (I'm just a student), and I don't know how Taiwanese websites transate your details. I hope this might help you guys
Sorry for my bad English