So, what do you mean by 'based under trust'?
Let me explain you a scenario we have used for Saman Bank. You go to the seller's website, select your favorite goods and click on the 'purchase' button, then you are redirected to the bank's site, there you have multiple choices of payment. One of these options is to enter your debit card's number, check digit, expiration date, and pin. If they are entered correctly the due amount is deduced from your account and you are redirected back to the seller's site with your transaction's result included. I think  it doesn't matter of what kind your card  is (debit or credit). I THINK IN NO CIRCUMSTANCES YOU MUST ASK FOR USER'S BANKING CREDENTIALS AT A SELLER'S SITE.