Is giving my credit card,debit card and bank account information to paypal and ebay safe?

There are rumours about money theft by unauthorized persons from your debit cards,credit cards and bank accounts.I am plotting to do business online.Will it be safe to give my credit card, debit card and bank account number to paypal and ebay.

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Tags: bank account number, bank accounts, credit card debit, Credit Cards, debit cards, ebay, money, rumours, unauthorized persons