The transaction method is for secure payment by credit cards or debit cards for goods or services with the use or mobile devices. The payment authorization center delivers a public portion of the authorization token to the service provider via the existing communication channels and the private portion of the authorization token is delivered to the mobile device via SMS or USSD or e-mail short message. The mobile device delivers the private authorization token to the service provider via a private local network based on bluetooth, infrared or other short radio frequency based technology. The credit card or debit card number is never revealed and a temporary card token replaces it.