Abstract: The invention presented describes the protection of transaction data in cash-free payment traffic from its creation to its processing by means of stock-exchange chip cards (4). In each payment transfer, transaction data TDi (10) is created on the individual payment procedure, and cumulative data SD (81) on the payment transactions since the last data exchange with the settlement position are summarized. The transaction data TDi is stored in the payment terminal. The cumulative data SD is stored in the security module. In each payment transaction, the cumulative data is supplemented by the new amount. The cumulative data is stored using a cumulative signature Ssn (82) which is applied to each supplement to the cumulative data. In this, the value of the previous cumulative signature is used as an initial value for the formation of the new cumulative signature. The key of the payment terminal or a separate individual key can be used. The cumulative signature is also stored in the security module.