According to an embodiment, a cryptographic processing device is described comprising a memory configured to store a first operand and a second operand and a cryptographic processor configured to determine, for cryptographically processing the data, the product of the first operand with the second operand by determining, for each result word index in a result word index range, a result data word for the result word index by accumulating products of sums of words of the first operand and the second operand and subtracting excess terms.