A method for calculating the modular inverse of a value in relation to a module is used for cryptographic calculations on a portable data carrier. The method includes determining a breakdown of the module into at least two factors, calculating a respective auxiliary value for each of the factors, wherein each auxiliary value is the modular inverse of the value in relation to the respective factor as module, and calculating the modular inverse of the value in relation to the module using the calculated auxiliary values. The method offers an increase in efficiency, with greater efficiency obtained the stronger the computing outlay depends on the length of the module in the inversion method. The method is suitable for execution by relatively low-power processors, and security of the calculation against spying attacks is not impaired. If security requirements are high, combining the method with suitable measures against spying presents no problems.