The invention relates to a method for calculating the modular inverses R of a value E in relation to a module M, wherein a breakdown of the module M is determined in at least two factors M1, M2, whereby each auxiliary value R1, R2 is calculated with respect to each of the factors M1, M2, whereby each auxiliary value R1, R2 is the modular inverse of the value E in relation to the respective factors M1, M2 as a module, and the modular inverse R is calculated at least by using the calculated auxiliary value R1, R2. A computer program product and a portable data carrier display corresponding characteristics. The invention also relates to an efficient method for modular inversion in terms of mechanical embodiment. Said method is especially suitable for use in cryptographic calculations on a portable data carrier.