Abstract: Provided is a method for securing against high-order side-channel attacks wherein a substep of field inversion is performed by a cryptographic device. The method includes computing (S1) a Dirac output value, adding (S2) said Dirac output value to one of said shares of the first set of shares to obtain a second set of shares, performing a conversion of the second set of shares (S3) from said (n+1) additive sharing to a (n+1)-multiplicative sharing, performing an inversion of each share of the (n+1)-multiplicative sharing (S4), performing a conversion of the inverted shares (S5) from said multiplicative sharing to a (n+1)-additive sharing to obtain a third set of shares, and adding (S6) said Dirac output value to one of said shares of the third set of shares. Other embodiments disclosed.