Chip card reader, system and method of performing a pairing operation on an elliptic curve

The invention relates to a cryptographic method which is implemented by a secure calculation module. During the method, the secure module subcontracts a non-secure calculation module with greater physical resources to perform a pairing operation f on an elliptic curve, such as to produce a result S as a function of at least two points A, B of an elliptic curve, and subsequently the secure module verifies the accuracy of the result provided by the non-secure module. Points A, B can also be masked by one or more random numbers prior to transmission to the non-secure module. The invention can be used to perform operations involving the pairing of two points of an elliptic curve, inversions of integers or divisions of integers.