Abstract: There is disclosed a countermeasure using the properties of the Montgomery multiplication for securing cryptographic systems such as RSA and DSA against, in particular, safe-error injection attacks. In the proposed algorithm, the binary exponentiation b=ad mod n is iteratively calculated using the Montgomery multiplication when the current bit di of the exponent d is equal to zero. In that case, the Montgomery multiplication of the actual result of the exponentiation calculation by R is realized. Thanks to this countermeasure, if there is any perturbation of the fault injection type introduced during the computation, it will have visible effect on the final result which renders such attack inefficient to deduce the current bit di of the private key d.