Protecting modular exponentiation in cryptographic operations

A method for protecting modular exponentiation in cryptographic operations executed by a processing unit, said modular exponentiations being based on a window method with a window size of k bits, using 2k pre-calculated variables (Yi=Xi mod N for i=0 to 2k−1), on input data X of n bits to obtain output data S of n bits, S=Xd mod N, where d is the exponent of size m bits and N is the modulus of n bits, comprising the steps of:

• blinding the pre-calculated variables by a blinding value B1 being a pseudo-random variable of the size of the modulus (n bits) and lower than the modulus (Yi=Yi×B1 mod N for i=0 to 2k−1)
• executing the modular exponentiation according to the window method which is based on the division of the exponent d into blocks of size of at most k bits representing a window, with the said blinded pre-calculated variables to obtain an intermediate result (A),
• unblinding the intermediate result by a unblinding value C1=(B1g)−1 mod N where g equals the concatenation of m/k times the value “1” coded on k bits, to obtain the output data S.