PROTECTING MODULAR EXPONENTIATION IN CRYPTOGRAPHIC OPERATIONS

The present invention proposes a method for executing a blinded modular exponentiation, based on a window method with a window size of k bits so 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 Bi being a pseudo-random variable of the size of the modulus (n bits) and lower than the modulus (Yj=Yi×B1 mod N for i=0 to 2k-1) .executing the modular exponentiation with the 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.