Patent ID: 8265266

Claim:
Cryptographic method during which, in order to carry out a modular exponentiation of type C=A B1 mod N, where A is an operand comprising a message on which a cryptographic operation is being performed, B1 is a first exponent, N is a modulus, and C is a result, comprising the following steps: masking, by a cryptographic device, the operand A by a random number s, carrying out, by the cryptographic device, a modular exponentiation of the masked operand by the exponent B1, then demasking, by the cryptographic device, the result of the exponentiation, by removing a contribution from the random number s from the result of the exponentiation, to thereby obtain a signed, encrypted or decrypted version of said message, wherein during the step of masking the operand A, the operand A is multiplied by a parameter in the form K s.B2 , where K is a constant and B2 is a second exponent such that B1.B2=1 mod φ(N).