Secure generation of an RSA signature of a message to be signed with a private exponent component d of an RSA key (p, q, N, d, e), by obtaining a hashed message, said hashed message being computed by hashing said message with a public hash function H:{0,1}*→Z*N, generating a first part of the RSA signature from said hashed message and said first private exponent component share, generating a second part of the RSA signature from said first part of the RSA signature and said second private exponent component share, determining the RSA signature from said second part of the RSA signature, and wherein the step of generation of a part of the RSA signature from the smaller private exponent component share among the first and second private exponent component shares is performed using a whitebox protection method and the step of generation of a part of the RSA signature from the bigger private exponent component share among the first and second private exponent component shares is performed using lower security requirements.