  After attacking the RSA by injecting fault and corresponding countermeasures,
works appear now about the need for protecting RSA public elements against
fault attacks. We provide here an extension of a recent attack based on the
public modulus corruption. The difficulty to decompose the "Left-To-Right"
exponentiation into partial multiplications is overcome by modifying the public
modulus to a number with known factorization. This fault model is justified
here by a complete study of faulty prime numbers with a fixed size. The good
success rate of this attack combined with its practicability raises the
question of using faults for changing algebraic properties of finite field
based cryptosystems.
