Decrypting the ciphertexts of RSA cryptosystem with ciphering function

The RSA is based on a trapdoor one-way function which is easy to compute but is most hard to revert without knowing the trapdoor. A cryptanalysis, presented in this paper, consists in finding a new decrypting key which plays the same role of the original trapdoor. To find this new decrypting key we must seek the composition maximum degree of the ciphering function in a given modulus N. This maximum degree (d_max) is obtained by applying the ciphering function to a restricted set of residues in the modulus N. We then define the new decrypting key by (e^d_max). Thanks to this new key, we can decrypt any ciphertext for a given modulus. The interest of this cryptanalysis, contrary to factorization, is that the search time of the decrypting key is independent from the modulus size.