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 decrypt key which plays the same role of the original trapdoor. To find this new decrypt key we must seek the maximum degree of ciphering function composition in a given modulus N. The 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 decrypt key by (e^d_max). Thanks to this new key, we can decrypt any cipher text for a given modulus. The interest of this cryptanalysis, contrary to factorization, is that the search of the decrypt key is independent from the modulus size.
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