Properties of the Euler Totient Function Modulo 24 and Some of its Cryptographic Implications

The work reported in this paper is directed towards the mathematical proof of the existence of a consistent structure for the Euler totient function ?(n) given n. This structure is extremely simple and follows from the exploitation of some of the very interesting properties relating to the integer 24 as demonstrated in the proofs. This result is of particular concern to cryptologists who are either attempting to break the RSA or ascertain its cryptographic viability. Furthermore, it is stipulated that the methods and properties relating to the integer 24, taken as a modulo, may have strong implications on the different attempts to solve the factorisation problem.