A Generalize Estimating the Ø(n) of Upper-Lower Bound to RSA Public Key Crytosystem

The RSA-768 (270 decimal digits) was factored by Kleinjung et al. on December 12, 2009, while the RSA-704 (212 decimal digits) was factored by Bai et al. on July 2, 2012. The RSA-200 (663 bits) was factored by Bahr et al. on May 9, 2005, while he RSA-210 (696 bits) was factored by Propper on September 26, 2013. In this paper the author will discuss an estimation method to approach the lower/upper bound of φ(n) to the RSA parameters. Our contribution may help researchers lock the (n) and the challenge RSA shortly.