Estimating the φ(n) of Upper/Lower Bound in its RSA Cryptosystem

The RSA-768 (270 decimal digits) was factored by Kleinjung et al. on December 12 2009, and the RSA-704 (212 decimal digits) was factored by Bai et al. on July 2, 2012. And the RSA-200 (663 bits) was factored by Bahr et al. on May 9, 2005. Until right now, there is no body successful to break the RSA210 (696 bits) currently. In this paper, we would discuss an estimation method to approach lower/upper bound of φ(n) in the RSA parameters. Our contribution may help researchers lock the φ(n) and the challenge RSA shortly.