International Association
for Cryptologic Research

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 RSA-210 (696 bits) currently. In this paper, we would discuss an estimation method to approach lower/upper bound of $\\phi(n)$ in the RSA parameters. Our contribution may help researchers lock the $\\phi(n)$ and the challenge RSA shortly.