Security Analysis of Another Vulnerability to RSA Algorithm

After the famous public key cryptographic system RSA came out in 1978, countless related articles have been discussed in the past 40 years. Even if a new generation of cryptographic algorithms comes out one after another, it still cannot conceal the enthusiasm of many people for RSA research. The research on RSA can not only be approached from a mathematical perspective, but can also be explored from the computer field. This research intends to analyze the public key parameter
$\boldsymbol{e}$
and private key parameter
$\boldsymbol{d}$
of RSA. This research aims to discuss another vulnerability which parameter
$\boldsymbol{ed}\equiv \mathbf{1} ( \boldsymbol{mod}\ \boldsymbol{n})$
or
$\boldsymbol{ed}\equiv \mathbf{1} ( \boldsymbol{mod}\ \boldsymbol{\varphi}(\boldsymbol{n}))$
, this is our main purpose. The authors conducted a large number of experiments to prove their viewpoint based on experimental data, is research method used in this article. A weakness problem results from improper selection of parameters such as
$\boldsymbol{ed}\ \mathbf{mod}\ \boldsymbol{n}$
congruent
$\boldsymbol{ed\ mod}\ \boldsymbol{\varphi}(\boldsymbol{n})$
. We will deepen to understanding of RSA algorithm and more security issues by this study.