It is possible that find the $a, b, c$ randomly in here? $$ abc \equiv 1{\pmod {\varphi (N)}} $$

Instead of $$ de \equiv 1{\pmod {\varphi (N)}} $$

in the RSA Algorithm.


It is possible that find the a, b, c randomly in here? $abc \equiv 1{\pmod {\varphi (N)}} $

The most obvious way is to select $a, b$ randomly (relatively prime to $\phi(N)$), and then compute $c = (ab)^{-1} \bmod{ \phi(N) }$. It is easy to show that if $a, b$ are chosen uniformly and independently from $\mathbb{Z}_{N}^*$, then $c$ is also chosen uniformly.

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