# Tag Info

For completeness, here is how to compute $d$ without resorting to the value of public exponent $e$. Compute $\delta = \gcd(p-1,q-1)$; Define $p' = p-1$ and $q' = (q-1)/\delta$; Compute $i_{q'} = (q')^{-1} \bmod p'$ and $d_{q'} = d_q \bmod q'$; Return $d = d_{q'} + q'[i_{q'} (d_{p}-d_{q'}) \bmod p']$. Note that the so-obtained value for $d$ is defined ...