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The fastest way to solve your problem instance is as outlined in the above comments. First choose yourself a random message $m$ with $1<m<n$. Now compute $c\equiv m^d \pmod n$. Try if any of the following equations holds, if an equation does hold you've found the public exponent $e$. $m \equiv c^3 \pmod n$ $m \equiv c^{17} \pmod n$ $m \equiv ...


The first (and hardest) step is to factor $n$; the easiest way to do this (given $e$ and $d$) is with this randomized procedure: Select a random value $z$ from the range $(2, n-2)$ Compute the value $\lambda = (ed-1)/2^k$, where $k$ is that integer that makes $\lambda$ an odd integer. Compute $t = z^\lambda \bmod n$. If $t = 1$ or $t = n-1$, we fail on ...

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