A trapdoor function is a function that is easy to perform one way, but has a secret that is required to perform the inverse calculation efficiently.

A trapdoor function is a function that is easy to perform one way, but has a secret that is required to perform the inverse calculation efficiently.

That is, if $f$ is a trapdoor function, then $y = f(x)$ is easy to compute, but $x = f^{-1}(y)$ is hard to compute without some special knowledge $k$. Given $k$, then it is easy to compute $y = f^{-1}(x, k)$.

The related Wikipedia article also contains a straight-forward explanation.

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