Definition:Trapdoor Function

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A trapdoor function is a mapping $f$ which is:

for a given $x$ in the domain of $f$ is easy to calculate
for a given $y$ in the image of $f$ is hard to calculate unless a specific piece of information $t$ is supplied, in which case it is easy.

That piece of information is known as the trapdoor.

Historical Note

The concept of a trapdoor function was invented by Whitfield Diffie and Martin Hellman in $1975$.