A trapdoor one-way function is a one-way function with an additional requirement. Informally, a one-way function might be described as a function for which evaluation in one direction is straightforward, while computation in the reverse direction is far more difficult. Such a function becomes a trapdoor one-way function when we add the requirement that computation in the reverse direction becomes straightforward when some additional (trapdoor) information is revealed [3].
While there are alternative descriptions [2] we might describe a trapdoor one-way function as a function f with domain X and range (codomain) Y where f (x) is ‘easy’ to compute for all \(x \in X\) but for ‘virtually all’ elements \(y \in Y\) it is ‘computationally infeasible’ to find an x such that f(x) = y. Yet, given certain trapdoor information z, it is easy to describe an ‘efficient’ function g z with domain Y and range X such that g z (y) = x and f(x) = y. Just as a bijective one-way functionwith identical...
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Robshaw, M. (2005). Trapdoor One-Way Function. In: van Tilborg, H.C.A. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA . https://doi.org/10.1007/0-387-23483-7_436
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