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The answer to this question at Crypto.SE is clear about what a trapdoor function is, but what makes a trapdoor function "injective"?

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1 ? – K.G. Sep 28 '13 at 20:17
@K.G. - From the link you posted above, an injective function is one that preserves distinctness. Following this, a injective trapdoor function must be a one-way function that is hard to invert (except when using secret key) and never maps elements of domain to the same element in the co-domain. is this correct? – user1068636 Sep 28 '13 at 20:27
"and never maps" different "elements of the domain to the same element in the co-domain". $\hspace{.77 in}$ – Ricky Demer Sep 28 '13 at 20:33
@RickyDemer - So if the trapdoor function was not injective we would have different elements mapping to the same elements in co-domain. What is the advantage of an injective trapdoor function ? Shouldn't we make it harder for an adversary to guess what an element of co-domain maps to in the domain? – user1068636 Sep 28 '13 at 20:36
up vote 4 down vote accepted

A trapdoor one-way injection is a trapdoor one-way function such that two different elements
of a single domain are never mapped to the same element of the corresponding codomain.
By Goldreich-Levin, if there exists an trapdoor one-way injection
then semantically secure public key encryption exists.

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