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I am interested in Extended Trapdoor Permutations (ETP). An Extended Trapdoor Permutation (ETP) is a collection of permutations $\{f_{\alpha}\}_{\alpha}$ along with four algorithms $I$ (index), $S$ (sample), $F$ (forward) and $F^{-1}$ (backward). A formal definition can be found in Goldreich's 'Foundation of Cryptography - Part 2' (Appendix C.1, There is also a brief description of them in Lindell's excellent Tutorial that can be found here (Section 4.3).

The RSA collection is a known ETP, what other instances of ETPs are known? References would be much appreciated.

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    $\begingroup$ Welcome to crypto.stackexchange - Can you include a definition of "Extended Trapdoor Permutation", or link to a work where the term is studied? $\endgroup$ – Ella Rose Jun 26 at 14:36

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