# Examples of extended trapdoor permutations

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.

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