Constructing pseudo-random permutations with a prescribed structure
Pseudorandom permutations have been introduced by \textit{M. Luby} and \textit{C. Rackoff} [SIAM J. Comput. 17, 373-386 (1988; Zbl 0644.94018)] as a formalization of block ciphers. They also showed how to construct such families of permutations that are indistinguishable from a random permutation. Here in the article, a further step is taken that shows how to construct pseudo-random permutations that satisfy a certain cycle restriction. It should be noted, however, that the construction works only for a fixed cycle type, and it is an open question whether this restriction can be removed.
scientific article; zbMATH DE number 1761151