Efficient Clebsch–Gordan transforms for permutations

Develop an efficient Clebsch–Gordan transform for permutations, as required to establish the efficiency of the cited quantum random-permutation simulation procedures.

Background

The paper explains that the efficiency of the cited ideal-cipher simulation procedures reduces to the efficiency of Clebsch–Gordan transforms for permutation representations. It identifies this computational problem as unresolved, making it a technical open problem underlying efficient quantum ideal-cipher simulation.