Condense to Conduct and Conduct to Condense

Abstract

In this paper, we present the first explicit examples of low-conductance permutations. The notion of conductance of permutations was introduced by Dodis et al. in "Indifferentiability of Confusion-Diffusion Networks", where the search for low-conductance permutations was first initiated and motivated. As part of our contribution, we not only provide these examples, but also offer a general characterization of the problem: we show that low-conductance permutations are equivalent to permutations possessing the information-theoretic properties of Multi-Source-Somewhere-Condensers, a specific variant of somewhere condensers.