# Condense to Conduct and Conduct to Condense

## TL;DR

This paper introduces the first explicit examples of low-conductance permutations and characterizes them as permutations with properties similar to Multi-Source-Somewhere-Condensers, advancing understanding in this area.

## Contribution

It provides explicit examples of low-conductance permutations and a general characterization linking them to Multi-Source-Somewhere-Condensers, a novel theoretical insight.

## Key findings

- First explicit examples of low-conductance permutations
- Low-conductance permutations are equivalent to permutations with properties of Multi-Source-Somewhere-Condensers
- Provides a theoretical framework connecting conductance and information-theoretic properties

## 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.