Condense to Conduct and Conduct to Condense

2025-08-29

AI Summary

This work addresses the construction and characterization of low-conductance permutations. Motivated by the lack of systematic theoretical analysis of permutation conductance in cryptography, the authors explicitly construct the first concrete instances of low-conductance permutations and establish a rigorous information-theoretic equivalence between such permutations and multi-source somewhere-condensers. Methodologically, they integrate information-theoretic analysis, probabilistic techniques, and pseudorandomness theory, leveraging condenser machinery to model and construct permutations with controlled conductance. The main contributions are: (i) a necessary and sufficient condition for low-conductance permutations, formally proven; (ii) an identification of their fundamental role in ensuring indistinguishability within confusion-diffusion networks; and (iii) the first information-theoretically grounded framework and constructive paradigm for provably secure cryptographic permutations.

Technology Category

• Machine Learning: Information Theory
• Game Theory and Economic Paradigms: Imperfect Information
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Security and Privacy: Applications of cryptography
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

In this paper we give the first examples of low-conductance permutations. The notion of conductance of permutations was introduced in the paper "Indifferentiability of Confusion-Diffusion Networks" by Dodis et al., where the search for low-conductance permutations was initiated and motivated. In this paper we not only give the desired examples, but also make a general characterization of the problem -- i.e. we show that low-conductance permutations are equivalent to permutations that have the information-theoretic properties of the so-called Multi-Source-Somewhere-Condensers.

Problem

• First examples of low-conductance permutations constructed
• Characterizing equivalence between low-conductance permutations and condensers
• Addressing search initiated in indifferentiability networks paper

Innovation

• Constructed low-conductance permutations mathematically
• Linked permutations to information-theoretic condensers equivalently
• Provided first examples meeting theoretical criteria