A Survey on Applications of H-Technique: Revisiting Security Analysis of PRP and PRF

Jha, Ashwin and Nandi, Mridul
(2022) A Survey on Applications of H-Technique: Revisiting Security Analysis of PRP and PRF.
Entropy, 24 (4). pp. 462-496. ISSN 1099-4300

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Official URL: https://www.mdpi.com/journal/entropy

Abstract

The Coefficients H Technique (also called H-technique), developed by Patarin in circa '91, is a tool to obtain upper bounds on distinguishing advantages. This tool is known to provide relatively simpler and (in some cases) tight bound proofs in comparison to some other well-known tools such as the Game-playing technique and Random Systems methodology. In this systematization of knowledge (SoK) paper, we aim to provide a brief survey on the H-technique. The SoK is in four parts: First, we redevelop the necessary nomenclatures and tools required to study the security of any symmetric key design, especially in the H-technique setting. Second, we give a full description of H-technique and some related tools. Third, we give (simple) H-technique based proofs for some popular symmetric-key designs, across different paradigms. Finally, we show that H-technique can actually provide optimal bounds on distinguishing advantage.

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