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

The Coefficients H technique (also called the H-technique), developed by Patarin circa 1991, is a tool used to obtain the upper bounds on distinguishing advantages. This tool is known to provide relatively simple 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 presented in four parts. First, we redevelop the necessary nomenclature and tools required to study the security of any symmetric-key design, especially in the H-technique setting. Second, we provide a full description of the H-technique and some related tools. Third, we present (simple) H-technique-based proofs for some popular symmetric-key designs, across different paradigms. Finally, we show that the H-technique can actually provide optimal bounds on distinguishing advantages.