SoK: Efficient Design and Implementation of Polynomial Hash Functions over Prime Fields

Jean Paul Degabriele, Jan Gilcher, Jérôme Govinden, Kenneth G. Paterson

IEEE Symposium on Security and Privacy 2024 · Day 2 · Continental Ballroom 6

This talk, presented by Jérôme Govinden and Jan Gilcher, delves into a comprehensive Systematization of Knowledge (SoK) regarding the design and implementation of polynomial hash functions over prime fields. The core objective of their research is to systematically explore the vast design space for these cryptographic primitives, aiming to create new, more efficient, and secure alternatives to established functions like **Poly1305**. The work highlights the apparent disconnect between existing designs, often optimized for older hardware paradigms, and the capabilities of modern computing architectures.

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This Systematization of Knowledge (SoK) is a critical, overdue re-evaluation of polynomial hash functions. It systematically dissects Poly1305's flaws and introduces novel, empirically validated designs that offer superior security-performance tradeoffs for modern 64-bit architectures. This isn't just theory; it's a clear roadmap for the next generation of cryptographic primitives.

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