The equivariant complexity of multiplication in finite field extensions
Jean-Marc Couveignes, Tony Ezome
TL;DR
This paper investigates the complexity of multiplying elements in finite field extensions using normal bases, leveraging algebraic curves' properties to analyze and potentially optimize the process.
Contribution
It introduces a novel approach connecting algebraic curve geometry with the complexity analysis of finite field multiplication in normal bases.
Findings
Complexity bounds derived from algebraic curve properties.
Method to control multiplication complexity via geometric techniques.
Potential for optimized algorithms in finite field arithmetic.
Abstract
We study the complexity of multiplication of two elements in a finite field extension given by their coordinates in a normal basis. We show how to control this complexity using the arithmetic and geometry of algebraic curves.
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