Normal Bases using 1-dimensional Algebraic Groups
classification
🧮 math.AG
keywords
basesgroupnormaladditivealgebraicalgorithmsallowingarithmetic
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This paper surveys and illustrates geometric methods for constructing normal bases allowing efficient finite field arithmetic. These bases are constructed using the additive group, the multiplicative group and the Lucas torus. We describe algorithms with quasi-linear complexity to multiply two elements given in each one of the bases.
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