Optimal Normal Bases Over Finite Fields
Duggirala Meher Krishna, and Duggirala Ravi
TL;DR
This paper presents a method for constructing near optimal normal bases in finite field extensions, enabling efficient multiplication with coefficients in smaller subfields, which improves algebraic computations.
Contribution
It introduces a novel construction method for near optimal normal bases with simplified multiplication properties in finite fields.
Findings
Product of two distinct basis elements can be expressed with smaller subfield coefficients.
The basis construction is applicable to all extensions except for squares of basis elements.
The method enhances computational efficiency in finite field arithmetic.
Abstract
In this paper, a method for constructing a near optimal normal basis for algebraic extensions of a finite field is described. In each extension, except for the squares of basis elements, the product of two distinct normal basis elements can be expressed as a linear combination of those two basis elements, with coefficients in a much smaller subfield.
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