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Everything about Normal basis
Mathematical theorem used in cryptography
In mathematics, specifically the algebraic theory of fields, a normal basis is a special kind of basis for Galois extensions of finite degree, characterised as forming a single orbit for the Galois group. The normal basis theorem states that any finite Galois extension of fields has a normal basis. In algebraic number theory, the study of the more refined question of the existence of a normal integral basis is part of Galois module theory. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Normal basisA 5-minute orientation
- Skim a recent paper: Molecular basis of normal and pathological puberty: from basic mechanisms to clinical implicationsInfluential work since 2022
- Pick up a classic book: Finite fieldsThe most-reprinted book on the subject
- Read the landmark paper: An efficient optimal normal basis type II multiplierCited 98 times
- Go sideways: Hilbert's Theorem 90A closely related topic
- Go sideways: Primitive element theoremA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
An efficient optimal normal basis type II multiplier
THE PRIMITIVE NORMAL BASIS THEOREM – WITHOUT A COMPUTER
Low complexity word-level sequential normal basis multipliers
Normal and pathological breast, the histological basis
The strong primitive normal basis theorem
On orders of optimal normal basis generators
Fast normal basis multiplication using general purpose processors
Variations of the Primitive Normal Basis Theorem
🆕 Influential since 2022
Molecular basis of normal and pathological puberty: from basic mechanisms to clinical implications
A spatial imaging-transcriptomics paradigm for deciphering the molecular basis of microscopic MRI in the normal brain and Alzheimer’s disease
Normal statistical fracture analysis of Roller-compacted concrete on the basis of non-linear elastic fracture mechanics
Allometry in limb regeneration and scale-invariant patterning as the basis of normal morphogenesis from different sizes of blastemas
How far is an extension of p-adic fields from having a normal integral basis?
đź“š Books worth reading
Finite fieldsDirk Hachenberger · 1997
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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