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The equivariant complexity of multiplication in finite field extensions

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Jean-Marc Couveignes, Tony Ezome

Number Theory · Submitted 26 Oct 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show how to control this complexity using the arithmetic and geometry of algebraic curves.

how it is stated · asserted 1.00 read the record →

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arXiv ID2110.13763 (version 2)
Pith IDRVX4DCR5, Pith's permanent record of this paper and its review
CitationJean-Marc Couveignes, Tony Ezome. "The equivariant complexity of multiplication in finite field extensions." arXiv:2110.13763 (2021). https://pith.science/paper/RVX4DCR5
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,207 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study the complexity of multiplication of two elements in a finite field extension given by their coordinates in a normal basis. background 0.60 0.57 0.05 asserted 0.65
s1 We show how to control this complexity using the arithmetic and geometry of algebraic curves. contribution 0.50 0.91 0.78 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.70 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original 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.

Human review

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How the literature uses it

1 arXiv paper cite this in 1 sentence

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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