Geometric primality tests using genus 1 & 2 curves

Eduardo Ruíz Duarte

doi:10.48550/arXiv.1710.04887

Geometric primality tests using genus 1 & 2 curves

Eduardo Ruíz Duarte

Algebra

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We revisit and generalize some geometric techniques behind deterministic primality testing for some integer sequences using curves of genus 1 over finite rings. Subsequently we develop a similar primality test using the Jacobian of a genus 2 curve.

Originele taal-2	English
Uitgever	arXiv
DOI's	https://doi.org/10.48550/arXiv.1710.04887
Status	Submitted - 13-okt.-2017

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@techreport{c9e56196620e47c2bc98793a12ddf298,

title = "Geometric primality tests using genus 1 & 2 curves",

abstract = "We revisit and generalize some geometric techniques behind deterministic primality testing for some integer sequences using curves of genus 1 over finite rings. Subsequently we develop a similar primality test using the Jacobian of a genus 2 curve.",

keywords = "elliptic curves, hyperelliptic curves, primality tests",

author = "{Ru{\'i}z Duarte}, Eduardo",

year = "2017",

month = oct,

day = "13",

doi = "10.48550/arXiv.1710.04887",

language = "English",

publisher = "arXiv",

type = "WorkingPaper",

institution = "arXiv",

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T1 - Geometric primality tests using genus 1 & 2 curves

AU - Ruíz Duarte, Eduardo

PY - 2017/10/13

Y1 - 2017/10/13

N2 - We revisit and generalize some geometric techniques behind deterministic primality testing for some integer sequences using curves of genus 1 over finite rings. Subsequently we develop a similar primality test using the Jacobian of a genus 2 curve.

AB - We revisit and generalize some geometric techniques behind deterministic primality testing for some integer sequences using curves of genus 1 over finite rings. Subsequently we develop a similar primality test using the Jacobian of a genus 2 curve.

KW - elliptic curves

KW - hyperelliptic curves

KW - primality tests

U2 - 10.48550/arXiv.1710.04887

DO - 10.48550/arXiv.1710.04887

M3 - Preprint

BT - Geometric primality tests using genus 1 & 2 curves

PB - arXiv

ER -

Geometric primality tests using genus 1 & 2 curves

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