Finding points on curves over finite fields

Joachim Von Zur Gathen; Igor Shparlinski; Alistair Sinclair

doi:10.1137/S0097539799351018

Finding points on curves over finite fields

Joachim Von Zur Gathen^*, Igor Shparlinski, Alistair Sinclair

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

106 Downloads (Pure)

Abstract

We solve two computational problems concerning plane algebraic curves over finite fields: generating a uniformly random point, and finding all points deterministically in amortized polynomial time (over a prime field, for nonexceptional curves).

Original language	English
Pages (from-to)	1436-1448
Number of pages	13
Journal	SIAM Journal on Computing
Volume	32
Issue number	6
DOIs	https://doi.org/10.1137/S0097539799351018
Publication status	Published - Sept 2003

Bibliographical note

Copyright SIAM Publications. Article archived for private and non-commercial use with the permission of the author and according to publisher conditions. For further information see http://www.siam.org/.

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@article{54aa91a4bd0a454f9856b6eed2ad0df9,

title = "Finding points on curves over finite fields",

abstract = "We solve two computational problems concerning plane algebraic curves over finite fields: generating a uniformly random point, and finding all points deterministically in amortized polynomial time (over a prime field, for nonexceptional curves).",

author = "\{Von Zur Gathen\}, Joachim and Igor Shparlinski and Alistair Sinclair",

note = "Copyright SIAM Publications. Article archived for private and non-commercial use with the permission of the author and according to publisher conditions. For further information see http://www.siam.org/.",

year = "2003",

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doi = "10.1137/S0097539799351018",

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volume = "32",

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issn = "0097-5397",

publisher = "Society for Industrial and Applied Mathematics Publications",

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TY - JOUR

T1 - Finding points on curves over finite fields

AU - Von Zur Gathen, Joachim

AU - Shparlinski, Igor

AU - Sinclair, Alistair

N1 - Copyright SIAM Publications. Article archived for private and non-commercial use with the permission of the author and according to publisher conditions. For further information see http://www.siam.org/.

PY - 2003/9

Y1 - 2003/9

N2 - We solve two computational problems concerning plane algebraic curves over finite fields: generating a uniformly random point, and finding all points deterministically in amortized polynomial time (over a prime field, for nonexceptional curves).

AB - We solve two computational problems concerning plane algebraic curves over finite fields: generating a uniformly random point, and finding all points deterministically in amortized polynomial time (over a prime field, for nonexceptional curves).

UR - https://www.scopus.com/pages/publications/0942288265

U2 - 10.1137/S0097539799351018

DO - 10.1137/S0097539799351018

M3 - Article

AN - SCOPUS:0942288265

SN - 0097-5397

VL - 32

SP - 1436

EP - 1448

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

IS - 6

ER -

Finding points on curves over finite fields

Abstract

Bibliographical note

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