On the non-idealness of cyclotomic families of pairing-friendly elliptic curves

Min Sha*

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

Let k D 2mpn for an odd prime p and integers m0 and n0. We obtain lower bounds for the values of cyclotomic families of pairing-friendly elliptic curves with embedding degree k and r.x/D k.x/. Our bounds imply that none of the families are ideal.

Original languageEnglish
Pages (from-to)417-440
Number of pages24
JournalJournal of Mathematical Cryptology
Volume8
Issue number4
DOIs
Publication statusPublished - 1 Dec 2014
Externally publishedYes

Keywords

  • Cyclotomic family
  • Cyclotomic polynomial
  • Ideal family
  • Pairing-friendly elliptic curve

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