Explicit formula for optimal ate pairing over cyclotomic family of elliptic curves

Hoon Hong, Eunjeong Lee, Hyang Sook Lee

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Pairings on elliptic curves play an important role in cryptography. We provide an explicit formula for vectors of polynomials describing optimal ate pairings over cyclotomic family of elliptic curves. The explicit formula is simple in that it only involves partitioning a certain cyclotomic polynomial. The simplicity of the formula allows us to analyze the sparsity of the vector.

Original languageEnglish
Pages (from-to)45-74
Number of pages30
JournalFinite Fields and their Applications
Volume34
DOIs
StatePublished - Jul 2015

Keywords

  • Cyclotomic polynomial
  • Elliptic curve
  • Pairing-based cryptosystem

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