Low-cost addition-subtraction sequences for the final exponentiation in pairings

Juan E. Guzmán-Trampe, Nareli Cruz-Cortés, Luis J. Dominguez Perez, Daniel Ortiz-Arroyo, Francisco Rodríguez-Henríquez

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

In this paper, we address the problem of finding low cost addition-subtraction sequences for situations where a doubling step is significantly cheaper than a non-doubling one. One application of this setting appears in the computation of the final exponentiation step of the reduced Tate pairing defined on ordinary elliptic curves. In particular, we report efficient addition-subtraction sequences for the Kachisa-Schaefer-Scott family of pairing-friendly elliptic curves, whose parameters involve computing the ulti-exponentiation of relatively large sequences of exponents with a size of up to 26 bits.

Original languageEnglish
Pages (from-to)1-17
Number of pages17
JournalFinite Fields and their Applications
Volume29
DOIs
StatePublished - Sep 2014

Keywords

  • Addition-subtraction sequences
  • Final exponentiation
  • Pairings

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