Extractors for binary elliptic curves

Reza Rezaeian Farashahi, Ruud Pellikaan, Andrey Sidorenko

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We propose a simple and efficient deterministic extractor for an ordinary elliptic curve E, defined over double-struck F sign2n, where n = 2ℓ and ℓ is a positive integer. Our extractor, for a given point P on E, outputs the first double-struck F sign2 -coefficient of the abscissa of the point P. We also propose a deterministic extractor for the main subgroup G of E, where E has minimal 2-torsion. We show that if a point P is chosen uniformly at random in G, the bits extracted from the point P are indistinguishable from a uniformly random bit-string of length ℓ.

Original languageEnglish
Pages (from-to)171-186
Number of pages16
JournalDesigns, Codes and Cryptography
Volume49
Issue number1-3
DOIs
Publication statusPublished - Dec 2008

Keywords

  • Deterministic extractor
  • Elliptic curve
  • Randomness

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    Farashahi, R. R., Pellikaan, R., & Sidorenko, A. (2008). Extractors for binary elliptic curves. Designs, Codes and Cryptography, 49(1-3), 171-186. https://doi.org/10.1007/s10623-008-9187-5