### Abstract

We propose a simple and efficient deterministic extractor for an ordinary elliptic curve E, defined over double-struck F sign_{2}^{n}, where n = 2ℓ and ℓ is a positive integer. Our extractor, for a given point P on E, outputs the first double-struck F sign_{2}^{ℓ} -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 language | English |
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Pages (from-to) | 171-186 |

Number of pages | 16 |

Journal | Designs, Codes and Cryptography |

Volume | 49 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Dec 2008 |

### Keywords

- Deterministic extractor
- Elliptic curve
- Randomness

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## Cite this

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