TY - JOUR

T1 - Extractors for binary elliptic curves

AU - Rezaeian Farashahi, R.

AU - Pellikaan, G.R.

AU - Sidorenko, A.

PY - 2008

Y1 - 2008

N2 - We propose a simple and efficient deterministic extractor for an ordinary elliptic curve E, defined over , where n = 2l and l is a positive integer. Our extractor, for a given point P on E, outputs the first -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.

AB - We propose a simple and efficient deterministic extractor for an ordinary elliptic curve E, defined over , where n = 2l and l is a positive integer. Our extractor, for a given point P on E, outputs the first -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.

U2 - 10.1007/s10623-008-9187-5

DO - 10.1007/s10623-008-9187-5

M3 - Article

VL - 49

SP - 171

EP - 186

JO - Designs, Codes and Cryptography

JF - Designs, Codes and Cryptography

SN - 0925-1022

IS - 1-3

ER -