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On randomness extraction in elliptic curves

A deterministic extractor for an elliptic curve, that converts a uniformly random point on the curve to a random $k$-bit-string with a distribution close to uniform, is an important tool in cryptography. Such extractors can be used for example in key derivation functions, in key exchange protocols and to design cryptographically secure pseudorandom number generator. In this paper, we present a simple and efficient deterministic extractor for an elliptic curve $E$ defined over $\mathbb{F}_{q^n}$, where $q$ is prime and $n$ is a positive integer. Our extractor, denoted by $\mathcal{D}_k$, for a given random point $P$ on $E$, outputs the $k$-first $\mathbb{F}_{q}$-coordinates of the abscissa of the point $P$. This extractor confirms the two conjectures stated by R. R. Farashahi and R. Pellikaan in \cite{qe} and by R. R. Farashahi, A. Sidorenko and R. Pellikaan in \cite{be}, related to the extraction of bits from coordinates of a point of an elliptic curve.

Auteur(s) : Ciss, Abdoul Aziz and Sow, Djiby
Pages : 290-297
Année de publication : 2011
Revue : Progress in cryptology—AFRICACRYPT 2011, Lecture Notes in Comput. Sci., 6737, Springer, Heidelberg,
N° de volume : 4
Type : Article
Mise en ligne par : SOW Djiby