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- W1496646054 abstract "This paper studies the task of two-sources randomness extractors for elliptic curves defined over finite fields $K$, where $K$ can be a prime or a binary field. In fact, we introduce new constructions of functions over elliptic curves which take in input two random points from two differents subgroups. In other words, for a ginven elliptic curve $E$ defined over a finite field $mathbb{F}_q$ and two random points $P in mathcal{P}$ and $Qin mathcal{Q}$, where $mathcal{P}$ and $mathcal{Q}$ are two subgroups of $E(mathbb{F}_q)$, our function extracts the least significant bits of the abscissa of the point $Poplus Q$ when $q$ is a large prime, and the $k$-first $mathbb{F}_p$ coefficients of the asbcissa of the point $Poplus Q$ when $q = p^n$, where $p$ is a prime greater than $5$. We show that the extracted bits are close to uniform. Our construction extends some interesting randomness extractors for elliptic curves, namely those defined in cite{op} and cite{ciss1,ciss2}, when $mathcal{P} = mathcal{Q}$. The proposed constructions can be used in any cryptographic schemes which require extraction of random bits from two sources over elliptic curves, namely in key exchange protole, design of strong pseudo-random number generators, etc." @default.
- W1496646054 created "2016-06-24" @default.
- W1496646054 creator A5031348130 @default.
- W1496646054 date "2014-03-12" @default.
- W1496646054 modified "2023-09-27" @default.
- W1496646054 title "Two-sources Randomness Extractors for Elliptic Curves" @default.
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