Extracting a uniform random bit-string over Jacobian of Hyperelliptic curves of Genus 2 [article]

Bernadette Faye
<span title="2017-03-23">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Here, we proposed an improved version of the deterministic random extractors SEJ and PEJ proposed by R. R. Farashahi in F in 2009. By using the Mumford's representation of a reduced divisor D of the Jacobian J(F_q) of a hyperelliptic curve H of genus 2 with odd characteristic, we extract a perfectly random bit string of the sum of abscissas of rational points on H in the support of D. By this new approach, we reduce in an elementary way the upper bound of the statistical distance of the
more &raquo; ... istic randomness extractors defined over F_q where q=p^n, for some positive integer n≥ 1 and p an odd prime.
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