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

Abstract. Here, we proposed an improved version of the deterministic random extractors SEJ and PEJ proposed by R. R. Farashahi in [5] in 2009. By using the Mumford’s representation of a reduced divisor D of the Jacobian J(Fq) 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 deterministic randomness extractors defined over Fq where q = p , for some positive integer n ≥ 1 and p an odd prime.