We propose two simple and efficient deterministic extractors for J(Fq), the Jacobian of a genus 2 hyperelliptic curve H defined over Fq, for some odd q. Our first extractor, SEJ, called sum extractor, for a given point D on J(Fq), outputs the sum of abscissas of rational points on H in the support of D, considering D as a reduced divisor. Similarly the second extractor, PEJ, called product extr...

Given two distributions over an n element set, we wish to check whether these distributions are statistically close by only sampling. We give a sublinear algorithm which uses O(n2/3ǫ−4 logn) independent samples from each distribution, runs in time linear in the sample size, makes no assumptions about the structure of the distributions, and distinguishes the cases when the distance between the d...

It is known that if a 2-universal hash function H is applied to elements of a block source (X1, . . . , XT ), where each item Xi has enough min-entropy conditioned on the previous items, then the output distribution (H,H(X1), . . . , H(XT )) will be “close” to the uniform distribution. We provide improved bounds on how much min-entropy per item is required for this to hold, both when we ask tha...