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

2017/03/23 by Bernadette Faye, Faye, Bernadette
Computer Science · #Cryptography and Residue Arithmetic #Chaos-based Image/Signal Encryption #Coding theory and cryptography

paper · pdf · doi:10.48550/arxiv.1703.08151

Abstract

Here, we proposed an improved version of the deterministic random extractors SEJ and PEJ proposed by R. R. Farashahi in \citeF in 2009. By using the Mumford's representation of a reduced divisor D of the Jacobian J(\mathbbF_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 deterministic randomness extractors defined over \mathbbF_q where q=pⁿ, for some positive integer n≥ 1 and p an odd prime.

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