Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Extractors are an important ingredient in designing key exchange protocols and secure pseudorandom sequences in the standard model. Elliptic and hyperelliptic curves are gaining more and more interest due to their fast arithmetic and the fact that no subexponential attacks against the discrete logarithm problem are known.#R##N##R##N#  propose two simple and efficient deterministic extractors for $J(\mathbb{F}_q)$, the Jacobian of a genus 2 hyperelliptic curve  H defined over $\mathbb{F}_q$, where  q = 2 n , called the  sum and  product extractors.#R##N##R##N#For non-supersingular hyperelliptic curves having a Jacobian with group order 2 m , where  m is odd,  propose the modified  sum and  product extractors for the main subgroup of $J(\mathbb{F}_q)$.  show that, if $D\in J(\mathbb{F}_q)$ is chosen uniformly at random, the bits extracted from  D are indistinguishable from a uniformly random bit-string of length  n .
['Reza Rezaeian Farashahi']
I am writing a research paper on a idea Extractors for Jacobians of Binary Genus-2 Hyperelliptic Curves
[{"from": "human", "value": "I am writing a research paper on a idea Extractors for Jacobians of Binary Genus-2 Hyperelliptic Curves"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Extractors are an important ingredient in designing key exchange protocols and secure pseudorandom sequences in the standard model. Elliptic and hyperelliptic curves are gaining more and more interest due to their fast arithmetic and the fact that no subexponential attacks against the discrete logarithm problem are known.#R##N##R##N#  propose two simple and efficient deterministic extractors for $J(\\mathbb{F}_q)$, the Jacobian of a genus 2 hyperelliptic curve  H defined over $\\mathbb{F}_q$, where  q = 2 n , called the  sum and  product extractors.#R##N##R##N#For non-supersingular hyperelliptic curves having a Jacobian with group order 2 m , where  m is odd,  propose the modified  sum and  product extractors for the main subgroup of $J(\\mathbb{F}_q)$.  show that, if $D\\in J(\\mathbb{F}_q)$ is chosen uniformly at random, the bits extracted from  D are indistinguishable from a uniformly random bit-string of length  n ."}]