Abstract
AbstractIn this paper we propose a very simple and efficient encoding function from \(\mathbb{F}q\) to points of a hyperelliptic curve over \(\mathbb{F}q\) of the form \(H\colon y^2=f(x)\) where f is an odd polynomial. Hyperelliptic curves of this type have been frequently considered in the literature to obtain Jacobians of good order and pairing-friendly curves.Our new encoding is nearly a bijection to the set of \(\mathbb{F}q\)-rational points on H. This makes it easy to construct well-behaved hash functions to the Jacobian J of H, as well as injective maps to \(J(\mathbb{F}q)\) which can be used to encode scalars for such applications as ElGamal encryption.The new encoding is already interesting in the genus 1 case, where it provides a well-behaved encoding to Joux’s supersingular elliptic curves.KeywordsHyperelliptic Curve CryptographyDeterministic EncodingHashing
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