We present families of (hyper)elliptic curve which admit an efficient deterministic encoding function.
Compared to Icart's formulae @cite_0 , this encoding has two drawbacks of limited practical impact: [itemsep=0pt,parsep=0pt,partopsep=0pt,topsep=0pt] it does not work for any elliptic curves, but only for Hessian curves; the subset of the curve which can be parameterized is slightly smaller than in Icart's case: we get @math points against approximately @math .
@cite_0
2131559681
We describe a new explicit function that given an elliptic curve E defined over @math , maps elements of @math into E in deterministic polynomial time and in a constant number of operations over @math . The function requires to compute a cube root. As an application we show how to hash deterministically into an elliptic curve.