Hashing into Hessian curves (Q486136)

Summary: We propose an encoding function from the elements of the finite field \(\mathbb F_q\) into points on a Hessian curve. Next, we present an injective encoding function from the set of all positive integers less than or equal to \(\ell\) into points on a Hessian curve over \(\mathbb F_q\) with odd \(q\) and \(\ell = (q - 1)/2\). We also present an injective encoding function from the bit strings of length \(k - 1\) into points on a Hessian curve over the binary finite field \(\mathbb F_{2^k}\).