Hashing into Hessian curves

We propose an encoding function from the elements of the finite field Fq 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 l into points on a Hessian curve over Fq with odd q and l = (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 F2k.