Efficient Encodings to Hyperelliptic Curves over Finite Fields

Many cryptosystems are based on the difficulty of the discrete logarithm problem in finite groups. In this case elliptic and hyperelliptic cryptosystems are more noticed because they provide good security with smaller size keys. Since these systems were used for cryptography, it has been an important issue to transform a random value in finite field into a random point on an elliptic or hyperelliptic curve in a deterministic and efficient method. In this paper we propose a deterministic encoding to hyperelliptic curves over finite field. For cryptographic desires it is important to have an injective encoding. In finite fields with characteristic three we obtain an injective encoding for genus two hyperelliptic curves.