Efficient Encodings to Hyperelliptic Curves over Finite Fields‎

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