Compact representation of domain parameters of hyperelliptic curve cryptosystems

Abstract

To achieve the same level of security, hyperelliptic curve cryptosystems (HCC) use a smaller field than elliptic curve cryptosystems (ECC). HCC has a more potential application to the product that has limited memory and computing power, for instance Smart cards. We discussed how to represent. the domain parameters of HCC in a compact way. The domain parameters include the field over which the curve is defined, the curve itself, the order of the Jocobian and the base point. In our method, the representation of HCC with genus g=4 over F-241 (It can provide the same level of security with 164 bits ECC) only uses 339 bits.