1. A hyperelliptic curve cryptography method comprising: a base-point generation step of generating, with a cryptographic processing unit communicatively coupled to a computer recording medium, a first divisor having a weight g 0 .smaller than a genus g of a hyperelliptic curve to serve as a base point where 1≦g 0 .<g; a computation-processing step of performing, with said cryptographic processing unit, scalar multiplication processing of divisors including said first divisor, wherein addition processing of said scalar multiplication processing comprises adding a second divisor with a weight of g to a third divisor with a weight smaller than g; and a cryptographic processing step comprising at least one of signature processing, generation of encrypted data, decryption processing, processing to share a cryptography key and authentication processing.