 As formula_58 and formula_59, it must be the case that formula_60 and thus formula_61 is a multiple root of formula_62.We conclude that the curve formula_63 has no singular points if and only if formula_62 has no multiple roots.Even though the definition of a hyperelliptic curve is quite easy when charformula_65, we should not forget about fields of characteristic 2 as hyperelliptic curve cryptography makes extensive use of such fields.