Effective generalized equations of secure hyperelliptic curve digital signature algorithms

A hyperelliptic curve digital signature algorithm (HECDSA) can be viewed as the hyperelliptic curve analogue of the standard digital signature algorithm (DSA). This article discusses divisor evaluations, the basic HECDSA, variants, two HECDSA equations and a 4-tuple HECDSA scheme, and puts forward a generalized equation for HECDSA. From this generalized equation, seven general HECDSA types are derived based on the efficiency requirements. Meanwhile, the securities of these general HECDSA types are analyzed in detail.