Fast scalar multiplication of degenerate divisors for hyperelliptic curve cryptosystems
Abstract Scalar multiplication is the main operation in the implementation of hyperelliptic curve cryptosystems, where the basic arithmetic of reduced divisor classes is required. In this work, some explicit formulas are proposed for the arithmetic of reduced divisor classes by exploiting Jacobian coordinates when the degenerate divisor is involved. Moreover, an efficiency analysis shows that the degenerate divisor as a base element can be a valid alternative in hyperelliptic curve cryptosystems as well.