Comparison of scalar multiplication on real hyperelliptic curves
Michael J. Jacobson, Monireh Rezai Rad, Renate Scheidler · Advances in Mathematics of Communications · 2014
Real hyperelliptic curves admit two structures suitable forcryptography --- the Jacobian (a finite abelian group) and theinfrastructure. Mireles Morales described precisely the relationshipbetween these two structures, and made the assertion that whenimplemented with balanced divisor arithmetic, the Jacobian genericallyyields more efficient arithmetic than the infrastructure forcryptographic applications. We confirm that this assertion holds forgenus two curves, through rigorous analysis and the first detailednumerical performance comparisons, showing that cryptographic keyagreement can be performed in the Jacobian without any extraoperations beyond those required for basic scalar multiplication. Wealso present a modified version of Mireles Morales' map that moreclearly reveals the algorithmic relationship between the twostructures.