Abstract In 2015, Mikhalkin introduced a refined count for the real rational curves in toric surface which pass through set consisting of points and pairs complex conjugated chosen generically on boundary surface. He then proved that result this depends only number each divisor. Using tropical geometry approach correspondence theorem, we address computation when are purely imaginary belonging t...

In 1989, Koblitz [3] first proposed the Jacobian of a conventional (imaginary) hyperelliptic curve for use in public-key cryptographic protocols. Hyperelliptic curves are in a sense generalizations of elliptic curves. The Jacobian is a finite abelian group which, like elliptic curve groups, has unique representatives of group elements and efficient arithmetic (divisor addition and reduction). A...