Abstract
It is a classical result that the addition law on the Jacobian of a hyperelliptic curve can be described in terms of explicit equations. Over the complex numbers, this can be done using theta function identities. Abstractly, the group law was written down by Cantor [1]. As observed by Koblitz [2], this makes it possible to use the set of points on the Jacobian of a hyperelliptic curve (or more succintly, a hyperelliptic Jacobian) over a finite field as the basis of a public-key cryptosystem.
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