Aspects of Pairing Based Cryptography on Jacobians of Genus Two Curves

By Christian Robenhagen Ravnshøj
PhD Dissertations
October 2008

The thesis concerns properties of Jacobians of genus two curves defined over a finite field. Such Jacobians have a wide range of applications in data security; e.g. netbanking and digital signature.

New properties of the Jacobians are proved; here, a description of the embedding of $\ell$-torsion points on the Jacobian and the matrix representation of the Frobenius endomorphism are the central results.

The properties of the Jacobians are exploited to develop a procedure to find generators of the $\ell$-torsion points on the Jacobian.

Thesis advisor: Johan P. Hansen
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