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GENERATORS OF JACOBIANS OF GENUS TWO CURVES
Jacobians genus two curves Frobenius endomorphism
2009/6/2
We prove that in most cases relevant to cryptography, the Frobenius
endomorphism on the Jacobian of a genus two curve is represented
by a diagonal matrix with respect to an appropriate basis of the ...
NON-CYCLIC SUBGROUPS OF JACOBIANS OF GENUS TWO CURVES
Jacobians hyperelliptic genus two curves pairings
2009/6/2
Let E be an elliptic curve de ned over a nite eld. Balasubramanian
and Koblitz have proved that if the `th roots of unity ` is not contained
in the ground eld, then a eld extension of the groun...
NON-CYCLIC SUBGROUPS OF JACOBIANS OF GENUS TWO CURVES WITH COMPLEX MULTIPLICATION
Jacobians hyperelliptic curves embedding degree complex multiplication
2009/6/2
Let E be an elliptic curve de ned over a nite eld. Balasubramanian
and Koblitz have proved that if the `th roots of unity ` is not contained
in the ground eld, then a eld extension of the groun...
DISTORTION MAPS FOR GENUS TWO CURVES
hyperelliptic curve cryptography pairings supersingular curves
2008/12/25
Distortion maps are a useful tool for pairing based cryptography.
Compared with elliptic curves, the case of hyperelliptic curves of genus g > 1
is more complicated since the full torsion subgroup h...
Efficient Divisor Class Halving on Genus Two Curves
hyperelliptic curve divisor class halving binary fields
2008/12/9
Efficient halving of divisor classes offers the possibility to improve scalar multiplication on hyperelliptic curves and is also a step towards giving hyperelliptic curve cryptosystems all the featur...