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The Brezing-Weng-Freeman method for certain genus two hyperelliptic curves
Brezing-Weng-Freeman method elliptic curve hyperelliptic curves
2009/6/12
We construct paring friendly curves of the form Y2 = X5+uX3+vX over large
finite prime fields. The ρ-value of our family is always less than 4. Our
method is based on the fact that, under a certain ...
Generating genus two hyperelliptic curves over large characteristic finite fields
hyperelliptic curve point counting
2009/6/9
In hyperelliptic curve cryptography, finding a suitable hyperelliptic
curve is an important fundamental problem. One of necessary
conditions is that the order of its Jacobian is a product of a large...
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...
High Performance Arithmetic for Hyperelliptic Curve Cryptosystems of Genus Two
High Performance Arithmetic Hyperelliptic Curve Cryptosystems Genus Two
2009/4/10
High Performance Arithmetic for Hyperelliptic Curve Cryptosystems of Genus Two.
A Complete Divisor Class Halving Algorithm for Hyperelliptic Curve Cryptosystems of Genus Two
hyperelliptic curve cryptosystems scalar multiplication divisor class halving
2009/3/31
We deal with a divisor class halving algorithm on hyperelliptic
curve cryptosystems (HECC), which can be used for scalar multiplication,
instead of a doubling algorithm. It is not obvious how to con...
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...