IACR News item: 02 April 2013
David Lubicz, Damien Robert
ePrint Reportall abelian varieties the usual Miller\'s algorithm to compute a
function associated to a principal divisor. We also explain how to
use the Frobenius morphism on abelian varieties defined over a
finite field in order to shorten the loop of the Weil and Tate
pairings algorithms. This extend preceding results about ate and
twisted ate pairings to all abelian varieties. Then building upon
the two preceding ingredients, we obtain a variant of optimal
pairings on abelian varieties. Finally, by introducing new addition
formulas, we explain how to compute optimal pairings on Kummer
varieties. We compare in term of performance the resulting
algorithms to the algorithms already known in the genus one and two
case.
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