International Association for Cryptologic Research

International Association
for Cryptologic Research

IACR News item: 02 April 2013

David Lubicz, Damien Robert
ePrint Report ePrint Report
In this paper, we use the theory of theta functions to generalize to

all 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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