Section: New Results

Pairings

Participants : Andreas Enge, Damien Robert.

The article [22] by D. Lubicz and D. Robert explaining how to compute optimal pairings on abelian varieties described by their theta models has been accepted for publication at Journal of Symbolic Computation.

In [24] , A. Enge and J. Milan report on the Apip implementation of cryptographic pairings on elliptic curves in Pari/Gp . For security levels equivalent to the different AES flavours, they exhibit suitable curves in parametric families and show that optimal ate and twisted ate pairings exist and can be efficiently evaluated. They provide a correct description of Miller's algorithm for signed binary expansions such as the NAF and extend a recent variant due to Boxall et al. to addition-subtraction chains. They analyse and compare several algorithms proposed in the literature for the final exponentiation. Finally, they give recommendations on which curve and pairing to choose at each security level.