Fixed argument pairings

Tate pairing multiplication costs with different r and k for various n.


A common scenario in many pairing-based cryptographic protocols is that one argument in the pairing is fixed as a long term secret key or a constant parameter in the system. In these situations, the runtime of Miller's algorithm can be significantly reduced by storing precomputed values that depend on the fixed argument, prior to the input or existence of the second argument. In light of recent developments in pairing computation, we show that the computation of the Miller loop can be sped up by up to 37% if precomputation is employed, with our method being up to 19.5% faster than the previous precomputation techniques.

Keywords: pairings, Miller's algorithm, Tate pairing, ate pairing, precomputation


Craig Costello, Douglas Stebila. Fixed argument pairings. In Michel Abdalla, Paulo S.L.M. Barreto, editors, Proc. 1st International Conference on Cryptology and Information Security in Latin America (LATINCRYPT) 2010, LNCS, vol. 6212, pp. 92-108. Springer, August 2010. © Springer.




This research was supported by:
  • Queensland Government Smart State PhD Scholarship