Efficient Delegation of Pairing Computation

Pairing computation requires a lot of efforts for portable small devices such as smart cards. It was first considered concretely by Chevallier-Mames et al. that the cards delegate computation of pairings to a powerful device. In this paper, we propose more efficient protocols than those of Chevallier-Mames et al. in two cases, and provide two new variants that would be useful in real applications.