Pseudo 8-Sparse Multiplication for Efficient Ate-Based Pairing on Barreto-Naehrig Curve

摘要

According to some recent implementation reports on Atebased pairings such as optimal ate pairing with Barreto-Naehrig curve whose embedding degree is 12, sparse multiplication accelerates Miller's loop calculation in a pairing calculation. Especially, 7-sparse multiplication is available when the implementation uses affine coordinates, where 7-sparse means that the multiplicand or multiplier has 7 zeros among 12 coefficients. This paper extends it to pseudo 8-sparse multiplication. Then, some experimental results together with theoretic calculation costs are shown in order to evaluate its efficiency.