Affine Pairings on ARM

Pairings on elliptic curves are being used in an increasing number of cryptographic applications on many different devices and platforms, but few performance numbers for cryptographic pairings have been reported on embedded and mobile devices.

In this paper we give performance numbers for affine and projective pairings on a dual-core Cortex A9 ARM processor and compare performance of the same implementation across three platforms: x86, x86-64 and ARM. Using a fast inversion in the base field and doing inversion in extension fields by using the norm map to convert to inversions in smaller fields, we find a very low ratio of inversion-to-multiplication costs on all three platforms. This favors using affine coordinates for pairing implementations, even for the current 128 bit minimum security level specified by NIST. Our implementation shows another platform where affine coordinates are a better choice. We compare with other reported performance numbers on ARM processors and find that our implementation of affine pairings compares favorably.