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As hardware capabilities increase, low-power devices such as smartphones represent a natural environment for the efficient implementation of cryptographic pairings. Few works in the literature have considered such platforms despite their growing importance in a post-PC world. In this paper, the authors investigate the efficient computation of the Optimal-Ate pairing over Barreto-Naehrig curves in software at different security levels on ARM processors. They exploit state-of-the-art techniques and propose new optimizations to speed up the computation in the tower field and curve arithmetic. In particular, they extend the concept of lazy reduction to inversion in extension fields, analyze an efficient alternative for the sparse multiplication used inside the Miller's algorithm and reduce further the cost of point/line evaluation formulas in affine and projective homogeneous coordinates.
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