Efficient Implementation of Bilinear Pairings on ARM Processors

Abstract. As hardware capabilities increase, low-power devices such as smartphones represent a natural environment for the efficient imple-mentation of cryptographic pairings. Few works in the literature have considered such platforms despite their growing importance in a post-PC world. In this paper, we investigate the efficient computation of the Optimal-Ate pairing over Barreto-Naehrig curves in software at differ-ent security levels on ARM processors. We exploit state-of-the-art tech-niques and propose new optimizations to speed up the computation in the tower field and curve arithmetic. In particular, we extend the concept of lazy reduction to inversion in extension fields, analyze an efficient al-ternative 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. In addition, we study the effi-ciency of using M-type sextic twists in the pairing computation and carry out a detailed comparison between affine and projective coordinate sys-tems. Our implementations on various mass-market smartphones and tablets significantly improve the state-of-the-art of pairing computation on ARM-powered devices, outperforming by at least a factor of 3.7 the best previous results in the literature

A non-interactive range proof with constant communication

Abstract. In a range proof, the prover convinces the verifier in zeroknowledge that he has encrypted or committed to a value a ∈ [0,H] where H is a public constant. Most of the previous non-interactive range proofs have been proven secure in the random oracle model. We show that one of the few previous non-interactive range proofs in the common reference string (CRS) model, proposed by Yuen et al. in COCOON 2009, is insecure. We then construct a secure non-interactive range proof that works in the CRS model. The new range proof can have (by different instantiations of the parameters) either very short communication (14 080 bits) and verifier’s computation (81 pairings), short combined CRS length and communication (log 1/2+o(1) H group elements), or very efficient prover’s computation (Θ(log H) exponentiations)