Parallel Computation of Optimal Ate Cryptographic Pairings at the 128, 192 and 256-bit security levels using elliptic net algorithm
share
Efficient computations of pairings with Miller Algorithm have recently received a great attention due to the many applications in cryptography. In this work, we give formulae for the optimal Ate pairing in terms of elliptic nets associated to twisted Barreto-Naehrig (BN) curve, Barreto-Lynn-Scott(BLS) curves and Kachisa-Schaefer-Scott(KSS) curves considered at the 128, 192 and 256-bit security levels, and Scott-Guillevic curve with embedding degree 54. We show how to parallelize the computation of these pairings when the elliptic net algorithm instead is used and we obtain except in the case of Kachisa-Schaefer-Scott(KSS) curves considered at the 256-bit security level, more efficient theoretical results with 8 processors compared to the case where the Miller algorithm is used. This work still confirms that BLS48 curves are the best for pairing-based cryptography at 256-bit security level <cit.>.
READ FULL TEXT