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Title:
Fast Final Exponentiation on BW and BLS Curves with Even Embedding Degrees at 128 bits security
Authors: Senegue Gomez Nyamsi, Emmanuel Fouotsa, Calvin Tcheka
Abstract:The final exponentiation is a crucial step in pairing computations, ensuring cor-
rectness and uniqueness of results in pairing-based cryptographic protocols. In
this work, we propose an efficient method for computing the hard part of the final
exponentiation on BW10-511, BW14-351 and BLS12 curves at 128 bits security
level. Our approach reduces the computation cost by optimizing the exponenti-
ation sequence and minimizing the number of required multiplications through
an improved addition chain strategy. The computation cost of our method for
the final exponentiation on these curves is about 25.6%, 33.2% and 10% faster
than the previously fastest result on BW10-511, BW14-351 and BLS12 curves
respectively. The correctness of our formulas has been verified by a Magma code.
ePrint: https://eprint.iacr.org/2025/1387
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