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See also Benger-Scott paper https://eprint.iacr.org/2009/556.pdf
Devigili et al https://eprint.iacr.org/2006/471.pdf has the costs between the different towerings and direct sextic: Timings
It seems like the same perf. And we can change representation (supranational/blst#101 (comment), supranational/blst#102 (review)) |
gbotrel
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Jun 17, 2022
ThomasPiellard
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Jun 20, 2022
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Compress
F_{p^k}elements (E24, E12, E6) when they are in the cyclotomic subgroup, i.e.z^{\Phi_k(p)} == 1. This works in particular to compress GT elements after a pairing. The compression ratio is 1/2 using Torus-based T2 lossless compression following "COMPRESSION IN FINITE FIELDS AND TORUS-BASED CRYPTOGRAPHY", K. RUBIN AND A. SILVERBERG (section 2).Note we can have a lossless compression with ratio 1/3 using CEILIDH (section 3) if we decide to change the extensions tower (e.g. Fp2-Fp4-Fp12 for E12). This would result is a slightly slower pairing though.