1---2id: H033title: GLV decomposition halves doublings; sub-scalars never exceed 128 bits4axis: A5kind: algebraic6statement: With the published basis, |k1|, |k2| < 2^128 for every k, and [k]P via interleaved wNAF uses ≈ 128 doublings instead7 of 256, giving ≈ 1.65× fewer group operations than wNAF alone.8motivation: Quantify the known constant-factor gain exactly in operation counts (A3).9assumptions: Affine operation model; wNAF window 4–5.10expected_contribution: Exact operation counts for the paper's baseline table.11related_work:12- gallant2001faster13- sica2002analysis14- hankerson2004guide15possible_counterexamples: A scalar with a 129-bit component (none found in 2 200 samples; the Sica–Ciet–Quisquater bound guarantees16 ≤ 128 + small).17verification_strategy: experiments/baselines/scalar_mult_opcount.py on 200 random scalars, all methods return the same point.18computational_budget: seconds19status: evaluated20classification: known_reproduced21evidence:22- results/baselines/scalar_mult_opcount.json23verdict: Max sub-scalar size 128 bits; 184 vs 304 group ops (GLV+wNAF vs wNAF), 2.07× vs double-and-add.24commands:25- .venv/bin/python experiments/baselines/scalar_mult_opcount.py26---2728# H03 — GLV decomposition halves doublings; sub-scalars never exceed 128 bits2930With the published basis, |k1|, |k2| < 2^128 for every k, and [k]P via interleaved wNAF uses ≈ 128 doublings instead of 256, giving ≈ 1.65× fewer group operations than wNAF alone.31