1---2id: H143title: 'Implementation choice dominates signature performance: three orders of magnitude between pure Python and libsecp256k1'4axis: B5kind: algorithmic6statement: ECDSA/Schnorr verification spans ≈ 10³× between the pure-Python reference and libsecp256k1, with k256 within a7 small factor of libsecp256k1; sign and verify costs differ by the cost of the second scalar multiplication.8motivation: Research question B5.9assumptions: Single-threaded, prehashed messages.10expected_contribution: Implementation table.11related_work:12- wuille2013libsecp256k113- bernstein2012high14possible_counterexamples: None (descriptive).15verification_strategy: sigbench + run_bench.py on laptop and M3U96a.16computational_budget: ≈ 30 min17status: evaluated18classification: empirical_observation19evidence:20- results/signature_benchmarks/summary.json21verdict: 'Schnorr verify: 7.4 ms (pure Python) vs 24.5 µs (k256) vs 13.2 µs (libsecp256k1): 560× spread; libsecp256k1 verifies22 1.9× faster than k256 while k256 signs 1.8× faster (table-based generator multiplication 8.3 µs vs blinded ecmult_gen 19.823 µs); ECDSA and Schnorr verification within 5 % in libsecp256k1.'24---2526# H14 — Implementation choice dominates signature performance: three orders of magnitude between pure Python and libsecp256k12728ECDSA/Schnorr verification spans ≈ 10³× between the pure-Python reference and libsecp256k1, with k256 within a small factor of libsecp256k1; sign and verify costs differ by the cost of the second scalar multiplication.29