---
id: H14
title: 'Implementation choice dominates signature performance: three orders of magnitude between pure Python and libsecp256k1'
axis: B
kind: algorithmic
statement: ECDSA/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.
motivation: Research question B5.
assumptions: Single-threaded, prehashed messages.
expected_contribution: Implementation table.
related_work:
- wuille2013libsecp256k1
- bernstein2012high
possible_counterexamples: None (descriptive).
verification_strategy: sigbench + run_bench.py on laptop and M3U96a.
computational_budget: ≈ 30 min
status: evaluated
classification: empirical_observation
evidence:
- results/signature_benchmarks/summary.json
verdict: 'Schnorr verify: 7.4 ms (pure Python) vs 24.5 µs (k256) vs 13.2 µs (libsecp256k1): 560× spread; libsecp256k1 verifies
  1.9× faster than k256 while k256 signs 1.8× faster (table-based generator multiplication 8.3 µs vs blinded ecmult_gen 19.8
  µs); ECDSA and Schnorr verification within 5 % in libsecp256k1.'
---

# H14 — Implementation choice dominates signature performance: three orders of magnitude between pure Python and libsecp256k1

ECDSA/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.