{ "experiment": "signature_benchmarks", "timestamp_utc": "2026-11-01T05:50:10+00:00", "command": "experiments/signature_benchmarks/run_bench.py --no-build --seed 34 --label M3U96a (Apple M3 Ultra)", "cwd": "/Users/simon-pierreboucher/wp34-sigbench", "seed": 34, "host": { "hostname": "MacStudnpierre2", "os": "Darwin 25.6.0 (26.6)", "machine": "arm64", "python": "3.14.5", "cpu": "Apple M3 Ultra", "cores": 28, "ram_gb": 96.0 }, "software": { "numpy": "2.4.4", "scipy": "1.17.1", "sympy": "1.14.0", "gmpy2": null, "z3": "4.16.0", "pysat": null, "ecdsa": null, "coincurve": null }, "params": { "seed": 34, "reps": 7, "batch_ops": 2000, "batch_min_sigs": 2000, "batch_sizes": [ 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048 ], "crosscheck_n": 1000, "python_crosscheck_n": 200, "bootstrap": 2000, "python_ops": 20, "rust_command": "/Users/simon-pierreboucher/wp34-sigbench/experiments/signature_benchmarks/sigbench/target/release/sigbench --seed 34 --reps 7 --batch-ops 2000 --batch-min-sigs 2000 --batch-sizes 1,2,4,8,16,32,64,128,256,512,1024,2048 --crosscheck-n 1000 --python-crosscheck-n 200 --bootstrap 2000 --vectors /Users/simon-pierreboucher/wp34-sigbench/data/vectors/bip340_test_vectors.csv --crosscheck-out /Users/simon-pierreboucher/wp34-sigbench/results/signature_benchmarks/crosscheck_triples_MacStudnpierre2.json" }, "measurements": { "correctness_gates": { "bip340_vectors_both_libraries": true, "cross_library_1000": true, "python_reference_200": true, "own_scalar_mult_agrees_with_k256": true, "batch_negative_controls_rejected": true, "all": true }, "bip340_vectors": { "both_all_pass": true, "file": "/Users/simon-pierreboucher/wp34-sigbench/data/vectors/bip340_test_vectors.csv", "k256": { "all_pass": true, "details": [ { "comment": "", "expected": true, "index": 0, "sign_checked": true, "sign_ok": true, "verify_ok": true }, { "comment": "", "expected": true, "index": 1, "sign_checked": true, "sign_ok": true, "verify_ok": true }, { "comment": "", "expected": true, "index": 2, "sign_checked": true, "sign_ok": true, "verify_ok": true }, { "comment": "test fails if msg is reduced modulo p or n", "expected": true, "index": 3, "sign_checked": true, "sign_ok": true, "verify_ok": true }, { "comment": "", "expected": true, "index": 4, "sign_checked": false, "sign_ok": null, "verify_ok": true }, { "comment": "public key not on the curve", "expected": false, "index": 5, "sign_checked": false, "sign_ok": null, "verify_ok": true }, { "comment": "has_even_y(R) is false", "expected": false, "index": 6, "sign_checked": false, "sign_ok": null, "verify_ok": true }, { "comment": "negated message", "expected": false, "index": 7, "sign_checked": false, "sign_ok": null, "verify_ok": true }, { "comment": "negated s value", "expected": false, "index": 8, "sign_checked": false, "sign_ok": null, "verify_ok": true }, { "comment": "sG - eP is infinite. Test fails in single verification if has_even_y(inf) is defined as true and x(inf) as 0", "expected": false, "index": 9, "sign_checked": false, "sign_ok": null, "verify_ok": true }, { "comment": "sG - eP is infinite. Test fails in single verification if has_even_y(inf) is defined as true and x(inf) as 1", "expected": false, "index": 10, "sign_checked": false, "sign_ok": null, "verify_ok": true }, { "comment": "sig[0:32] is not an X coordinate on the curve", "expected": false, "index": 11, "sign_checked": false, "sign_ok": null, "verify_ok": true }, { "comment": "sig[0:32] is equal to field size", "expected": false, "index": 12, "sign_checked": false, "sign_ok": null, "verify_ok": true }, { "comment": "sig[32:64] is equal to curve order", "expected": false, "index": 13, "sign_checked": false, "sign_ok": null, "verify_ok": true }, { "comment": "public key is not a valid X coordinate because it exceeds the field size", "expected": false, "index": 14, "sign_checked": false, "sign_ok": null, "verify_ok": true }, { "comment": "message of size 0 (added 2022-12)", "expected": true, "index": 15, "sign_checked": true, "sign_ok": true, "verify_ok": true }, { "comment": "message of size 1 (added 2022-12)", "expected": true, "index": 16, "sign_checked": true, "sign_ok": true, "verify_ok": true }, { "comment": "message of size 17 (added 2022-12)", "expected": true, "index": 17, "sign_checked": true, "sign_ok": true, "verify_ok": true }, { "comment": "message of size 100 (added 2022-12)", "expected": true, "index": 18, "sign_checked": true, "sign_ok": true, "verify_ok": true } ], "library": "k256 (RustCrypto)", "n_vectors": 19, "sign_cases": 8, "sign_pass": 8, "verify_pass": 19 }, "libsecp256k1": { "all_pass": true, "details": [ { "comment": "", "expected": true, "index": 0, "sign_checked": true, "sign_ok": true, "verify_ok": true }, { "comment": "", "expected": true, "index": 1, "sign_checked": true, "sign_ok": true, "verify_ok": true }, { "comment": "", "expected": true, "index": 2, "sign_checked": true, "sign_ok": true, "verify_ok": true }, { "comment": "test fails if msg is reduced modulo p or n", "expected": true, "index": 3, "sign_checked": true, "sign_ok": true, "verify_ok": true }, { "comment": "", "expected": true, "index": 4, "sign_checked": false, "sign_ok": null, "verify_ok": true }, { "comment": "public key not on the curve", "expected": false, "index": 5, "sign_checked": false, "sign_ok": null, "verify_ok": true }, { "comment": "has_even_y(R) is false", "expected": false, "index": 6, "sign_checked": false, "sign_ok": null, "verify_ok": true }, { "comment": "negated message", "expected": false, "index": 7, "sign_checked": false, "sign_ok": null, "verify_ok": true }, { "comment": "negated s value", "expected": false, "index": 8, "sign_checked": false, "sign_ok": null, "verify_ok": true }, { "comment": "sG - eP is infinite. Test fails in single verification if has_even_y(inf) is defined as true and x(inf) as 0", "expected": false, "index": 9, "sign_checked": false, "sign_ok": null, "verify_ok": true }, { "comment": "sG - eP is infinite. Test fails in single verification if has_even_y(inf) is defined as true and x(inf) as 1", "expected": false, "index": 10, "sign_checked": false, "sign_ok": null, "verify_ok": true }, { "comment": "sig[0:32] is not an X coordinate on the curve", "expected": false, "index": 11, "sign_checked": false, "sign_ok": null, "verify_ok": true }, { "comment": "sig[0:32] is equal to field size", "expected": false, "index": 12, "sign_checked": false, "sign_ok": null, "verify_ok": true }, { "comment": "sig[32:64] is equal to curve order", "expected": false, "index": 13, "sign_checked": false, "sign_ok": null, "verify_ok": true }, { "comment": "public key is not a valid X coordinate because it exceeds the field size", "expected": false, "index": 14, "sign_checked": false, "sign_ok": null, "verify_ok": true }, { "comment": "message of size 0 (added 2022-12)", "expected": true, "index": 15, "sign_checked": true, "sign_ok": true, "verify_ok": true }, { "comment": "message of size 1 (added 2022-12)", "expected": true, "index": 16, "sign_checked": true, "sign_ok": true, "verify_ok": true }, { "comment": "message of size 17 (added 2022-12)", "expected": true, "index": 17, "sign_checked": true, "sign_ok": true, "verify_ok": true }, { "comment": "message of size 100 (added 2022-12)", "expected": true, "index": 18, "sign_checked": true, "sign_ok": true, "verify_ok": true } ], "library": "libsecp256k1 (rust-secp256k1)", "n_vectors": 19, "sign_cases": 8, "sign_pass": 8, "verify_pass": 19 }, "n_vectors": 19 }, "cross_library_checks": { "all_pass": true, "ecdsa_k256_sign_libsecp_verify_pass": 1000, "ecdsa_libsecp_sign_k256_verify_pass": 1000, "ecdsa_signatures_byte_identical": 1000, "n": 1000, "schnorr_k256_sign_libsecp_verify_pass": 1000, "schnorr_libsecp_sign_k256_verify_pass": 1000, "schnorr_signatures_byte_identical": 1000 }, "python_reference_crosscheck": { "n": 200, "source": "/Users/simon-pierreboucher/wp34-sigbench/results/signature_benchmarks/crosscheck_triples_MacStudnpierre2.json", "ecdsa_k256_sig_verified_by_python": 200, "ecdsa_libsecp_sig_verified_by_python": 200, "ecdsa_python_resign_identical": 200, "schnorr_k256_sig_verified_by_python": 200, "schnorr_libsecp_sig_verified_by_python": 200, "schnorr_python_resign_identical": 200, "tampered_sig_rejected_by_python": 200, "elapsed_s": 13.45, "resign_checked": true, "all_pass": true }, "sign_verify": { "ecdsa_sign_k256": { "iqr_ns": 53.79175000000032, "mean_ns": 18883.256, "median_ns": 18848.625, "min_ns": 18831.646, "ns_per_op_samples": [ 18907.8335, 18834.229, 18874.104, 18848.625, 18840.125, 19046.2295, 18831.646 ], "ops_per_rep": 2000, "ops_per_s": 53054.26788426212, "q1_ns": 18837.177, "q3_ns": 18890.96875, "reps": 7, "sd_ns": 76.78433267221082 }, "ecdsa_sign_libsecp256k1": { "iqr_ns": 769.5517499999987, "mean_ns": 29011.006, "median_ns": 29199.1875, "min_ns": 28564.396, "ns_per_op_samples": [ 29199.1875, 29428.3955, 29259.375, 29477.021, 28564.396, 28583.125, 28565.542 ], "ops_per_rep": 2000, "ops_per_s": 34247.52829166908, "q1_ns": 28574.3335, "q3_ns": 29343.88525, "reps": 7, "sd_ns": 422.1895762165573 }, "ecdsa_verify_k256": { "iqr_ns": 34.57249999999476, "mean_ns": 33574.8215, "median_ns": 33524.0625, "min_ns": 33494.9795, "ns_per_op_samples": [ 33531.6665, 33524.0625, 33530.0, 33496.4795, 33496.042, 33494.9795, 33950.5205 ], "ops_per_rep": 2000, "ops_per_s": 29829.320357578978, "q1_ns": 33496.26075, "q3_ns": 33530.833249999996, "reps": 7, "sd_ns": 166.49122054806097 }, "ecdsa_verify_libsecp256k1": { "iqr_ns": 37.5, "mean_ns": 16691.279857142858, "median_ns": 16680.3545, "min_ns": 16664.75, "ns_per_op_samples": [ 16734.8125, 16712.1875, 16680.3545, 16676.167, 16704.8335, 16665.854, 16664.75 ], "ops_per_rep": 2000, "ops_per_s": 59950.76423585601, "q1_ns": 16671.0105, "q3_ns": 16708.5105, "reps": 7, "sd_ns": 26.501544514289243 }, "schnorr_sign_k256": { "iqr_ns": 401.4482500000013, "mean_ns": 14996.696428571431, "median_ns": 14837.9585, "min_ns": 14731.3335, "ns_per_op_samples": [ 15160.396, 15131.4585, 15626.7705, 14837.9585, 14737.125, 14731.3335, 14751.833 ], "ops_per_rep": 2000, "ops_per_s": 67394.71605881631, "q1_ns": 14744.479, "q3_ns": 15145.92725, "reps": 7, "sd_ns": 332.8919594697641 }, "schnorr_sign_libsecp256k1": { "iqr_ns": 80.92725000000064, "mean_ns": 24748.6905, "median_ns": 24717.3335, "min_ns": 24694.75, "ns_per_op_samples": [ 24863.1045, 24694.75, 24697.854, 24838.604, 24717.3335, 24725.146, 24704.0415 ], "ops_per_rep": 2000, "ops_per_s": 40457.438501608594, "q1_ns": 24700.94775, "q3_ns": 24781.875, "reps": 7, "sd_ns": 70.94606669975937 }, "schnorr_verify_k256": { "iqr_ns": 430.46875, "mean_ns": 32320.133928571428, "median_ns": 32497.646, "min_ns": 31759.083, "ns_per_op_samples": [ 31759.083, 32652.521, 32539.5625, 32138.75, 32096.625, 32556.75, 32497.646 ], "ops_per_rep": 2000, "ops_per_s": 30771.459569717757, "q1_ns": 32117.6875, "q3_ns": 32548.15625, "reps": 7, "sd_ns": 327.5571907110819 }, "schnorr_verify_libsecp256k1": { "iqr_ns": 161.56224999999904, "mean_ns": 17099.41664285714, "median_ns": 16944.1665, "min_ns": 16924.729, "ns_per_op_samples": [ 16968.4165, 16944.1665, 16942.3335, 16941.8125, 16924.729, 17238.854, 17735.6045 ], "ops_per_rep": 2000, "ops_per_s": 59017.36152085144, "q1_ns": 16942.073, "q3_ns": 17103.63525, "reps": 7, "sd_ns": 301.51599255853716 } }, "scalar_mult": { "glv_note": "k256: every constant-time multiplication goes through lincomb(), which always applies the GLV decomposition (no public feature toggle); the vartime path uses GLV + wNAF-5; the only non-GLV reference is our own wNAF-5 double-and-add above. libsecp256k1: the GLV endomorphism has been unconditional since v0.1 (USE_ENDOMORPHISM removed) and ecmult is not exposed by rust-secp256k1's public API; mul_tweak maps to secp256k1_ec_pubkey_tweak_mul (constant-time ecmult_const) and from_secret_key to ecmult_gen (precomputed generator table).", "k256_generator_mul_ct_glv": { "iqr_ns": 57.45799999999872, "mean_ns": 22889.636785714283, "median_ns": 22876.0625, "min_ns": 22856.104, "ns_per_op_samples": [ 22856.104, 22876.0625, 22913.3955, 22868.396, 22857.5415, 22928.5, 22927.458 ], "ops_per_rep": 2000, "ops_per_s": 43713.816571361436, "q1_ns": 22862.96875, "q3_ns": 22920.42675, "reps": 7, "sd_ns": 32.39150473099511 }, "k256_mul_by_generator_precomputed_table": { "iqr_ns": 30.05199999999968, "mean_ns": 10807.788571428571, "median_ns": 10800.4165, "min_ns": 10788.1665, "ns_per_op_samples": [ 10788.1665, 10842.333, 10805.729, 10800.4165, 10836.125, 10788.75, 10793.0 ], "ops_per_rep": 2000, "ops_per_s": 92589.0219141086, "q1_ns": 10790.875, "q3_ns": 10820.927, "reps": 7, "sd_ns": 22.439008947271418 }, "k256_mul_by_generator_vartime_table": { "iqr_ns": 215.25025000000096, "mean_ns": 9460.776714285716, "median_ns": 9426.2085, "min_ns": 9328.0, "ns_per_op_samples": [ 9344.583, 9370.229, 9328.0, 9426.2085, 9611.104, 9591.625, 9553.6875 ], "ops_per_rep": 2000, "ops_per_s": 106087.19295780481, "q1_ns": 9357.405999999999, "q3_ns": 9572.65625, "reps": 7, "sd_ns": 121.70761815647116 }, "k256_point_mul_ct_glv": { "iqr_ns": 555.0832499999997, "mean_ns": 23166.4405, "median_ns": 23236.7295, "min_ns": 22841.8125, "ns_per_op_samples": [ 22870.521, 22864.479, 22841.8125, 23385.479, 23459.6875, 23506.375, 23236.7295 ], "ops_per_rep": 2000, "ops_per_s": 43035.31613603368, "q1_ns": 22867.5, "q3_ns": 23422.58325, "reps": 7, "sd_ns": 299.61088978011685 }, "k256_point_mul_vartime_glv_wnaf": { "iqr_ns": 18.03125, "mean_ns": 19012.967214285713, "median_ns": 19015.3125, "min_ns": 18989.0625, "ns_per_op_samples": [ 19036.125, 19025.3125, 19013.229, 19017.854, 19015.3125, 18993.875, 18989.0625 ], "ops_per_rep": 2000, "ops_per_s": 52589.19620700422, "q1_ns": 19003.552, "q3_ns": 19021.58325, "reps": 7, "sd_ns": 16.6036476987667 }, "libsecp256k1_generator_mul_ecmult_gen": { "iqr_ns": 157.67725000000064, "mean_ns": 23915.16957142857, "median_ns": 23797.458, "min_ns": 23744.854, "ns_per_op_samples": [ 23766.4375, 23796.729, 23797.458, 23744.854, 23897.917, 24422.1875, 23980.604 ], "ops_per_rep": 2000, "ops_per_s": 42021.29487947831, "q1_ns": 23781.58325, "q3_ns": 23939.2605, "reps": 7, "sd_ns": 238.27830419742892 }, "libsecp256k1_point_mul_tweak_ecmult_const": { "iqr_ns": 52.25, "mean_ns": 15656.592285714287, "median_ns": 15607.6665, "min_ns": 15591.271, "ns_per_op_samples": [ 15653.75, 15650.396, 15893.4165, 15607.6665, 15600.9375, 15598.7085, 15591.271 ], "ops_per_rep": 2000, "ops_per_s": 64071.07686469339, "q1_ns": 15599.823, "q3_ns": 15652.073, "reps": 7, "sd_ns": 107.42499066280944 }, "own_wnaf5_agrees_with_k256_64_cases": true, "own_wnaf5_point_mul_no_glv": { "iqr_ns": 489.82274999999936, "mean_ns": 29217.413571428566, "median_ns": 28983.8955, "min_ns": 28971.625, "ns_per_op_samples": [ 29524.583, 29412.6875, 29671.479, 28971.625, 28973.8335, 28983.8955, 28983.7915 ], "op_counts_example": { "adds": 52, "doublings": 257, "identity_adds": 1, "mixed_adds": 0 }, "ops_per_rep": 2000, "ops_per_s": 34501.91848780299, "q1_ns": 28978.8125, "q3_ns": 29468.63525, "reps": 7, "sd_ns": 307.5477235153144 } }, "batch_verification": { "equation": "sum_i a_i s_i G = sum_i a_i R_i + sum_i a_i e_i P_i, a_1 = 1, a_i uniform 128-bit from ChaCha20(seed); R_i = lift_x(r_i), P_i = lift_x(pk_i); merged into one MSM with 2b+1 terms whose result must be the identity", "msm_algorithms": { "k256_lincomb_ct": "k256 0.14 library: constant-time GLV + radix-16 fixed-window interleaving (benchmarked up to ct_lincomb_max_batch)", "k256_lincomb_vartime": "k256 0.14 library: GLV decomposition + wNAF-5 multiscalar (wnaf crate), variable time", "pippenger": "own implementation: bucket method with c-bit windows (c = pippenger_window(2b+1)), mixed additions into buckets, running-sum trick", "straus_wnaf5": "own implementation: interleaved Straus with width-5 wNAF recoding, per-term odd-multiple tables (1 dbl + 7 adds), projective additions" }, "negative_controls": { "all_invalid_batches_rejected": true, "batch_size": 64, "cases": { "r_plus_one": { "k256_lincomb_ct": true, "k256_lincomb_vartime": true, "pippenger": true, "straus_wnaf5": true, "unmodified_batch_accepted": true }, "s_plus_one": { "k256_lincomb_ct": true, "k256_lincomb_vartime": true, "pippenger": true, "straus_wnaf5": true, "unmodified_batch_accepted": true }, "wrong_message": { "k256_lincomb_ct": true, "k256_lincomb_vartime": true, "pippenger": true, "straus_wnaf5": true, "unmodified_batch_accepted": true } } }, "results": [ { "algorithm": "straus_wnaf5", "batch_size": 1, "msm_only_ns_per_sig_median": 37863.703, "msm_only_ns_per_sig_samples": [ 37904.747, 37863.703, 37877.7395, 37838.8055, 37833.0995, 37857.391, 39200.6545 ], "n_batches_per_rep": 2000, "n_terms": 3, "op_counts_per_batch": { "adds": 107, "doublings": 259, "identity_adds": 1, "mixed_adds": 0 }, "op_counts_per_signature": { 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