{ "experiment": "signature_benchmarks", "timestamp_utc": "2026-11-01T05:49:56+00:00", "command": "experiments/signature_benchmarks/run_bench.py --no-build --seed 34 --label Laptop (Apple M5 Max)", "cwd": "/Users/simon-pierreboucher/Desktop/UQO/Recherche/Recherche-UQO/mathematiques/beyond-square-root-barrier", "seed": 34, "host": { "hostname": "MacBookPro-de-simon-pierre-2.local", "os": "Darwin 27.0.0 (27.0)", "machine": "arm64", "python": "3.12.13", "cpu": "Apple M5 Max", "cores": 18, "ram_gb": 48.0 }, "software": { "numpy": "2.5.4", "scipy": "1.18.1", "sympy": "1.14.0", "gmpy2": "2.3.2", "z3": "5.3.3", "pysat": "1.9.dev17", "ecdsa": "0.19.2", "coincurve": "21.0.0" }, "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/Desktop/UQO/Recherche/Recherche-UQO/mathematiques/beyond-square-root-barrier/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/Desktop/UQO/Recherche/Recherche-UQO/mathematiques/beyond-square-root-barrier/data/vectors/bip340_test_vectors.csv --crosscheck-out /Users/simon-pierreboucher/Desktop/UQO/Recherche/Recherche-UQO/mathematiques/beyond-square-root-barrier/results/signature_benchmarks/crosscheck_triples_MacBookPro-de-simon-pierre-2.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/Desktop/UQO/Recherche/Recherche-UQO/mathematiques/beyond-square-root-barrier/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/Desktop/UQO/Recherche/Recherche-UQO/mathematiques/beyond-square-root-barrier/results/signature_benchmarks/crosscheck_triples_MacBookPro-de-simon-pierre-2.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": 11.27, "resign_checked": true, "all_pass": true }, "sign_verify": { "ecdsa_sign_k256": { "iqr_ns": 304.8125, "mean_ns": 15284.860142857144, "median_ns": 15267.4375, "min_ns": 15064.0625, "ns_per_op_samples": [ 15743.146, 15066.979, 15087.896, 15064.0625, 15334.375, 15430.125, 15267.4375 ], "ops_per_rep": 2000, "ops_per_s": 65498.87628490374, "q1_ns": 15077.4375, "q3_ns": 15382.25, "reps": 7, "sd_ns": 247.9589146798846 }, "ecdsa_sign_libsecp256k1": { "iqr_ns": 16.53074999999808, "mean_ns": 23624.657714285713, "median_ns": 23630.833, "min_ns": 23605.9795, "ns_per_op_samples": [ 23635.979, 23631.604, 23605.9795, 23634.833, 23616.4585, 23630.833, 23616.917 ], "ops_per_rep": 2000, "ops_per_s": 42317.594136440304, "q1_ns": 23616.68775, "q3_ns": 23633.2185, "reps": 7, "sd_ns": 11.504451674087065 }, "ecdsa_verify_k256": { "iqr_ns": 503.8962500000016, "mean_ns": 24928.16671428571, "median_ns": 25012.0835, "min_ns": 24629.3125, "ns_per_op_samples": [ 24629.3125, 25012.0835, 25263.0625, 25127.417, 24655.729, 24636.729, 25172.8335 ], "ops_per_rep": 2000, "ops_per_s": 39980.67574018773, "q1_ns": 24646.229, "q3_ns": 25150.12525, "reps": 7, "sd_ns": 279.0554955178958 }, "ecdsa_verify_libsecp256k1": { "iqr_ns": 88.03099999999904, "mean_ns": 12607.327357142856, "median_ns": 12615.604, "min_ns": 12460.521, "ns_per_op_samples": [ 12771.9375, 12615.604, 12660.5, 12562.8125, 12629.1455, 12460.521, 12550.771 ], "ops_per_rep": 2000, "ops_per_s": 79266.9142119553, "q1_ns": 12556.79175, "q3_ns": 12644.82275, "reps": 7, "sd_ns": 97.63935664121043 }, "schnorr_sign_k256": { "iqr_ns": 198.40599999999904, "mean_ns": 11589.74107142857, "median_ns": 11569.0835, "min_ns": 11451.0625, "ns_per_op_samples": [ 11724.208, 11460.4585, 11473.25, 11843.8125, 11569.0835, 11606.3125, 11451.0625 ], "ops_per_rep": 2000, "ops_per_s": 86437.27050634564, "q1_ns": 11466.85425, "q3_ns": 11665.26025, "reps": 7, "sd_ns": 148.8012614021435 }, "schnorr_sign_libsecp256k1": { "iqr_ns": 381.5829999999987, "mean_ns": 20523.824285714283, "median_ns": 20548.1875, "min_ns": 20246.0205, "ns_per_op_samples": [ 20275.1875, 20256.5, 20246.0205, 20548.1875, 21046.021, 20634.208, 20660.6455 ], "ops_per_rep": 2000, "ops_per_s": 48666.092812322255, "q1_ns": 20265.84375, "q3_ns": 20647.42675, "reps": 7, "sd_ns": 292.8722850149957 }, "schnorr_verify_k256": { "iqr_ns": 716.9579999999987, "mean_ns": 24617.791714285715, "median_ns": 24486.6875, "min_ns": 24107.1045, "ns_per_op_samples": [ 24330.7915, 25160.667, 25005.6455, 24996.354, 24486.6875, 24237.292, 24107.1045 ], "ops_per_rep": 2000, "ops_per_s": 40838.51684716441, "q1_ns": 24284.04175, "q3_ns": 25000.99975, "reps": 7, "sd_ns": 426.9255283433374 }, "schnorr_verify_libsecp256k1": { "iqr_ns": 116.33324999999968, "mean_ns": 13187.339285714286, "median_ns": 13197.0415, "min_ns": 13020.3545, "ns_per_op_samples": [ 13243.1045, 13124.9585, 13274.208, 13020.3545, 13197.0415, 13159.6875, 13292.0205 ], "ops_per_rep": 2000, "ops_per_s": 75774.55901764044, "q1_ns": 13142.323, "q3_ns": 13258.65625, "reps": 7, "sd_ns": 95.0860352276898 } }, "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": 6.63550000000032, "mean_ns": 16414.24692857143, "median_ns": 16409.729, "min_ns": 16409.375, "ns_per_op_samples": [ 16409.375, 16429.4375, 16409.458, 16409.5, 16419.6665, 16412.5625, 16409.729 ], "ops_per_rep": 2000, "ops_per_s": 60939.45853706664, "q1_ns": 16409.479, "q3_ns": 16416.1145, "reps": 7, "sd_ns": 7.665692496596951 }, "k256_mul_by_generator_precomputed_table": { "iqr_ns": 338.90625, "mean_ns": 8261.479214285715, "median_ns": 8293.0625, "min_ns": 7994.396, "ns_per_op_samples": [ 8293.0625, 8606.5835, 8386.3125, 8420.75, 8029.4375, 7994.396, 8099.8125 ], "ops_per_rep": 2000, "ops_per_s": 120582.71597494894, "q1_ns": 8064.625, "q3_ns": 8403.53125, "reps": 7, "sd_ns": 228.1658502745058 }, "k256_mul_by_generator_vartime_table": { "iqr_ns": 316.4375, "mean_ns": 6602.491071428572, "median_ns": 6577.479, "min_ns": 6422.6455, "ns_per_op_samples": [ 6611.146, 6577.479, 6428.0835, 6423.8125, 6422.6455, 6880.646, 6873.625 ], "ops_per_rep": 2000, "ops_per_s": 152033.93275752, "q1_ns": 6425.948, "q3_ns": 6742.3855, "reps": 7, "sd_ns": 202.59678569295977 }, "k256_point_mul_ct_glv": { "iqr_ns": 248.96875, "mean_ns": 17254.71121428571, "median_ns": 17153.25, "min_ns": 16850.646, "ns_per_op_samples": [ 16850.646, 17905.354, 17073.0625, 17454.9165, 17230.9165, 17153.25, 17114.833 ], "ops_per_rep": 2000, "ops_per_s": 58297.990176788655, "q1_ns": 17093.94775, "q3_ns": 17342.9165, "reps": 7, "sd_ns": 339.1434369828955 }, "k256_point_mul_vartime_glv_wnaf": { "iqr_ns": 196.0, "mean_ns": 13868.470214285713, "median_ns": 13955.729, "min_ns": 13498.625, "ns_per_op_samples": [ 14025.625, 13895.271, 13955.729, 13967.125, 14031.4375, 13705.479, 13498.625 ], "ops_per_rep": 2000, "ops_per_s": 71655.16040043483, "q1_ns": 13800.375, "q3_ns": 13996.375, "reps": 7, "sd_ns": 196.92330397641646 }, "libsecp256k1_generator_mul_ecmult_gen": { "iqr_ns": 208.21875, "mean_ns": 19722.449285714283, "median_ns": 19804.583, "min_ns": 19531.0415, "ns_per_op_samples": [ 19531.0415, 19580.5625, 19646.354, 19851.25, 19809.229, 19804.583, 19834.125 ], "ops_per_rep": 2000, "ops_per_s": 50493.36307661717, "q1_ns": 19613.45825, "q3_ns": 19821.677, "reps": 7, "sd_ns": 132.85145081125296 }, "libsecp256k1_point_mul_tweak_ecmult_const": { "iqr_ns": 111.74974999999904, "mean_ns": 11528.723214285714, "median_ns": 11468.0835, "min_ns": 11425.875, "ns_per_op_samples": [ 11635.4165, 11811.0625, 11451.4375, 11434.8335, 11474.354, 11468.0835, 11425.875 ], "ops_per_rep": 2000, "ops_per_s": 87198.52798420939, "q1_ns": 11443.1355, "q3_ns": 11554.88525, "reps": 7, "sd_ns": 143.23537223042376 }, "own_wnaf5_agrees_with_k256_64_cases": true, "own_wnaf5_point_mul_no_glv": { "iqr_ns": 256.1875, "mean_ns": 21225.032642857142, "median_ns": 21122.021, "min_ns": 20927.8955, "ns_per_op_samples": [ 21647.479, 21092.104, 20927.8955, 21122.021, 21322.4375, 21372.6665, 21090.625 ], "op_counts_example": { "adds": 52, "doublings": 257, "identity_adds": 1, "mixed_adds": 0 }, "ops_per_rep": 2000, "ops_per_s": 47343.954444510775, "q1_ns": 21091.3645, "q3_ns": 21347.552, "reps": 7, "sd_ns": 239.57660758542949 } }, "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": 27251.2275, "msm_only_ns_per_sig_samples": [ 27680.5905, 27248.0795, 27251.2275, 27441.3385, 27224.7355, 27624.9845, 27247.457 ], "n_batches_per_rep": 2000, "n_terms": 3, "op_counts_per_batch": { "adds": 107, "doublings": 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