SPB Git

spb/wp34_uqo

Public
4.5 KB · 148 lines json
1{2 "experiment": "secp256k1_parameter_verification",3 "timestamp_utc": "2026-11-01T05:40:39+00:00",4 "command": "experiments/baselines/secp256k1_facts.py",5 "cwd": "/Users/simon-pierreboucher/Desktop/UQO/Recherche/Recherche-UQO/mathematiques/beyond-square-root-barrier",6 "seed": null,7 "host": {8  "hostname": "MacBookPro-de-simon-pierre-2.local",9  "os": "Darwin 27.0.0 (27.0)",10  "machine": "arm64",11  "python": "3.12.13",12  "cpu": "Apple M5 Max",13  "cores": 18,14  "ram_gb": 48.015 },16 "software": {17  "numpy": "2.5.4",18  "scipy": "1.18.1",19  "sympy": "1.14.0",20  "gmpy2": "2.3.2",21  "z3": "5.3.3",22  "pysat": "1.9.dev17",23  "ecdsa": "0.19.2",24  "coincurve": "21.0.0"25 },26 "params": {27  "gp_version": "2.19.0"28 },29 "measurements": {30  "python": {31   "p_is_prime": true,32   "p_equals_2^256-2^32-977": true,33   "p_mod_3": 1,34   "p_mod_4": 3,35   "n_is_prime": true,36   "G_on_curve": true,37   "nG_is_infinity": true,38   "cofactor": 1,39   "discriminant_nonzero": true,40   "j_invariant": 0,41   "trace_t": "432420386565659656852420866390673177327",42   "hasse_bound_ok": true,43   "hasse_exact": true,44   "anomalous": false,45   "frobenius_discriminant": "-276180966231670251052810340486134462307742726569900724701098994184861751821723",46   "disc_is_minus3_times_square": true,47   "conductor_f": "303414439467246543595250775667605759171",48   "beta_cubed_is_1_mod_p": true,49   "lambda_cubed_is_1_mod_n": true,50   "beta^2+beta+1=0 mod p": true,51   "lambda^2+lambda+1=0 mod n": true,52   "phi_G_on_curve": true,53   "phi_G_equals_lambda_G": true,54   "phi2_G_equals_lambda2_G": true,55   "beta_lambda2_mismatch": true,56   "glv_basis_v1": true,57   "glv_basis_v2": true,58   "glv_basis_det_is_n": true,59   "x0_points_exist": false,60   "embedding_degree_le_100": null,61   "twist_order": "115792089237316195423570985008687907853702405052206223696310004874299507848991",62   "twist_small_factors": {63    "3": 2,64    "13": 2,65    "3319": 1,66    "22639": 167   },68   "twist_cofactor_bits": 220,69   "twist_cofactor_is_prime": true,70   "n_minus_1_small_factors": {71    "2": 6,72    "3": 1,73    "149": 1,74    "631": 175   },76   "p_minus_1_small_factors": {77    "2": 1,78    "3": 1,79    "7": 1,80    "13441": 181   },82   "glv_basis_rederived_from_euclid": true,83   "glv_euclid_candidates": [84    [85     "367917413016453100223835821029139468248",86     "64502973549206556628585045361533709077"87    ],88    [89     "64502973549206556628585045361533709077",90     "-303414439467246543595250775667605759171"91    ],92    [93     "45402545270420317080910594221470922863",94     "1581575170885439274604838923699562504932"95    ]96   ]97  },98  "pari_gp": {99   "p_is_prime": true,100   "n_is_prime": true,101   "ellcard": "115792089237316195423570985008687907852837564279074904382605163141518161494337",102   "G_on_curve": true,103   "nG_is_infinity": true,104   "trace_t": "432420386565659656852420866390673177327",105   "j_invariant": 0,106   "beta_cubed_is_1_mod_p": true,107   "lambda_cubed_is_1_mod_n": true,108   "phi_G_equals_lambda_G": true,109   "twist_small_primes": "[3, 13, 3319, 22639, 1013176677300131846900870239606035638738100997248092069256697437031]",110   "twist_small_exponents": "[2, 2, 1, 1, 1]",111   "twist_cofactor_is_prime": true,112   "twist_cofactor_bits": 220,113   "embedding_degree": "19298681539552699237261830834781317975472927379845817397100860523586360249056",114   "n_minus_1_small_primes": "[2, 3, 149, 631, 6414488540731361226607730496888035255996436684289152125202372832747357]",115   "p_minus_1_small_primes": "[2, 3, 7, 13441, 205115282021455665897114700593932402728804164701536103180137503955397371]",116   "frobenius_discriminant": "-276180966231670251052810340486134462307742726569900724701098994184861751821723",117   "disc_is_minus3_times_square": true,118   "cube_roots_unity_mod_p": [119    55594575648329892869085402983802832744385952214688224221778511981742606582254,120    60197513588986302554485582024885075108884032450952339817679072026166228089408121   ],122   "cube_roots_unity_mod_n": [123    78074008874160198520644763525212887401909906723592317393988542598630163514318,124    37718080363155996902926221483475020450927657555482586988616620542887997980018125   ],126   "kronecker_7_p": -1,127   "num_roots_x3_plus_7": 0128  },129  "agreement": {130   "p_prime": true,131   "n_prime": true,132   "order_equals_n": true,133   "trace": true,134   "j": true,135   "phi_lambda": true,136   "twist_cofactor_prime": true,137   "twist_cofactor_bits": true,138   "embedding_degree_gt_100": true,139   "beta_in_gp_roots": true,140   "lambda_in_gp_roots": true,141   "x0_points": true,142   "cm_discriminant": true,143   "frobenius_discriminant": true144  },145  "all_agree": true146 },147 "elapsed_s": 4.495148}
Files · c732f7e320257301eb619a8227b914374a41aac4
Menu

Theme