{"id":"W2085540322","doi":"10.1109/tvlsi.2011.2158595","title":"Efficient FPGA Implementations of Point Multiplication on Binary Edwards and Generalized Hessian Curves Using Gaussian Normal Basis","year":2011,"lang":"en","type":"article","venue":"IEEE Transactions on Very Large Scale Integration (VLSI) Systems","topic":"Cryptography and Residue Arithmetic","field":"Computer Science","cited_by":79,"is_retracted":false,"has_abstract":true,"ca_institutions":"Western University","funders":"Division of Electrical, Communications and Cyber Systems; CMC Microsystems","keywords":"Elliptic curve cryptography; Hessian matrix; Lookup table; Elliptic curve point multiplication; Multiplication (music); Elliptic curve; Binary number; Edwards curve; Mathematics; Computer science; Parallel computing; Arithmetic; Algorithm; Applied mathematics; Combinatorics; Schoof's algorithm; Pure mathematics; Encryption; Public-key cryptography","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005001448,0.0002623208,0.0003114582,0.0005873707,0.0004694387,0.00008950717,0.0002998187,0.0001181298,0.00005707434],"category_scores_gemma":[0.000005514912,0.0002251235,0.0002033452,0.0007085874,0.00009593721,0.0003027206,0.000006426014,0.0002143946,0.00001210417],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008899107,"about_ca_system_score_gemma":0.00006382837,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008598232,"about_ca_topic_score_gemma":0.0002656477,"domain_scores_codex":[0.9977809,0.0003108757,0.0006703339,0.0004976201,0.0004261829,0.0003140764],"domain_scores_gemma":[0.998749,0.00008703457,0.0002572644,0.0005732175,0.0001878912,0.0001456348],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.002153405,0.02330417,0.006368637,0.004670491,0.002639809,0.0001140152,0.1040554,0.3802366,0.2420561,0.07565103,0.004158005,0.1545924],"study_design_scores_gemma":[0.002767296,0.0009724105,0.01292809,0.001521981,0.0002279663,0.0001040364,0.003037572,0.7878017,0.1893399,0.0001390118,0.0002752506,0.0008847645],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1769188,0.0001553065,0.8207852,0.0002228509,0.0007911043,0.0006040579,0.0001363876,0.000106753,0.0002795411],"genre_scores_gemma":[0.9890704,0.00008748692,0.01046739,0.000122063,0.00003376208,0.0001360343,0.00001293953,0.00001903541,0.00005090099],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8121516,"threshold_uncertainty_score":0.9180269,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02770676403880055,"score_gpt":0.2670120190335478,"score_spread":0.2393052549947472,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}