{"id":"W3036855880","doi":"10.1515/jmc-2015-0057","title":"A subexponential-time, polynomial quantum space algorithm for inverting the CM group action","year":2020,"lang":"en","type":"article","venue":"Journal of Mathematical Cryptology","topic":"Cryptography and Residue Arithmetic","field":"Computer Science","cited_by":9,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"Banff International Research Station for Mathematical Innovation and Discovery; Canada First Research Excellence Fund; Public Works and Government Services Canada; Royal Bank of Canada","keywords":"Isogeny; Mathematics; Polynomial; Group (periodic table); Quantum algorithm; Action (physics); Quantum computer; Time complexity; Quantum; Cryptosystem; Multiplication (music); Group action; Discrete mathematics; Space (punctuation); Algorithm; Algebra over a field; Elliptic curve; Combinatorics; Pure mathematics; Computer science; Cryptography; Mathematical analysis; Quantum mechanics; Physics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009853767,0.0004744512,0.0005533867,0.0007566578,0.0007527127,0.001522966,0.001494901,0.001050868,0.008019126],"category_scores_gemma":[0.002843625,0.0002151454,0.0006169025,0.0008606272,0.001481856,0.002543814,0.002297413,0.001923816,0.001601856],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001532129,"about_ca_system_score_gemma":0.002494883,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001528151,"about_ca_topic_score_gemma":0.001801477,"domain_scores_codex":[0.9989039,0.0002065576,0.00006384569,0.0002596948,0.000368649,0.0001973464],"domain_scores_gemma":[0.998498,0.0005324663,0.0001131902,0.0005317701,0.0002137273,0.0001108409],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.001056563,0.0004510393,0.001921215,0.0002234397,0.00006722435,0.0002057367,0.0006523886,0.02921621,0.043671,0.6130849,0.01090769,0.2985427],"study_design_scores_gemma":[0.0005800606,0.0004001162,0.0007946864,0.00003925492,0.00007240261,0.000362633,0.000294769,0.4615394,0.05832338,0.4527942,0.02469962,0.00009941374],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.0954126,0.0002804136,0.8771147,0.001557337,0.0001671848,0.0002208896,0.000144348,0.002873375,0.02222917],"genre_scores_gemma":[0.6212695,0.0001494574,0.3686518,0.0003175828,0.00009773874,0.00014696,0.0002374201,0.0002172127,0.008912273],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.008019126,"threshold_uncertainty_score":0.02682662,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03095288594065633,"score_gpt":0.2680828124425766,"score_spread":0.2371299265019203,"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."}}