{"id":"W4391661073","doi":"10.1090/conm/796/16008","title":"Deuring for the people: Supersingular elliptic curves with prescribed endomorphism ring in general characteristic","year":2024,"lang":"en","type":"other","venue":"Contemporary mathematics - American Mathematical Society","topic":"Cryptography and Residue Arithmetic","field":"Computer Science","cited_by":15,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Nederlandse Organisatie voor Wetenschappelijk Onderzoek; Academia Sinica","keywords":"Supersingular elliptic curve; Endomorphism ring; Mathematics; Schoof's algorithm; Counting points on elliptic curves; Endomorphism; Elliptic curve; Ring (chemistry); Elliptic curve point multiplication; Cryptography; Edwards curve; Polynomial ring; Modular elliptic curve; Twists of curves; Algebra over a field; Polynomial; Number theory; Order (exchange); Discrete mathematics; Pure mathematics; Algorithm; Quarter period","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.000772901,0.0007052443,0.001337246,0.0001865935,0.0001416349,0.000341502,0.001455289,0.0001804236,0.00007792823],"category_scores_gemma":[0.0001395465,0.0004522048,0.0006377351,0.001006207,0.0006750464,0.0001552973,0.0003729021,0.0006292204,0.00007013958],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007338882,"about_ca_system_score_gemma":0.000189083,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001005117,"about_ca_topic_score_gemma":0.00002787695,"domain_scores_codex":[0.996885,0.00009634398,0.0008118135,0.0008618572,0.0006597794,0.0006852131],"domain_scores_gemma":[0.9967584,0.001162015,0.0005210161,0.001319356,0.00006059675,0.0001786372],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00005494423,0.002438451,0.000214983,0.07046729,0.004636812,0.0003296692,0.04480506,0.00003728522,0.0003893685,0.3085173,0.5648545,0.003254333],"study_design_scores_gemma":[0.004913216,0.001304526,0.0003080958,0.05598155,0.00224761,0.0006033289,0.006808626,0.6729797,0.0002550617,0.1343903,0.1137514,0.006456578],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.0003999789,0.02095678,0.9346507,0.002424956,0.0003483927,0.004081005,0.00008713503,0.0008981192,0.03615296],"genre_scores_gemma":[0.03461458,0.003491464,0.8434311,0.001722219,0.0009687614,0.002756168,0.00008190515,0.002165023,0.1107688],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.6729424,"threshold_uncertainty_score":0.999793,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02011824785244935,"score_gpt":0.2495519920542751,"score_spread":0.2294337442018258,"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."}}