{"id":"W2791996780","doi":"10.1007/s12095-018-0292-7","title":"Compositional inverses of permutation polynomials of the form xrh(xs) over finite fields","year":2018,"lang":"en","type":"article","venue":"Cryptography and Communications","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":28,"is_retracted":false,"has_abstract":false,"ca_institutions":"Carleton University","funders":"National Key Research and Development Program of China; Program for New Century Excellent Talents in University","keywords":"Permutation (music); Finite field; Mathematics; Combinatorics; Polynomial; Inverse; Discrete mathematics; Cyclic permutation; Field (mathematics); Permutation matrix; Pure mathematics; Symmetric group; Physics","routes":{"ca_aff":true,"ca_fund":false,"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":[0.0002069628,0.00007860843,0.0001151931,0.000154871,0.0003880705,0.00003104827,0.001151718,0.00005143589,0.00002618006],"category_scores_gemma":[0.00002587266,0.00006335338,0.0001489046,0.0007085735,0.0007569667,0.0002168945,0.0004427361,0.00009931812,9.62409e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000003016688,"about_ca_system_score_gemma":0.00003051071,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003238344,"about_ca_topic_score_gemma":0.00004486197,"domain_scores_codex":[0.9992961,0.0001336733,0.0002350183,0.0001164379,0.0001247442,0.00009399411],"domain_scores_gemma":[0.998127,0.0003916115,0.000173021,0.001130538,0.0001455238,0.00003230246],"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":[0.00001318033,0.0001100107,0.009207386,0.00001389173,0.00004688478,2.88907e-8,0.002716989,0.000003263568,0.002911336,0.9786161,0.0002116708,0.006149272],"study_design_scores_gemma":[0.0008987414,0.0004308589,0.1940879,0.0002152325,0.00009458161,0.000008665864,0.0006117236,0.005272035,0.0272478,0.7615936,0.00918753,0.0003513468],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7702626,0.0008902376,0.2134214,0.00247458,0.0002477513,0.0002994135,0.00006445935,0.00006994532,0.01226958],"genre_scores_gemma":[0.9882365,0.0001272967,0.01131297,0.0002804662,0.00001716945,0.00001250373,0.000006275907,0.000002958018,0.000003837922],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2179739,"threshold_uncertainty_score":0.2984764,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01906510945952677,"score_gpt":0.2589763174456607,"score_spread":0.2399112079861339,"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."}}