Anulamento Duplo de Frobenius para Primos Gêmeos em Curvas Elípticas Não-CM e Proposta de Criptografia por Sincronia de Frobenius (FSC)

Anulamento Duplo de Frobenius para Primos Gêmeos em Curvas Elípticas Não-CM e Proposta de Criptografia por Sincronia de Frobenius (FSC) | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 16 March 2026 V1 Latest version Share on Anulamento Duplo de Frobenius para Primos Gêmeos em Curvas Elípticas Não-CM e Proposta de Criptografia por Sincronia de Frobenius (FSC) Author : Rodolfo Carneiro Moroz 0009-0007-7014-552X [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.177368700.06631923/v1 103 views 50 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Este trabalho investiga o anulamento simultâneo dos traços de Frobenius 𝑎 𝑝 ( 𝐸 ) = 0, 𝑎 𝑝 +2 ( 𝐸 ) = 0 para curvas elípticas 𝐸 /ℚ e primos gêmeos. Extensas computações sugerem que tais coincidências são extremamente raras para curvas sem multiplicação complexa (não-CM) e inexistentes para curvas com CM, devido a obstruções de congruência modular. Formalizou-se esse fenômeno por meio da introdução do conceito de primo gêmeo de aniquilação dupla de Frobenius (par-FD) para uma curva. Experimentos realizados para 𝑝 < 5000 identificaram exatamente um par para uma família simples de curvas não-CM, a saber ( 𝑝, 𝑝 + 2) = (17,19) para as curvas 𝐸: 𝑦 2 = 𝑥 3 + A(p) 𝑥 + B(p). O trabalho propõe, então, diversas conjecturas sobre a unicidade estrutural, a finitude e a caracterização pela teoria de Hecke dos pares-FD, sugerindo ainda uma nova proposta para o uso desse possível invariante em aplicações criptográficas. Supplementary Material File (artigo_elípticas.pdf) Download 242.67 KB Information & Authors Information Version history V1 Version 1 16 March 2026 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords elliptic curves frobenius trace hecke eigenvalues post-quantum cryptography twin primes Authors Affiliations Rodolfo Carneiro Moroz 0009-0007-7014-552X [email protected] View all articles by this author Metrics & Citations Metrics Article Usage 103 views 50 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Rodolfo Carneiro Moroz. Anulamento Duplo de Frobenius para Primos Gêmeos em Curvas Elípticas Não-CM e Proposta de Criptografia por Sincronia de Frobenius (FSC). Authorea . 16 March 2026. DOI: https://doi.org/10.22541/au.177368700.06631923/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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