{"id":2701,"date":"2016-07-01T00:00:09","date_gmt":"2016-06-30T22:00:09","guid":{"rendered":"https:\/\/cyberawareness.sk\/?p=2701"},"modified":"2024-10-28T14:29:11","modified_gmt":"2024-10-28T13:29:11","slug":"problem-faktorizacie-v-asymetrickej-kryptografii","status":"publish","type":"post","link":"https:\/\/cyberawareness.sk\/en\/2016\/07\/01\/problem-faktorizacie-v-asymetrickej-kryptografii\/","title":{"rendered":"Probl\u00e9m faktoriz\u00e1cie v asymetrickej kryptografii"},"content":{"rendered":"<div data-elementor-type=\"wp-post\" data-elementor-id=\"2701\" class=\"elementor elementor-2701\">\n\t\t\t\t<div class=\"elementor-element elementor-element-fa18013 e-flex e-con-boxed e-con e-parent\" data-id=\"fa18013\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-6e108e7 e-flex e-con-boxed e-con e-child\" data-id=\"6e108e7\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-749fbad elementor-widget elementor-widget-ucaddon_square_icon_box\" data-id=\"749fbad\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"ucaddon_square_icon_box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\n<!-- start Icon Box -->\n\t\t<link id='font-awesome-css' href='https:\/\/cyberawareness.sk\/wp-content\/plugins\/unlimited-elements-for-elementor\/assets_libraries\/font-awesome6\/fontawesome-all.min.css' type='text\/css' rel='stylesheet' >\n\t\t<link id='font-awesome-4-shim-css' href='https:\/\/cyberawareness.sk\/wp-content\/plugins\/unlimited-elements-for-elementor\/assets_libraries\/font-awesome6\/fontawesome-v4-shims.min.css' type='text\/css' rel='stylesheet' >\n\t\t<link id='uc_ac_assets_file_blox_boxed_small_square_icon_box_css_0-css' href='https:\/\/cyberawareness.sk\/wp-content\/uploads\/ac_assets\/blox-boxed-small-square-icon-box\/blox-boxed-small-square-icon-box.css' type='text\/css' rel='stylesheet' >\n\n<style>\/* widget: Icon Box *\/\n\n#uc_square_icon_box_elementor_749fbad * { \n\tbox-sizing: border-box; \n}\n\n#uc_square_icon_box_elementor_749fbad{\n\tfont-family: inherit;\n    transition:0.3s;\n    position:relative;\n}\n\n#uc_square_icon_box_elementor_749fbad .blox-boxed-small-square-icon-box-icon{\n\t\n\tposition:relative;\n    display:flex;\n    justify-content:center;\n    align-items:center;\n    transform:rotate(0deg);\n    z-index:2;\n}\n#uc_square_icon_box_elementor_749fbad .ue-icon {\n  display:inline-block;\n}\n#uc_square_icon_box_elementor_749fbad .blox-boxed-small-square-icon-box-icon > div{\n\t\n\tposition:relative;\n    display:flex;\n    justify-content:center;\n    align-items:center;\n    transform:rotate(-0deg);\n}\n#uc_square_icon_box_elementor_749fbad .ue-icon-inner{\n    line-height:1em;\n\t} \t\n\n\n#uc_square_icon_box_elementor_749fbad .ue-icon-inner svg{\n    height:1em;\n    width:1em;\n\t} \t\n\t\n.blox-boxed-small-square-icon-box-heading{\n\tfont-size:21px;\n\t}\n\n\n#uc_square_icon_box_elementor_749fbad:hover\n{\n  position:relative;\n  z-index:1;\n}\n\n\n#uc_square_icon_box_elementor_749fbad .ue_box_button\n{\n  text-align:center;\n  text-decoration:none;\n  display:inline-block;\n  transition:0.3s;\n}\n\n\n#uc_square_icon_box_elementor_749fbad span.line\n{\n  display:block;\n  position:absolute;\n  top:0;\n  left:0;\n  width:0px;\n  transition:0.3s;\n}\n\n#uc_square_icon_box_elementor_749fbad:hover span.line\n{\n  width:100%;\n}\n\n#uc_square_icon_box_elementor_749fbad .ue-title-separator span\n{\n  display:inline-block;\n  transition:0.3s;\n}\n\n\n\n\n\n<\/style>\n\n<div class=\"square_icon_box\" id=\"uc_square_icon_box_elementor_749fbad\">\n  \n  \t\t  \n  \n              <div class=\"ue-icon\">\n       <a style=\"display:inline-block; text-decoration:none;\" href=\"https:\/\/cyberawareness.sk\/wp-content\/uploads\/2024\/10\/7CAE74F7081A4700B5487F1C9464E0A4.pdf\" >         <div class=\"blox-boxed-small-square-icon-box-icon\" style=\"background-color: ;\">\n           <div class=\"ue-icon-inner\"><i class='fas fa-book'><\/i><\/div>\n         <\/div>\n       <\/a>       <\/div>\n         \n  \t\t        <div class=\"blox-boxed-small-square-icon-box-heading\">\n        \tPr\u00e1ca\n        <\/div>\n          \n  \t\t  \n  \n          \n  \t\t        \n          \n  \t\t  \n<\/div>\n<!-- end Icon Box -->\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8e851db elementor-widget elementor-widget-text-editor\" data-id=\"8e851db\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><strong>Autor: <\/strong>J\u00e1n Kotrady<br \/><strong>\u0160kolite\u013e: <\/strong>RNDr. Rastislav Krivo\u0161-Bellu\u0161 PhD.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e5a0a23 elementor-widget elementor-widget-heading\" data-id=\"e5a0a23\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Abstrakt<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b77c4c2 elementor-widget elementor-widget-text-editor\" data-id=\"b77c4c2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Cie\u013eom pr\u00e1ce je analyzova\u0165 pou\u017eitie probl\u00e9mu faktoriz\u00e1cie v asymetrickej kryptografii. Pr\u00e1ca popisuje jednotliv\u00e9 faktoriza\u010dn\u00e9 algoritmy, analyzuje ich \u010dasov\u00fa zlo\u017eitos\u0165 a porovn\u00e1va faktoriza\u010dn\u00e9 algoritmy v kontexte asymetrickej kryptografie implementovan\u00edm vybran\u00fdch faktoriza\u010dn\u00fdch algoritmov. Pr\u00e1ca je venovan\u00e1 Fermatovej faktoriz\u00e1cii, Pollard p-1 a Pollard rho faktoriza\u010dn\u00fdm algoritmom. Vybran\u00e9 faktoriza\u010dn\u00e9 algoritmy s\u00fa porovn\u00e1van\u00e9 na vopred pripravenej vzorke d\u00e1t so \u0161pecifick\u00fdmi vlastnos\u0165ami. Okrem klasick\u00fdch met\u00f3d faktoriz\u00e1cie sa pr\u00e1ca zaober\u00e1 aj faktoriz\u00e1ciou algoritmom najv\u00e4\u010d\u0161ieho spolo\u010dn\u00e9ho delite\u013ea. T\u00e1to \u010das\u0165 pr\u00e1ce poukazuje na st\u00e1le existuj\u00faci probl\u00e9m chybne generovan\u00fdch k\u013e\u00fa\u010dov a zaznamen\u00e1va signifikantn\u00e9 v\u00fdsledky faktoriz\u00e1cie algoritmom najv\u00e4\u010d\u0161ieho spolo\u010dn\u00e9ho delite\u013ea na re\u00e1lnej vzorke verejn\u00fdch modulov. V pr\u00e1ci sa n\u00e1m podarilo faktorizova\u0165 a\u017e 66 modulov, 1024 a\u017e 2048 bitov\u00e9ho kryptografick\u00e9ho syst\u00e9mu RSA, \u010do st\u00e1le znamen\u00e1 ve\u013ek\u00e9 bezpe\u010dnostn\u00e9 riziko kryptografick\u00e9ho syst\u00e9mu RSA.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e39a89a elementor-widget elementor-widget-heading\" data-id=\"e39a89a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Ciele<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-05fb267 elementor-widget elementor-widget-text-editor\" data-id=\"05fb267\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Zatia\u013e nezverejnen\u00e9<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-89aa96b elementor-widget elementor-widget-heading\" data-id=\"89aa96b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Literat\u00fara<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d149794 elementor-widget elementor-widget-text-editor\" data-id=\"d149794\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Zatia\u013e nezverejnen\u00e9<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a432df6 elementor-widget elementor-widget-heading\" data-id=\"a432df6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Priebeh pr\u00e1ce<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f13991a elementor-widget elementor-widget-text-editor\" data-id=\"f13991a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Zatia\u013e nezverejnen\u00e9<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Autor: J\u00e1n Kotrady<br \/>\n\u0160kolite\u013e: RNDr. Rastislav Krivo\u0161-Bellu\u0161 PhD.<\/p>","protected":false},"author":8,"featured_media":2397,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ocean_post_layout":"full-width","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"","ocean_second_sidebar":"","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"","ocean_custom_header_template":"","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"","ocean_menu_typo_font_family":"","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"default","ocean_disable_heading":"default","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"default","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":"","ocean_post_oembed":"","ocean_post_self_hosted_media":"","ocean_post_video_embed":"","ocean_link_format":"","ocean_link_format_target":"self","ocean_quote_format":"","ocean_quote_format_link":"post","ocean_gallery_link_images":"on","ocean_gallery_id":[],"footnotes":""},"categories":[12],"tags":[],"class_list":["post-2701","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-bakalarske-prace","entry","has-media"],"_links":{"self":[{"href":"https:\/\/cyberawareness.sk\/en\/wp-json\/wp\/v2\/posts\/2701","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cyberawareness.sk\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cyberawareness.sk\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cyberawareness.sk\/en\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/cyberawareness.sk\/en\/wp-json\/wp\/v2\/comments?post=2701"}],"version-history":[{"count":5,"href":"https:\/\/cyberawareness.sk\/en\/wp-json\/wp\/v2\/posts\/2701\/revisions"}],"predecessor-version":[{"id":2707,"href":"https:\/\/cyberawareness.sk\/en\/wp-json\/wp\/v2\/posts\/2701\/revisions\/2707"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/cyberawareness.sk\/en\/wp-json\/wp\/v2\/media\/2397"}],"wp:attachment":[{"href":"https:\/\/cyberawareness.sk\/en\/wp-json\/wp\/v2\/media?parent=2701"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cyberawareness.sk\/en\/wp-json\/wp\/v2\/categories?post=2701"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cyberawareness.sk\/en\/wp-json\/wp\/v2\/tags?post=2701"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}