{"id":8957,"date":"2024-11-22T10:07:27","date_gmt":"2024-11-22T03:07:27","guid":{"rendered":"https:\/\/onesme.vn\/blog\/?p=8957"},"modified":"2025-11-27T23:52:24","modified_gmt":"2025-11-27T16:52:24","slug":"rsa-la-gi-cach-thuc-hoat-dong","status":"publish","type":"post","link":"https:\/\/onesme.vn\/blog\/tin-tuc-su-kien\/rsa-la-gi-cach-thuc-hoat-dong.html","title":{"rendered":"RSA l\u00e0 g\u00ec? C\u00e1ch th\u1ee9c ho\u1ea1t \u0111\u1ed9ng, \u1ee9ng d\u1ee5ng trong b\u1ea3o m\u1eadt\u00a0"},"content":{"rendered":"<p><strong>RSA l\u00e0 g\u00ec? <\/strong>\u0110\u00e2y l\u00e0 m\u1ed9t trong nh\u1eefng thu\u1eadt to\u00e1n m\u00e3 h\u00f3a ph\u1ed5 bi\u1ebfn nh\u1ea5t \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i trong b\u1ea3o m\u1eadt d\u1eef li\u1ec7u s\u1ed1. C\u00f4ng ngh\u1ec7 RSA gi\u00fap \u0111\u1ea3m b\u1ea3o m\u1ed9t ng\u01b0\u1eddi d\u00f9ng khi t\u1ea1o ra ch\u1eef k\u00fd s\u1ed1 th\u00ec ch\u1eef k\u00fd \u0111\u00f3 l\u00e0 duy nh\u1ea5t. V\u00ec v\u1eady, c\u00f4ng ngh\u1ec7 n\u00e0y n\u00e2ng \u0111\u1ed9 an to\u00e0n c\u1ee7a th\u00f4ng tin l\u00ean m\u1ee9c r\u1ea5t cao.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_43 ez-toc-wrap-left counter-hierarchy ez-toc-counter ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">M\u1ee5c l\u1ee5c<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" area-label=\"ez-toc-toggle-icon-1\"><label for=\"item-6a062eb7484e2\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #000000;color:#000000\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input  type=\"checkbox\" id=\"item-6a062eb7484e2\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/onesme.vn\/blog\/tin-tuc-su-kien\/rsa-la-gi-cach-thuc-hoat-dong.html\/#RSA_la_gi\" title=\"RSA l\u00e0 g\u00ec?\">RSA l\u00e0 g\u00ec?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/onesme.vn\/blog\/tin-tuc-su-kien\/rsa-la-gi-cach-thuc-hoat-dong.html\/#RSA_la_viet_tat_cua_tu_gi\" title=\"RSA l\u00e0 vi\u1ebft t\u1eaft c\u1ee7a t\u1eeb g\u00ec?\">RSA l\u00e0 vi\u1ebft t\u1eaft c\u1ee7a t\u1eeb g\u00ec?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/onesme.vn\/blog\/tin-tuc-su-kien\/rsa-la-gi-cach-thuc-hoat-dong.html\/#Ma_hoa_RSA_la_gi\" title=\"M\u00e3 h\u00f3a RSA l\u00e0 g\u00ec?\">M\u00e3 h\u00f3a RSA l\u00e0 g\u00ec?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/onesme.vn\/blog\/tin-tuc-su-kien\/rsa-la-gi-cach-thuc-hoat-dong.html\/#Thuat_toan_RSA_la_gi\" title=\"Thu\u1eadt to\u00e1n RSA l\u00e0 g\u00ec?\">Thu\u1eadt to\u00e1n RSA l\u00e0 g\u00ec?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/onesme.vn\/blog\/tin-tuc-su-kien\/rsa-la-gi-cach-thuc-hoat-dong.html\/#He_ma_hoa_RSA_hoat_dong_nhu_the_nao\" title=\"H\u1ec7 m\u00e3 h\u00f3a RSA ho\u1ea1t \u0111\u1ed9ng nh\u01b0 th\u1ebf n\u00e0o?\">H\u1ec7 m\u00e3 h\u00f3a RSA ho\u1ea1t \u0111\u1ed9ng nh\u01b0 th\u1ebf n\u00e0o?<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/onesme.vn\/blog\/tin-tuc-su-kien\/rsa-la-gi-cach-thuc-hoat-dong.html\/#Tao_khoa\" title=\"T\u1ea1o kh\u00f3a\">T\u1ea1o kh\u00f3a<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/onesme.vn\/blog\/tin-tuc-su-kien\/rsa-la-gi-cach-thuc-hoat-dong.html\/#Ma_hoa\" title=\"M\u00e3 h\u00f3a\">M\u00e3 h\u00f3a<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/onesme.vn\/blog\/tin-tuc-su-kien\/rsa-la-gi-cach-thuc-hoat-dong.html\/#_Giai_ma\" title=\"\u00a0Gi\u1ea3i m\u00e3\">\u00a0Gi\u1ea3i m\u00e3<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/onesme.vn\/blog\/tin-tuc-su-kien\/rsa-la-gi-cach-thuc-hoat-dong.html\/#Nguyen_ly_bao_mat\" title=\"Nguy\u00ean l\u00fd b\u1ea3o m\u1eadt\">Nguy\u00ean l\u00fd b\u1ea3o m\u1eadt<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/onesme.vn\/blog\/tin-tuc-su-kien\/rsa-la-gi-cach-thuc-hoat-dong.html\/#RSA_ung_dung_trong_linh_vuc_nao\" title=\"RSA \u1ee9ng d\u1ee5ng trong l\u0129nh v\u1ef1c n\u00e0o?\">RSA \u1ee9ng d\u1ee5ng trong l\u0129nh v\u1ef1c n\u00e0o?<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"RSA_la_gi\"><\/span><b>RSA l\u00e0 g\u00ec?<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><b>RSA l\u00e0 g\u00ec? <\/b>\u0110\u00e2y l\u00e0 m\u1ed9t trong nh\u1eefng thu\u1eadt to\u00e1n m\u00e3 h\u00f3a ph\u1ed5 bi\u1ebfn nh\u1ea5t \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i trong b\u1ea3o m\u1eadt d\u1eef li\u1ec7u s\u1ed1. C\u00f4ng ngh\u1ec7 RSA gi\u00fap \u0111\u1ea3m b\u1ea3o m\u1ed9t ng\u01b0\u1eddi d\u00f9ng khi t\u1ea1o ra <strong><a href=\"https:\/\/onesme.vn\/blog\/san-pham\/chu-ky-so-tu-xa-vnpt.html\" target=\"_blank\" rel=\"noopener\">ch\u1eef k\u00fd s\u1ed1<\/a><\/strong> n\u00e0o \u0111\u00f3 th\u00ec ch\u1eef k\u00fd \u0111\u00f3 s\u1ebd l\u00e0 duy nh\u1ea5t. Ng\u01b0\u1eddi kh\u00e1c kh\u00f4ng th\u1ec3 gi\u1ea3 m\u1ea1o, ho\u1eb7c t\u1ea9y x\u00f3a. Ch\u1ec9 duy nh\u1ea5t ng\u01b0\u1eddi s\u1edf h\u1eefu kh\u00f3a b\u00ed m\u1eadt m\u1edbi c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng v\u00e0 t\u1ea1o ch\u1eef k\u00fd s\u1ed1 \u0111\u00f3.<\/p>\n<figure id=\"attachment_8958\" aria-describedby=\"caption-attachment-8958\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-8958 size-full\" title=\"RSA l\u00e0 g\u00ec m\u00e0 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i trong b\u1ea3o m\u1eadt d\u1eef li\u1ec7u s\u1ed1?\" src=\"https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-1.jpg\" alt=\"RSA l\u00e0 g\u00ec m\u00e0 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i trong b\u1ea3o m\u1eadt d\u1eef li\u1ec7u s\u1ed1?\" width=\"800\" height=\"532\" srcset=\"https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-1.jpg 800w, https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-1-300x200.jpg 300w, https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-1-768x511.jpg 768w, https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-1-150x100.jpg 150w, https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-1-696x463.jpg 696w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><figcaption id=\"caption-attachment-8958\" class=\"wp-caption-text\">RSA l\u00e0 g\u00ec m\u00e0 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i trong b\u1ea3o m\u1eadt d\u1eef li\u1ec7u s\u1ed1?<\/figcaption><\/figure>\n<p>Thu\u1eadt to\u00e1n RSA, ph\u00e1t tri\u1ec3n b\u1edfi c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc Ron Rivest, Adi Shamir v\u00e0 Leonard Adleman v\u00e0o n\u0103m 1977, l\u00e0 vi\u1ebft t\u1eaft c\u1ee7a c\u00e1c ch\u1eef c\u00e1i \u0111\u1ea7u c\u1ee7a t\u00ean h\u1ecd. RSA d\u1ef1a tr\u00ean nguy\u00ean t\u1eafc m\u00e3 h\u00f3a kh\u00f3a c\u00f4ng khai, n\u01a1i m\u1ed9t kh\u00f3a \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 m\u00e3 h\u00f3a th\u00f4ng tin v\u00e0 m\u1ed9t kh\u00f3a kh\u00e1c \u0111\u1ec3 gi\u1ea3i m\u00e3.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"RSA_la_viet_tat_cua_tu_gi\"><\/span><b>RSA l\u00e0 vi\u1ebft t\u1eaft c\u1ee7a t\u1eeb g\u00ec?<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><b>RSA<\/b> l\u00e0 t\u1eeb vi\u1ebft t\u1eaft t\u00ean c\u1ee7a ba nh\u00e0 s\u00e1ng l\u1eadp: Ron Rivest, Adi Shamir, v\u00e0 Leonard Adleman. H\u1ecd \u0111\u00e3 ph\u00e1t tri\u1ec3n thu\u1eadt to\u00e1n n\u00e0y \u0111\u1ec3 gi\u1ea3i quy\u1ebft b\u00e0i to\u00e1n b\u1ea3o m\u1eadt trong vi\u1ec7c truy\u1ec1n t\u1ea3i th\u00f4ng tin qua c\u00e1c h\u1ec7 th\u1ed1ng m\u1ea1ng, \u0111\u1ea3m b\u1ea3o an to\u00e0n d\u1eef li\u1ec7u v\u00e0 th\u00f4ng tin c\u00e1 nh\u00e2n.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Ma_hoa_RSA_la_gi\"><\/span><b>M\u00e3 h\u00f3a RSA l\u00e0 g\u00ec?<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>M\u00e3 h\u00f3a RSA l\u00e0 qu\u00e1 tr\u00ecnh \u00e1p d\u1ee5ng thu\u1eadt to\u00e1n RSA \u0111\u1ec3 m\u00e3 h\u00f3a d\u1eef li\u1ec7u. Thu\u1eadt to\u00e1n n\u00e0y s\u1eed d\u1ee5ng c\u00e1c ph\u00e9p t\u00ednh s\u1ed1 h\u1ecdc ph\u1ee9c t\u1ea1p, \u0111\u1eb7c bi\u1ec7t l\u00e0 vi\u1ec7c ph\u00e2n t\u00edch c\u00e1c s\u1ed1 nguy\u00ean l\u1edbn th\u00e0nh c\u00e1c th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1, nh\u1eb1m \u0111\u1ea3m b\u1ea3o an to\u00e0n v\u00e0 b\u1ea3o m\u1eadt cho qu\u00e1 tr\u00ecnh m\u00e3 h\u00f3a v\u00e0 gi\u1ea3i m\u00e3. Ph\u01b0\u01a1ng ph\u00e1p n\u00e0y d\u1ef1a tr\u00ean \u0111\u1ed9 kh\u00f3 c\u1ee7a vi\u1ec7c gi\u1ea3i quy\u1ebft b\u00e0i to\u00e1n ph\u00e2n t\u00edch nguy\u00ean t\u1ed1.<\/p>\n<p>\u0110i\u1ec3m \u0111\u1eb7c bi\u1ec7t c\u1ee7a RSA l\u00e0 t\u00ednh b\u1ea3o m\u1eadt r\u1ea5t cao, d\u1ef1a tr\u00ean vi\u1ec7c gi\u1ea3i m\u00e3 th\u00f4ng tin m\u00e0 kh\u00f4ng c\u00f3 kh\u00f3a ri\u00eang l\u00e0 c\u1ef1c k\u1ef3 kh\u00f3 kh\u0103n.<\/p>\n<figure id=\"attachment_8960\" aria-describedby=\"caption-attachment-8960\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-8960\" src=\"https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-2.jpg\" alt=\"\" width=\"800\" height=\"499\" srcset=\"https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-2.jpg 800w, https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-2-300x187.jpg 300w, https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-2-768x479.jpg 768w, https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-2-150x94.jpg 150w, https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-2-696x434.jpg 696w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><figcaption id=\"caption-attachment-8960\" class=\"wp-caption-text\">RSA c\u00f3 t\u00ednh b\u1ea3o m\u1eadt r\u1ea5t cao<\/figcaption><\/figure>\n<h2><span class=\"ez-toc-section\" id=\"Thuat_toan_RSA_la_gi\"><\/span><b>Thu\u1eadt to\u00e1n RSA l\u00e0 g\u00ec?<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><b>Thu\u1eadt to\u00e1n RSA l\u00e0 g\u00ec?<\/b> \u0110\u00e2y l\u00e0 ho\u1ea1t \u0111\u1ed9ng d\u1ef1a tr\u00ean nguy\u00ean l\u00fd c\u1ee7a to\u00e1n h\u1ecdc, \u0111\u1eb7c bi\u1ec7t l\u00e0 b\u00e0i to\u00e1n ph\u00e2n t\u00edch c\u00e1c s\u1ed1 nguy\u00ean t\u1ed1 l\u1edbn. C\u1ee5 th\u1ec3, RSA s\u1eed d\u1ee5ng hai s\u1ed1 nguy\u00ean t\u1ed1 l\u1edbn \u0111\u1ec3 t\u1ea1o th\u00e0nh kh\u00f3a c\u00f4ng khai v\u00e0 kh\u00f3a ri\u00eang. Khi m\u1ed9t th\u00f4ng \u0111i\u1ec7p \u0111\u01b0\u1ee3c m\u00e3 h\u00f3a b\u1eb1ng kh\u00f3a c\u00f4ng khai, ch\u1ec9 kh\u00f3a ri\u00eang t\u01b0\u01a1ng \u1ee9ng m\u1edbi c\u00f3 th\u1ec3 gi\u1ea3i m\u00e3 \u0111\u01b0\u1ee3c. Quy tr\u00ecnh bao g\u1ed3m ba b\u01b0\u1edbc ch\u00ednh: t\u1ea1o kh\u00f3a, m\u00e3 h\u00f3a, v\u00e0 gi\u1ea3i m\u00e3.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"He_ma_hoa_RSA_hoat_dong_nhu_the_nao\"><\/span><b>H\u1ec7 m\u00e3 h\u00f3a RSA ho\u1ea1t \u0111\u1ed9ng nh\u01b0 th\u1ebf n\u00e0o?<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>RSA ho\u1ea1t \u0111\u1ed9ng tr\u00ean nguy\u00ean t\u1eafc m\u00e3 h\u00f3a b\u1eb1ng kh\u00f3a c\u00f4ng khai v\u00e0 gi\u1ea3i m\u00e3 b\u1eb1ng kh\u00f3a ri\u00eang t\u01b0. \u0110\u00e2y l\u00e0 n\u1ec1n t\u1ea3ng c\u1ee7a nhi\u1ec1u \u1ee9ng d\u1ee5ng b\u1ea3o m\u1eadt nh\u01b0 HTTPS, ch\u1eef k\u00fd s\u1ed1, v\u00e0 truy\u1ec1n t\u1ea3i d\u1eef li\u1ec7u an to\u00e0n. Quy tr\u00ecnh c\u1ee7a RSA g\u1ed3m 3 giai \u0111o\u1ea1n ch\u00ednh: T\u1ea1o kh\u00f3a, M\u00e3 h\u00f3a, v\u00e0 Gi\u1ea3i m\u00e3.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Tao_khoa\"><\/span><b>T\u1ea1o kh\u00f3a<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Giai \u0111o\u1ea1n t\u1ea1o kh\u00f3a di\u1ec5n ra nh\u01b0 sau:<\/p>\n<ul>\n<li>Qu\u00e1 tr\u00ecnh b\u1eaft \u0111\u1ea7u b\u1eb1ng vi\u1ec7c t\u1ea1o c\u1eb7p kh\u00f3a g\u1ed3m kh\u00f3a c\u00f4ng khai (public key) v\u00e0 kh\u00f3a b\u00ed m\u1eadt (private key).<\/li>\n<li>Ch\u1ecdn hai s\u1ed1 nguy\u00ean t\u1ed1 l\u1edbn p v\u00e0 q.<\/li>\n<li>T\u00ednh to\u00e1n modulus (n) b\u1eb1ng c\u00e1ch nh\u00e2n p v\u00e0 q: n = p * q.<\/li>\n<li>T\u00ednh to\u00e1n h\u00e0m Euler (phi) c\u1ee7a n: phi = (p \u2013 1) * (q \u2013 1).<\/li>\n<li>Ch\u1ecdn m\u1ed9t s\u1ed1 nguy\u00ean e sao cho 1 &lt; e &lt; phi v\u00e0 e l\u00e0 s\u1ed1 nguy\u00ean t\u1ed1 c\u00f9ng nhau v\u1edbi phi.<\/li>\n<li>C\u00e1ch t\u00ednh kh\u00f3a b\u00ed m\u1eadt d b\u1eb1ng c\u00e1ch t\u00ecm ngh\u1ecbch \u0111\u1ea3o modular c\u1ee7a e theo modulo phi nh\u01b0 sau: d = e^(-1) mod phi.<\/li>\n<li>Kh\u00f3a c\u00f4ng khai g\u1ed3m c\u1eb7p (n, e), trong khi kh\u00f3a b\u00ed m\u1eadt bao g\u1ed3m c\u1eb7p (n, d).<\/li>\n<li class=\"mceTemp\">\n<p><figure id=\"attachment_8961\" aria-describedby=\"caption-attachment-8961\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-8961 size-full\" title=\"C\u01a1 ch\u1ebf ho\u1ea1t \u0111\u1ed9ng c\u1ee7a RSA d\u1ef1a tr\u00ean vi\u1ec7c s\u1eed d\u1ee5ng 2 kh\u00f3a kh\u00e1c nhau g\u1ed3m kh\u00f3a c\u00f4ng khai v\u00e0 kh\u00f3a b\u00ed m\u1eadt.\" src=\"https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-3.jpg\" alt=\"C\u01a1 ch\u1ebf ho\u1ea1t \u0111\u1ed9ng c\u1ee7a RSA d\u1ef1a tr\u00ean vi\u1ec7c s\u1eed d\u1ee5ng 2 kh\u00f3a kh\u00e1c nhau g\u1ed3m kh\u00f3a c\u00f4ng khai v\u00e0 kh\u00f3a b\u00ed m\u1eadt.\" width=\"800\" height=\"392\" srcset=\"https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-3.jpg 800w, https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-3-300x147.jpg 300w, https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-3-768x376.jpg 768w, https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-3-150x74.jpg 150w, https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-3-696x341.jpg 696w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><figcaption id=\"caption-attachment-8961\" class=\"wp-caption-text\">C\u01a1 ch\u1ebf ho\u1ea1t \u0111\u1ed9ng c\u1ee7a RSA d\u1ef1a tr\u00ean vi\u1ec7c s\u1eed d\u1ee5ng 2 kh\u00f3a kh\u00e1c nhau g\u1ed3m kh\u00f3a c\u00f4ng khai v\u00e0 kh\u00f3a b\u00ed m\u1eadt.<\/figcaption><\/figure><\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Ma_hoa\"><\/span><b>M\u00e3 h\u00f3a<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Quy tr\u00ecnh m\u00e3 h\u00f3a th\u00f4ng tin l\u00e0:<\/p>\n<ul>\n<li>\u0110\u1ec3 m\u00e3 h\u00f3a m\u1ed9t th\u00f4ng \u0111i\u1ec7p (plaintext), chia n\u00f3 th\u00e0nh c\u00e1c kh\u1ed1i nh\u1ecf h\u01a1n.<\/li>\n<li>M\u1ed7i kh\u1ed1i \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n b\u1eb1ng m\u1ed9t s\u1ed1 nguy\u00ean m (nh\u1ecf h\u01a1n n).<\/li>\n<li>\u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c m\u00e3 h\u00f3a: ciphertext = m^e mod n.<\/li>\n<li>K\u1ebft qu\u1ea3 l\u00e0 ciphertext (v\u0103n b\u1ea3n m\u00e3 h\u00f3a).<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"_Giai_ma\"><\/span><b>\u00a0Gi\u1ea3i m\u00e3<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Gi\u1ea3i m\u00e3 v\u0103n b\u1ea3n di\u1ec5n ra theo c\u00e1c b\u01b0\u1edbc sau:<\/p>\n<ul>\n<li>Khi nh\u1eadn \u0111\u01b0\u1ee3c ciphertext, \u0111\u1ec3 gi\u1ea3i m\u00e3 ch\u00fang ta s\u1eed d\u1ee5ng kh\u00f3a b\u00ed m\u1eadt (n, d).<\/li>\n<li>S\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c gi\u1ea3i m\u00e3: plaintext = ciphertext^d mod n.<\/li>\n<li>K\u1ebft qu\u1ea3 thu \u0111\u01b0\u1ee3c l\u00e0 plaintext (v\u0103n b\u1ea3n g\u1ed1c).<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Nguyen_ly_bao_mat\"><\/span><b>Nguy\u00ean l\u00fd b\u1ea3o m\u1eadt<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>H\u1ec7 m\u00e3 h\u00f3a RSA an to\u00e0n nh\u1edd s\u1ef1 ph\u1ee9c t\u1ea1p trong vi\u1ec7c ph\u00e2n t\u00edch s\u1ed1 nguy\u00ean l\u1edbn th\u00e0nh c\u00e1c th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1. \u0110i\u1ec1u n\u00e0y khi\u1ebfn vi\u1ec7c t\u00ednh to\u00e1n kh\u00f3a b\u00ed m\u1eadt t\u1eeb kh\u00f3a c\u00f4ng khai g\u1ea7n nh\u01b0 kh\u00f4ng th\u1ec3 th\u1ef1c hi\u1ec7n \u0111\u01b0\u1ee3c trong th\u1eddi gian ng\u1eafn, \u0111\u1ea3m b\u1ea3o an ninh cho h\u1ec7 th\u1ed1ng m\u00e3 h\u00f3a.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"RSA_ung_dung_trong_linh_vuc_nao\"><\/span><b>RSA \u1ee9ng d\u1ee5ng trong l\u0129nh v\u1ef1c n\u00e0o?<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<figure id=\"attachment_8962\" aria-describedby=\"caption-attachment-8962\" style=\"width: 800px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-8962\" src=\"https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-4.jpg\" alt=\"\" width=\"800\" height=\"534\" srcset=\"https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-4.jpg 800w, https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-4-300x200.jpg 300w, https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-4-768x513.jpg 768w, https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-4-150x100.jpg 150w, https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-4-696x465.jpg 696w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><figcaption id=\"caption-attachment-8962\" class=\"wp-caption-text\">RSA \u1ee9ng d\u1ee5ng trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau<\/figcaption><\/figure>\n<p>RSA l\u00e0 m\u1ed9t trong nh\u1eefng thu\u1eadt to\u00e1n m\u00e3 h\u00f3a c\u00f4ng khai ph\u1ed5 bi\u1ebfn nh\u1ea5t hi\u1ec7n nay, \u0111\u01b0\u1ee3c \u1ee9ng d\u1ee5ng r\u1ed9ng r\u00e3i trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 \u1ee9ng d\u1ee5ng ti\u00eau bi\u1ec3u c\u1ee7a RSA:<\/p>\n<p>&#8211; <strong><a href=\"https:\/\/vnpt.vn\/doanh-nghiep\/tu-van\/tao-chu-ky-so-cong-cong.html\" target=\"_blank\" rel=\"noopener\">Ch\u1eef k\u00fd s\u1ed1<\/a> <\/strong>(Digital Signatures)<\/p>\n<p>&#8211; B\u1ea3o m\u1eadt giao d\u1ecbch t\u00e0i ch\u00ednh:<\/p>\n<p>&#8211; M\u00e3 h\u00f3a d\u1eef li\u1ec7u<\/p>\n<p>&#8211; H\u1ec7 th\u1ed1ng ch\u1ee9ng th\u1ef1c (Authentication Systems)<\/p>\n<p>&#8211; Giao th\u1ee9c HTTPS v\u00e0 SSL\/TLS<\/p>\n<p>&#8211; H\u1ec7 th\u1ed1ng VPN<\/p>\n<p>&#8211; Ch\u1ee9ng ch\u1ec9 s\u1ed1 (Digital Certificates)<\/p>\n<p>Ngo\u00e0i ra, m\u1ed9t \u1ee9ng d\u1ee5ng c\u1ee5 th\u1ec3 l\u00e0 <strong><a href=\"https:\/\/onesme.vn\/enterprise\/service\/161?type=SERVICE\" target=\"_blank\" rel=\"noopener\">VNPT SmartCA<\/a><\/strong>, gi\u1ea3i ph\u00e1p k\u00fd s\u1ed1 t\u1eeb xa s\u1eed d\u1ee5ng RSA \u0111\u1ec3 \u0111\u1ea3m b\u1ea3o an to\u00e0n v\u00e0 b\u1ea3o m\u1eadt cho c\u00e1c giao d\u1ecbch tr\u1ef1c tuy\u1ebfn. VNPT SmartCA \u00e1p d\u1ee5ng c\u00f4ng ngh\u1ec7 m\u00e3 h\u00f3a hi\u1ec7n \u0111\u1ea1i, \u0111\u01b0\u1ee3c \u0111\u00e1nh gi\u00e1 cao v\u1ec1 m\u1ee9c \u0111\u1ed9 b\u1ea3o m\u1eadt, gi\u00fap \u0111\u1ea3m b\u1ea3o t\u00ednh h\u1ee3p ph\u00e1p v\u00e0 to\u00e0n v\u1eb9n c\u1ee7a c\u00e1c giao d\u1ecbch.<\/p>\n<p><strong>Xem th\u00eam:<\/strong> <a href=\"https:\/\/onesme.vn\/blog\/san-pham\/chu-ky-so-tu-xa-vnpt.html\" target=\"_blank\" rel=\"noopener\"><strong>Ch\u1eef k\u00fd s\u1ed1 t\u1eeb xa VNPT Smart CA \u2013 B\u1ea3o m\u1eadt tuy\u1ec7t \u0111\u1ed1i, k\u00fd s\u1ed1 m\u1ecdi l\u00fac m\u1ecdi n\u01a1i<\/strong><\/a><\/p>\n<figure id=\"attachment_8963\" aria-describedby=\"caption-attachment-8963\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-8963 size-full\" title=\"VNPT SmartCA s\u1eed d\u1ee5ng RSA \u0111\u1ec3 \u0111\u1ea3m b\u1ea3o an to\u00e0n v\u00e0 b\u1ea3o m\u1eadt cho c\u00e1c giao d\u1ecbch tr\u1ef1c tuy\u1ebfn.\" src=\"https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-5.jpg\" alt=\"VNPT SmartCA s\u1eed d\u1ee5ng RSA \u0111\u1ec3 \u0111\u1ea3m b\u1ea3o an to\u00e0n v\u00e0 b\u1ea3o m\u1eadt cho c\u00e1c giao d\u1ecbch tr\u1ef1c tuy\u1ebfn.\" width=\"800\" height=\"534\" srcset=\"https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-5.jpg 800w, https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-5-300x200.jpg 300w, https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-5-768x513.jpg 768w, https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-5-150x100.jpg 150w, https:\/\/onesme.vn\/blog\/wp-content\/uploads\/2024\/11\/rsa-la-gi-onesme-5-696x465.jpg 696w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><figcaption id=\"caption-attachment-8963\" class=\"wp-caption-text\">VNPT SmartCA s\u1eed d\u1ee5ng RSA \u0111\u1ec3 \u0111\u1ea3m b\u1ea3o an to\u00e0n v\u00e0 b\u1ea3o m\u1eadt cho c\u00e1c giao d\u1ecbch tr\u1ef1c tuy\u1ebfn.<\/figcaption><\/figure>\n<p>\u0110\u01b0\u1ee3c \u0111\u00e1nh gi\u00e1 cao v\u1ec1 t\u00ednh ti\u1ec7n d\u1ee5ng v\u00e0 b\u1ea3o m\u1eadt, VNPT SmartCA \u0111\u00e1p \u1ee9ng c\u00e1c ti\u00eau chu\u1ea9n an to\u00e0n c\u1ee7a ch\u00e2u \u00c2u v\u00e0 Vi\u1ec7t Nam, \u0111\u1ed3ng th\u1eddi h\u1ed7 tr\u1ee3 \u0111a n\u1ec1n t\u1ea3ng cho c\u00e1c d\u1ecbch v\u1ee5 c\u00f4ng, t\u00e0i ch\u00ednh v\u00e0 doanh nghi\u1ec7p.<\/p>\n<p><a href=\"https:\/\/onesme.vn\/blog\/\" target=\"_blank\" rel=\"noopener\"><strong>Gi\u1ea3i ph\u00e1p<\/strong><\/a> n\u00e0y kh\u00f4ng ch\u1ec9 \u0111\u1ea3m b\u1ea3o an ninh th\u00f4ng tin m\u00e0 c\u00f2n mang l\u1ea1i s\u1ef1 linh ho\u1ea1t v\u00e0 ti\u1ebft ki\u1ec7m chi ph\u00ed cho c\u00e1c c\u00e1 nh\u00e2n v\u00e0 t\u1ed5 ch\u1ee9c. VNPT \u0111\u00e3 v\u00e0 \u0111ang kh\u00f4ng ng\u1eebng ph\u00e1t tri\u1ec3n v\u00e0 c\u1ea3i ti\u1ebfn VNPT SmartCA \u0111\u1ec3 \u0111\u00e1p \u1ee9ng nhu c\u1ea7u ng\u00e0y c\u00e0ng cao c\u1ee7a ng\u01b0\u1eddi d\u00f9ng trong b\u1ed1i c\u1ea3nh chuy\u1ec3n \u0111\u1ed5i s\u1ed1.<\/p>\n<p>Hy v\u1ecdng qua b\u00e0i vi\u1ebft n\u00e0y b\u1ea1n \u0111\u00e3 hi\u1ec3u \u0111\u01b0\u1ee3c RSA l\u00e0 g\u00ec v\u00e0 v\u00ec sao RSA l\u1ea1i quan tr\u1ecdng trong b\u1ea3o m\u1eadt th\u00f4ng tin v\u00e0 \u0111\u1ea3m b\u1ea3o an to\u00e0n c\u00e1c giao d\u1ecbch tr\u1ef1c tuy\u1ebfn. V\u1edbi kh\u1ea3 n\u0103ng b\u1ea3o m\u1eadt cao v\u00e0 t\u00ednh \u1ee9ng d\u1ee5ng linh ho\u1ea1t, RSA ti\u1ebfp t\u1ee5c l\u00e0 m\u1ed9t trong nh\u1eefng c\u00f4ng c\u1ee5 ch\u1ee7 l\u1ef1c trong l\u0129nh v\u1ef1c b\u1ea3o m\u1eadt th\u00f4ng tin.<\/p>\n<p>\u0110\u1ec3 t\u00ecm hi\u1ec3u th\u00eam v\u1ec1 c\u00e1c <a href=\"https:\/\/onesme.vn\/enterprise\" target=\"_blank\" rel=\"noopener\"><strong>s\u1ea3n ph\u1ea9m<\/strong><\/a> &#8211; d\u1ecbch v\u1ee5 c\u1ee7a VNPT, vui l\u00f2ng li\u00ean h\u1ec7 Hotline ho\u1eb7c truy c\u1eadp k\u00eanh t\u01b0 v\u1ea5n mi\u1ec5n ph\u00ed c\u1ee7a <a href=\"https:\/\/onesme.vn\/\" target=\"_blank\" rel=\"noopener\"><strong>oneSME<\/strong><\/a> \u0111\u1ec3 nh\u1eadn \u0111\u01b0\u1ee3c h\u1ed7 tr\u1ee3 t\u01b0 v\u1ea5n gi\u1ea3i ph\u00e1p chi ti\u1ebft:<\/p>\n<p><strong>Xem th\u00eam:\u00a0<\/strong><strong><a href=\"https:\/\/onesme.vn\/blog\/giai-phap\/chu-ky-so-an-toan-giao-dich.html\" target=\"_blank\" rel=\"noopener\">Ch\u1eef k\u00fd s\u1ed1 g\u00f3p ph\u1ea7n \u0111\u1ea3m b\u1ea3o x\u00e1c th\u1ef1c an to\u00e0n c\u00e1c giao d\u1ecbch t\u00e0i ch\u00ednh, ng\u00e2n h\u00e0ng<\/a><\/strong><\/p>\n<p>_____________<\/p>\n<p>Website:<strong><a href=\"https:\/\/onesme.vn\"> https:\/\/onesme.vn<\/a><\/strong><\/p>\n<p>Hotline: <b>1800 1260<\/b><\/p>\n<p>Email: onesme@vnpt.vn<\/p>\n<p>T\u01b0 v\u1ea5n mi\u1ec5n ph\u00ed:<strong><a href=\"https:\/\/onesme.vn\/enterprise\/contact-us\"> https:\/\/onesme.vn\/enterprise\/contact-us<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>RSA l\u00e0 g\u00ec? \u0110\u00e2y l\u00e0 m\u1ed9t trong nh\u1eefng thu\u1eadt to\u00e1n m\u00e3 h\u00f3a ph\u1ed5 bi\u1ebfn nh\u1ea5t \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i trong b\u1ea3o m\u1eadt d\u1eef li\u1ec7u s\u1ed1. C\u00f4ng ngh\u1ec7 RSA gi\u00fap \u0111\u1ea3m b\u1ea3o m\u1ed9t ng\u01b0\u1eddi d\u00f9ng khi t\u1ea1o ra ch\u1eef k\u00fd s\u1ed1 th\u00ec ch\u1eef k\u00fd \u0111\u00f3 l\u00e0 duy nh\u1ea5t. V\u00ec v\u1eady, c\u00f4ng ngh\u1ec7 n\u00e0y n\u00e2ng \u0111\u1ed9 [&hellip;]<\/p>\n","protected":false},"author":40,"featured_media":8959,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"class_list":{"0":"post-8957","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-tin-tuc-su-kien"},"_links":{"self":[{"href":"https:\/\/onesme.vn\/blog\/wp-json\/wp\/v2\/posts\/8957","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/onesme.vn\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/onesme.vn\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/onesme.vn\/blog\/wp-json\/wp\/v2\/users\/40"}],"replies":[{"embeddable":true,"href":"https:\/\/onesme.vn\/blog\/wp-json\/wp\/v2\/comments?post=8957"}],"version-history":[{"count":7,"href":"https:\/\/onesme.vn\/blog\/wp-json\/wp\/v2\/posts\/8957\/revisions"}],"predecessor-version":[{"id":11258,"href":"https:\/\/onesme.vn\/blog\/wp-json\/wp\/v2\/posts\/8957\/revisions\/11258"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/onesme.vn\/blog\/wp-json\/wp\/v2\/media\/8959"}],"wp:attachment":[{"href":"https:\/\/onesme.vn\/blog\/wp-json\/wp\/v2\/media?parent=8957"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/onesme.vn\/blog\/wp-json\/wp\/v2\/categories?post=8957"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/onesme.vn\/blog\/wp-json\/wp\/v2\/tags?post=8957"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}