{"id":478482,"date":"2023-08-09T09:33:31","date_gmt":"2023-08-09T09:33:31","guid":{"rendered":""},"modified":"2023-09-05T11:16:50","modified_gmt":"2023-09-05T11:16:50","slug":"post-quantum-cryptography","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/vn\/wiki\/post-quantum-cryptography\/","title":{"rendered":"M\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed"},"content":{"rendered":"<p>M\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed l\u00e0 m\u1ed9t ph\u01b0\u01a1ng ph\u00e1p m\u00e3 h\u00f3a ti\u00ean ti\u1ebfn \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf \u0111\u1ec3 ch\u1ed1ng l\u1ea1i c\u00e1c cu\u1ed9c t\u1ea5n c\u00f4ng t\u1eeb m\u00e1y t\u00ednh l\u01b0\u1ee3ng t\u1eed, m\u1ed9t lo\u1ea1i m\u00e1y m\u1edbi h\u1ee9a h\u1eb9n s\u1ee9c m\u1ea1nh t\u00ednh to\u00e1n v\u00f4 song v\u00e0 c\u00f3 kh\u1ea3 n\u0103ng ph\u00e1 v\u1ee1 c\u00e1c s\u01a1 \u0111\u1ed3 m\u1eadt m\u00e3 truy\u1ec1n th\u1ed1ng. Khi m\u00e1y t\u00ednh l\u01b0\u1ee3ng t\u1eed ti\u1ebfp t\u1ee5c ph\u00e1t tri\u1ec3n, nhu c\u1ea7u v\u1ec1 c\u00e1c ph\u01b0\u01a1ng ph\u00e1p m\u00e3 h\u00f3a an to\u00e0n c\u00f3 th\u1ec3 ch\u1ed1ng l\u1ea1i c\u00e1c cu\u1ed9c t\u1ea5n c\u00f4ng d\u1ef1a tr\u00ean l\u01b0\u1ee3ng t\u1eed ng\u00e0y c\u00e0ng tr\u1edf n\u00ean quan tr\u1ecdng. M\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed nh\u1eb1m m\u1ee5c \u0111\u00edch b\u1ea3o v\u1ec7 c\u00e1c k\u00eanh th\u00f4ng tin v\u00e0 li\u00ean l\u1ea1c nh\u1ea1y c\u1ea3m trong k\u1ef7 nguy\u00ean \u0111i\u1ec7n to\u00e1n h\u1eadu l\u01b0\u1ee3ng t\u1eed.<\/p>\n<h2>L\u1ecbch s\u1eed ngu\u1ed3n g\u1ed1c c\u1ee7a m\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed v\u00e0 l\u1ea7n \u0111\u1ea7u ti\u00ean \u0111\u1ec1 c\u1eadp \u0111\u1ebfn n\u00f3<\/h2>\n<p>Kh\u00e1i ni\u1ec7m m\u1eadt m\u00e3 sau l\u01b0\u1ee3ng t\u1eed b\u1eaft ngu\u1ed3n t\u1eeb \u0111\u1ea7u nh\u1eefng n\u0103m 1990 khi Peter Shor v\u00e0 Lov Grover \u0111\u1ed9c l\u1eadp ph\u00e1t hi\u1ec7n ra c\u00e1c thu\u1eadt to\u00e1n l\u01b0\u1ee3ng t\u1eed c\u00f3 th\u1ec3 gi\u1ea3i quy\u1ebft m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3 m\u1ed9t s\u1ed1 v\u1ea5n \u0111\u1ec1 nh\u1ea5t \u0111\u1ecbnh, bao g\u1ed3m ph\u00e2n t\u00edch c\u00e1c s\u1ed1 nguy\u00ean l\u1edbn v\u00e0 t\u00ecm ki\u1ebfm c\u01a1 s\u1edf d\u1eef li\u1ec7u ch\u01b0a \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp, v\u1ed1n l\u00e0 tr\u1ecdng t\u00e2m c\u1ee7a nhi\u1ec1u m\u1eadt m\u00e3 kh\u00f3a c\u00f4ng khai. h\u1ec7 th\u1ed1ng. N\u0103m 1994, nh\u00e0 to\u00e1n h\u1ecdc Daniel Bernstein \u0111\u00e3 kh\u1edfi x\u01b0\u1edbng vi\u1ec7c kh\u00e1m ph\u00e1 c\u00e1c thu\u1eadt to\u00e1n m\u1eadt m\u00e3 c\u00f3 th\u1ec3 ch\u1ed1ng l\u1ea1i c\u00e1c cu\u1ed9c t\u1ea5n c\u00f4ng l\u01b0\u1ee3ng t\u1eed v\u00e0 \u0111i\u1ec1u n\u00e0y \u0111\u00e1nh d\u1ea5u s\u1ef1 kh\u1edfi \u0111\u1ea7u c\u1ee7a nghi\u00ean c\u1ee9u m\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed.<\/p>\n<h2>Th\u00f4ng tin chi ti\u1ebft v\u1ec1 m\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed<\/h2>\n<p>M\u1eadt m\u00e3 sau l\u01b0\u1ee3ng t\u1eed \u0111\u1ec1 c\u1eadp \u0111\u1ebfn m\u1ed9t nh\u00f3m thu\u1eadt to\u00e1n m\u1eadt m\u00e3 \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf \u0111\u1ec3 b\u1ea3o m\u1eadt tr\u01b0\u1edbc c\u00e1c \u0111\u1ed1i th\u1ee7 l\u01b0\u1ee3ng t\u1eed. Kh\u00f4ng gi\u1ed1ng nh\u01b0 c\u00e1c thu\u1eadt to\u00e1n m\u1eadt m\u00e3 c\u1ed5 \u0111i\u1ec3n d\u1ef1a tr\u00ean c\u00e1c v\u1ea5n \u0111\u1ec1 to\u00e1n h\u1ecdc kh\u00f3 nh\u01b0 ph\u00e2n t\u00edch c\u00e1c s\u1ed1 l\u1edbn v\u00e0 logarit r\u1eddi r\u1ea1c, c\u00e1c s\u01a1 \u0111\u1ed3 m\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed d\u1ef1a tr\u00ean c\u00e1c nguy\u00ean t\u1eafc to\u00e1n h\u1ecdc thay th\u1ebf. Nh\u1eefng nguy\u00ean t\u1eafc n\u00e0y th\u01b0\u1eddng li\u00ean quan \u0111\u1ebfn m\u1eadt m\u00e3 d\u1ef1a tr\u00ean m\u1ea1ng, m\u1eadt m\u00e3 d\u1ef1a tr\u00ean m\u00e3, m\u1eadt m\u00e3 d\u1ef1a tr\u00ean h\u00e0m b\u0103m, h\u1ec7 th\u1ed1ng \u0111a th\u1ee9c \u0111a bi\u1ebfn v\u00e0 c\u00e1c c\u1ea5u tr\u00fac to\u00e1n h\u1ecdc kh\u00e1c c\u00f3 \u0111\u1ed9 ph\u1ee9c t\u1ea1p cao v\u00e0 kh\u1ea3 n\u0103ng ch\u1ed1ng l\u1ea1i c\u00e1c cu\u1ed9c t\u1ea5n c\u00f4ng l\u01b0\u1ee3ng t\u1eed v\u1ed1n c\u00f3.<\/p>\n<h2>C\u1ea5u tr\u00fac b\u00ean trong c\u1ee7a m\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed v\u00e0 c\u00e1ch th\u1ee9c ho\u1ea1t \u0111\u1ed9ng c\u1ee7a n\u00f3<\/h2>\n<p>C\u00e1c thu\u1eadt to\u00e1n m\u00e3 h\u00f3a h\u1eadu l\u01b0\u1ee3ng t\u1eed s\u1eed d\u1ee5ng c\u00e1c c\u1ea5u tr\u00fac to\u00e1n h\u1ecdc v\u1eabn kh\u00f3 gi\u1ea3i ngay c\u1ea3 \u0111\u1ed1i v\u1edbi m\u00e1y t\u00ednh l\u01b0\u1ee3ng t\u1eed. V\u00ed d\u1ee5, m\u1eadt m\u00e3 d\u1ef1a tr\u00ean m\u1ea1ng d\u1ef1a tr\u00ean \u0111\u1ed9 ph\u1ee9c t\u1ea1p c\u1ee7a vi\u1ec7c t\u00ecm vect\u01a1 ng\u1eafn nh\u1ea5t trong m\u1ea1ng, \u0111i\u1ec1u n\u00e0y \u0111\u01b0\u1ee3c cho l\u00e0 kh\u00f4ng kh\u1ea3 thi v\u1ec1 m\u1eb7t t\u00ednh to\u00e1n \u0111\u1ed1i v\u1edbi c\u1ea3 m\u00e1y t\u00ednh c\u1ed5 \u0111i\u1ec3n v\u00e0 l\u01b0\u1ee3ng t\u1eed. T\u01b0\u01a1ng t\u1ef1, m\u1eadt m\u00e3 d\u1ef1a tr\u00ean m\u00e3 d\u1ef1a tr\u00ean \u0111\u1ed9 kh\u00f3 gi\u1ea3i m\u00e3 m\u1ed9t s\u1ed1 m\u00e3 s\u1eeda l\u1ed7i nh\u1ea5t \u0111\u1ecbnh, \u0111i\u1ec1u n\u00e0y c\u0169ng \u0111\u1eb7t ra th\u00e1ch th\u1ee9c \u0111\u1ed1i v\u1edbi c\u00e1c thu\u1eadt to\u00e1n l\u01b0\u1ee3ng t\u1eed.<\/p>\n<p>\u0110\u1ec3 \u0111\u1ea1t \u0111\u01b0\u1ee3c b\u1ea3o m\u1eadt d\u1eef li\u1ec7u, c\u00e1c h\u1ec7 th\u1ed1ng m\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed k\u1ebft h\u1ee3p c\u00e1c thu\u1eadt to\u00e1n m\u00e3 h\u00f3a v\u00e0 gi\u1ea3i m\u00e3 t\u1eadn d\u1ee5ng c\u00e1c c\u1ea5u tr\u00fac to\u00e1n h\u1ecdc ph\u1ee9c t\u1ea1p n\u00e0y. Khi m\u00e3 h\u00f3a d\u1eef li\u1ec7u, thu\u1eadt to\u00e1n m\u00e3 h\u00f3a h\u1eadu l\u01b0\u1ee3ng t\u1eed s\u1ebd chuy\u1ec3n v\u0103n b\u1ea3n g\u1ed1c th\u00e0nh v\u0103n b\u1ea3n m\u00e3 h\u00f3a theo c\u00e1ch m\u00e0 k\u1ebb t\u1ea5n c\u00f4ng, d\u00f9 l\u00e0 c\u1ed5 \u0111i\u1ec3n hay l\u01b0\u1ee3ng t\u1eed, s\u1ebd c\u1ef1c k\u1ef3 kh\u00f3 \u0111\u1ea3o ng\u01b0\u1ee3c qu\u00e1 tr\u00ecnh m\u00e0 kh\u00f4ng c\u00f3 kh\u00f3a gi\u1ea3i m\u00e3 th\u00edch h\u1ee3p.<\/p>\n<h2>Ph\u00e2n t\u00edch c\u00e1c t\u00ednh n\u0103ng ch\u00ednh c\u1ee7a m\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed<\/h2>\n<p>M\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed cung c\u1ea5p m\u1ed9t s\u1ed1 t\u00ednh n\u0103ng ch\u00ednh khi\u1ebfn n\u00f3 tr\u1edf th\u00e0nh l\u1ef1a ch\u1ecdn \u0111\u1ea7y h\u1ee9a h\u1eb9n cho b\u1ea3o m\u1eadt d\u1eef li\u1ec7u trong t\u01b0\u01a1ng lai:<\/p>\n<ol>\n<li>\n<p><strong>Kh\u00e1ng l\u01b0\u1ee3ng t\u1eed:<\/strong> \u01afu \u0111i\u1ec3m ch\u00ednh c\u1ee7a m\u1eadt m\u00e3 sau l\u01b0\u1ee3ng t\u1eed l\u00e0 kh\u1ea3 n\u0103ng ch\u1ed1ng l\u1ea1i c\u00e1c cu\u1ed9c t\u1ea5n c\u00f4ng t\u1eeb m\u00e1y t\u00ednh l\u01b0\u1ee3ng t\u1eed. V\u00ec c\u00e1c thu\u1eadt to\u00e1n l\u01b0\u1ee3ng t\u1eed c\u00f3 th\u1ec3 gi\u1ea3i quy\u1ebft c\u00e1c v\u1ea5n \u0111\u1ec1 m\u00e0 m\u00e1y t\u00ednh c\u1ed5 \u0111i\u1ec3n g\u1eb7p kh\u00f3 kh\u0103n m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3, n\u00ean c\u00e1c s\u01a1 \u0111\u1ed3 m\u1eadt m\u00e3 truy\u1ec1n th\u1ed1ng c\u00f3 th\u1ec3 tr\u1edf n\u00ean d\u1ec5 b\u1ecb t\u1ea5n c\u00f4ng. M\u1eb7t kh\u00e1c, c\u00e1c thu\u1eadt to\u00e1n m\u00e3 h\u00f3a h\u1eadu l\u01b0\u1ee3ng t\u1eed cung c\u1ea5p kh\u1ea3 n\u0103ng b\u1ea3o v\u1ec7 m\u1ea1nh m\u1ebd ch\u1ed1ng l\u1ea1i c\u00e1c cu\u1ed9c t\u1ea5n c\u00f4ng d\u1ef1a tr\u00ean l\u01b0\u1ee3ng t\u1eed n\u00e0y.<\/p>\n<\/li>\n<li>\n<p><strong>Kh\u1ea3 n\u0103ng t\u01b0\u01a1ng th\u00edch:<\/strong> M\u1eb7c d\u00f9 m\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed gi\u1edbi thi\u1ec7u c\u00e1c thu\u1eadt to\u00e1n m\u1edbi nh\u01b0ng n\u00f3 \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf \u0111\u1ec3 c\u00f9ng t\u1ed3n t\u1ea1i v\u1edbi c\u00e1c h\u1ec7 th\u1ed1ng m\u1eadt m\u00e3 hi\u1ec7n c\u00f3. Kh\u1ea3 n\u0103ng t\u01b0\u01a1ng th\u00edch n\u00e0y \u0111\u1ea3m b\u1ea3o qu\u00e1 tr\u00ecnh chuy\u1ec3n \u0111\u1ed5i su\u00f4n s\u1ebb sang c\u00e1c ph\u01b0\u01a1ng ph\u00e1p m\u00e3 h\u00f3a kh\u00e1ng l\u01b0\u1ee3ng t\u1eed m\u00e0 kh\u00f4ng \u1ea3nh h\u01b0\u1edfng \u0111\u1ebfn c\u00e1c ti\u00eau chu\u1ea9n b\u1ea3o m\u1eadt hi\u1ec7n t\u1ea1i.<\/p>\n<\/li>\n<li>\n<p><strong>B\u1ea3o m\u1eadt l\u00e2u d\u00e0i:<\/strong> C\u00e1c thu\u1eadt to\u00e1n m\u00e3 h\u00f3a h\u1eadu l\u01b0\u1ee3ng t\u1eed nh\u1eb1m m\u1ee5c \u0111\u00edch duy tr\u00ec t\u00ednh b\u1ea3o m\u1eadt ngay c\u1ea3 khi c\u00f4ng ngh\u1ec7 \u0111i\u1ec7n to\u00e1n l\u01b0\u1ee3ng t\u1eed ph\u00e1t tri\u1ec3n. Ch\u00fang cung c\u1ea5p s\u1ef1 b\u1ea3o v\u1ec7 l\u00e2u d\u00e0i tr\u01b0\u1edbc nh\u1eefng ti\u1ebfn b\u1ed9 ti\u1ec1m n\u0103ng trong t\u01b0\u01a1ng lai c\u1ee7a thu\u1eadt to\u00e1n l\u01b0\u1ee3ng t\u1eed.<\/p>\n<\/li>\n<li>\n<p><strong>M\u1eadt m\u00e3 kh\u00f3a c\u00f4ng khai:<\/strong> Nhi\u1ec1u s\u01a1 \u0111\u1ed3 m\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed t\u1eadp trung v\u00e0o vi\u1ec7c t\u0103ng c\u01b0\u1eddng m\u1eadt m\u00e3 kh\u00f3a c\u00f4ng khai, \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i \u0111\u1ec3 truy\u1ec1n v\u00e0 x\u00e1c th\u1ef1c d\u1eef li\u1ec7u an to\u00e0n trong c\u00e1c \u1ee9ng d\u1ee5ng kh\u00e1c nhau.<\/p>\n<\/li>\n<li>\n<p><strong>C\u01a1 s\u1edf to\u00e1n h\u1ecdc \u0111a d\u1ea1ng:<\/strong> M\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed d\u1ef1a tr\u00ean nhi\u1ec1u n\u1ec1n t\u1ea3ng to\u00e1n h\u1ecdc kh\u00e1c nhau, \u0111\u1ea3m b\u1ea3o nhi\u1ec1u t\u00f9y ch\u1ecdn b\u1ea3o m\u1eadt ph\u00f9 h\u1ee3p v\u1edbi c\u00e1c y\u00eau c\u1ea7u kh\u00e1c nhau.<\/p>\n<\/li>\n<\/ol>\n<h2>C\u00e1c lo\u1ea1i m\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed<\/h2>\n<p>M\u1eadt m\u00e3 sau l\u01b0\u1ee3ng t\u1eed bao g\u1ed3m m\u1ed9t s\u1ed1 lo\u1ea1i thu\u1eadt to\u00e1n, m\u1ed7i lo\u1ea1i d\u1ef1a tr\u00ean c\u00e1c c\u1ea5u tr\u00fac to\u00e1n h\u1ecdc ri\u00eang bi\u1ec7t \u0111\u1ec3 kh\u00e1ng l\u01b0\u1ee3ng t\u1eed. C\u00e1c lo\u1ea1i ch\u00ednh bao g\u1ed3m:<\/p>\n<table>\n<thead>\n<tr>\n<th>Ki\u1ec3u<\/th>\n<th>Thu\u1eadt to\u00e1n m\u1eabu<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>D\u1ef1a tr\u00ean m\u1ea1ng<\/td>\n<td>NTRU, Kyber, NewHope<\/td>\n<\/tr>\n<tr>\n<td>D\u1ef1a tr\u00ean m\u00e3<\/td>\n<td>McEliece, RQC<\/td>\n<\/tr>\n<tr>\n<td>D\u1ef1a tr\u00ean h\u00e0m b\u0103m<\/td>\n<td>XMSS, SPHINCS<\/td>\n<\/tr>\n<tr>\n<td>\u0110a th\u1ee9c nhi\u1ec1u bi\u1ebfn<\/td>\n<td>C\u1ea7u v\u1ed3ng, d\u1ea7u v\u00e0 gi\u1ea5m kh\u00f4ng c\u00e2n b\u1eb1ng (UOV)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>M\u1ed7i lo\u1ea1i c\u00f3 nh\u1eefng \u0111i\u1ec3m m\u1ea1nh v\u00e0 \u0111i\u1ec3m y\u1ebfu ri\u00eang v\u00e0 s\u1ef1 ph\u00f9 h\u1ee3p c\u1ee7a ch\u00fang ph\u1ee5 thu\u1ed9c v\u00e0o tr\u01b0\u1eddng h\u1ee3p s\u1eed d\u1ee5ng c\u1ee5 th\u1ec3 v\u00e0 y\u00eau c\u1ea7u b\u1ea3o m\u1eadt.<\/p>\n<h2>C\u00e1c c\u00e1ch s\u1eed d\u1ee5ng m\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed, c\u00e1c v\u1ea5n \u0111\u1ec1 v\u00e0 gi\u1ea3i ph\u00e1p li\u00ean quan \u0111\u1ebfn vi\u1ec7c s\u1eed d\u1ee5ng<\/h2>\n<p>M\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong nhi\u1ec1u \u1ee9ng d\u1ee5ng v\u00e0 t\u00ecnh hu\u1ed1ng kh\u00e1c nhau \u0111\u1ec3 \u0111\u1ea3m b\u1ea3o an to\u00e0n d\u1eef li\u1ec7u. M\u1ed9t s\u1ed1 tr\u01b0\u1eddng h\u1ee3p s\u1eed d\u1ee5ng ph\u1ed5 bi\u1ebfn bao g\u1ed3m:<\/p>\n<ol>\n<li>\n<p><strong>Truy\u1ec1n th\u00f4ng an to\u00e0n:<\/strong> C\u00e1c thu\u1eadt to\u00e1n m\u00e3 h\u00f3a h\u1eadu l\u01b0\u1ee3ng t\u1eed c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c t\u00edch h\u1ee3p v\u00e0o c\u00e1c giao th\u1ee9c truy\u1ec1n th\u00f4ng (v\u00ed d\u1ee5: TLS) \u0111\u1ec3 b\u1ea3o m\u1eadt vi\u1ec7c truy\u1ec1n d\u1eef li\u1ec7u gi\u1eefa m\u00e1y ch\u1ee7 v\u00e0 m\u00e1y kh\u00e1ch, b\u1ea3o v\u1ec7 th\u00f4ng tin nh\u1ea1y c\u1ea3m kh\u1ecfi c\u00e1c cu\u1ed9c t\u1ea5n c\u00f4ng l\u01b0\u1ee3ng t\u1eed trong qu\u00e1 tr\u00ecnh truy\u1ec1n t\u1ea3i.<\/p>\n<\/li>\n<li>\n<p><strong>Ch\u1eef k\u00fd s\u1ed1:<\/strong> L\u01b0\u1ee3c \u0111\u1ed3 ch\u1eef k\u00fd h\u1eadu l\u01b0\u1ee3ng t\u1eed c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 x\u00e1c minh t\u00ednh x\u00e1c th\u1ef1c v\u00e0 t\u00ednh to\u00e0n v\u1eb9n c\u1ee7a t\u00e0i li\u1ec7u k\u1ef9 thu\u1eadt s\u1ed1, \u0111\u1ea3m b\u1ea3o r\u1eb1ng ch\u00fang kh\u00f4ng b\u1ecb gi\u1ea3 m\u1ea1o ho\u1eb7c gi\u1ea3 m\u1ea1o.<\/p>\n<\/li>\n<li>\n<p><strong>Trao \u0111\u1ed5i kh\u00f3a:<\/strong> C\u00e1c thu\u1eadt to\u00e1n trao \u0111\u1ed5i kh\u00f3a kh\u00e1ng l\u01b0\u1ee3ng t\u1eed t\u1ea1o \u0111i\u1ec1u ki\u1ec7n thu\u1eadn l\u1ee3i cho vi\u1ec7c thi\u1ebft l\u1eadp an to\u00e0n c\u00e1c kh\u00f3a m\u00e3 h\u00f3a chung gi\u1eefa c\u00e1c b\u00ean trong phi\u00ean giao ti\u1ebfp.<\/p>\n<\/li>\n<\/ol>\n<p>Tuy nhi\u00ean, vi\u1ec7c \u00e1p d\u1ee5ng m\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed c\u0169ng \u0111\u1eb7t ra m\u1ed9t s\u1ed1 th\u00e1ch th\u1ee9c:<\/p>\n<ul>\n<li>\n<p><strong>Hi\u1ec7u su\u1ea5t:<\/strong> C\u00e1c thu\u1eadt to\u00e1n m\u00e3 h\u00f3a h\u1eadu l\u01b0\u1ee3ng t\u1eed c\u00f3 th\u1ec3 c\u00f3 c\u01b0\u1eddng \u0111\u1ed9 t\u00ednh to\u00e1n chuy\u00ean s\u00e2u h\u01a1n so v\u1edbi c\u00e1c thu\u1eadt to\u00e1n c\u1ed5 \u0111i\u1ec3n, d\u1eabn \u0111\u1ebfn c\u00e1c v\u1ea5n \u0111\u1ec1 ti\u1ec1m \u1ea9n v\u1ec1 hi\u1ec7u su\u1ea5t tr\u00ean c\u00e1c thi\u1ebft b\u1ecb b\u1ecb h\u1ea1n ch\u1ebf v\u1ec1 t\u00e0i nguy\u00ean.<\/p>\n<\/li>\n<li>\n<p><strong>Ti\u00eau chu\u1ea9n h\u00f3a v\u00e0 kh\u1ea3 n\u0103ng t\u01b0\u01a1ng t\u00e1c:<\/strong> V\u1edbi nhi\u1ec1u thu\u1eadt to\u00e1n h\u1eadu l\u01b0\u1ee3ng t\u1eed \u0111ang \u0111\u01b0\u1ee3c ph\u00e1t tri\u1ec3n, vi\u1ec7c \u0111\u1ea1t \u0111\u01b0\u1ee3c ti\u00eau chu\u1ea9n h\u00f3a v\u00e0 \u0111\u1ea3m b\u1ea3o kh\u1ea3 n\u0103ng t\u01b0\u01a1ng t\u00e1c gi\u1eefa c\u00e1c h\u1ec7 th\u1ed1ng kh\u00e1c nhau tr\u1edf n\u00ean quan tr\u1ecdng \u0111\u1ec3 \u00e1p d\u1ee5ng r\u1ed9ng r\u00e3i.<\/p>\n<\/li>\n<li>\n<p><strong>Di chuy\u1ec3n v\u00e0 qu\u1ea3n l\u00fd kh\u00f3a:<\/strong> Vi\u1ec7c chuy\u1ec3n \u0111\u1ed5i t\u1eeb m\u1eadt m\u00e3 c\u1ed5 \u0111i\u1ec3n sang m\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed \u0111\u00f2i h\u1ecfi ph\u1ea3i l\u1eadp k\u1ebf ho\u1ea1ch v\u00e0 xem x\u00e9t c\u1ea9n th\u1eadn vi\u1ec7c qu\u1ea3n l\u00fd kh\u00f3a \u0111\u1ec3 duy tr\u00ec t\u00ednh b\u1ea3o m\u1eadt trong qu\u00e1 tr\u00ecnh di chuy\u1ec3n.<\/p>\n<\/li>\n<\/ul>\n<h2>C\u00e1c \u0111\u1eb7c \u0111i\u1ec3m ch\u00ednh v\u00e0 so s\u00e1nh kh\u00e1c v\u1edbi c\u00e1c thu\u1eadt ng\u1eef t\u01b0\u01a1ng t\u1ef1<\/h2>\n<p>\u0110\u1ec3 hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 m\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed v\u00e0 s\u1ef1 kh\u00e1c bi\u1ec7t c\u1ee7a n\u00f3 v\u1edbi c\u00e1c thu\u1eadt ng\u1eef li\u00ean quan, h\u00e3y xem x\u00e9t c\u00e1c so s\u00e1nh sau:<\/p>\n<ol>\n<li>\n<p><strong>M\u1eadt m\u00e3 l\u01b0\u1ee3ng t\u1eed so v\u1edbi M\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed:<\/strong> M\u1eadt m\u00e3 l\u01b0\u1ee3ng t\u1eed, th\u01b0\u1eddng \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 ph\u00e2n ph\u1ed1i kh\u00f3a l\u01b0\u1ee3ng t\u1eed (QKD), l\u00e0 m\u1ed9t l\u0129nh v\u1ef1c nghi\u00ean c\u1ee9u t\u1eadp trung v\u00e0o giao ti\u1ebfp an to\u00e0n b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng c\u00e1c nguy\u00ean t\u1eafc l\u01b0\u1ee3ng t\u1eed. M\u1eb7c d\u00f9 m\u1eadt m\u00e3 l\u01b0\u1ee3ng t\u1eed cung c\u1ea5p b\u1ea3o m\u1eadt v\u00f4 \u0111i\u1ec1u ki\u1ec7n cho vi\u1ec7c trao \u0111\u1ed5i kh\u00f3a nh\u01b0ng n\u00f3 v\u1ed1n kh\u00f4ng gi\u1ea3i quy\u1ebft \u0111\u01b0\u1ee3c c\u00e1c m\u1ed1i lo ng\u1ea1i v\u1ec1 b\u1ea3o m\u1eadt sau l\u01b0\u1ee3ng t\u1eed. M\u1eb7t kh\u00e1c, m\u1eadt m\u00e3 sau l\u01b0\u1ee3ng t\u1eed \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf \u0111\u1eb7c bi\u1ec7t \u0111\u1ec3 ch\u1ed1ng l\u1ea1i c\u00e1c cu\u1ed9c t\u1ea5n c\u00f4ng l\u01b0\u1ee3ng t\u1eed.<\/p>\n<\/li>\n<li>\n<p><strong>M\u1eadt m\u00e3 \u0111\u1ed1i x\u1ee9ng v\u00e0 b\u1ea5t \u0111\u1ed1i x\u1ee9ng:<\/strong> M\u1eadt m\u00e3 \u0111\u1ed1i x\u1ee9ng s\u1eed d\u1ee5ng c\u00f9ng m\u1ed9t kh\u00f3a cho c\u1ea3 m\u00e3 h\u00f3a v\u00e0 gi\u1ea3i m\u00e3, l\u00e0m cho n\u00f3 hi\u1ec7u qu\u1ea3 nh\u01b0ng y\u00eau c\u1ea7u ph\u00e2n ph\u1ed1i kh\u00f3a an to\u00e0n. M\u1eadt m\u00e3 b\u1ea5t \u0111\u1ed1i x\u1ee9ng, c\u00f2n \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 m\u1eadt m\u00e3 kh\u00f3a c\u00f4ng khai, s\u1eed d\u1ee5ng c\u00e1c kh\u00f3a kh\u00e1c nhau \u0111\u1ec3 m\u00e3 h\u00f3a v\u00e0 gi\u1ea3i m\u00e3, mang l\u1ea1i t\u00ednh b\u1ea3o m\u1eadt n\u00e2ng cao. M\u1eadt m\u00e3 sau l\u01b0\u1ee3ng t\u1eed ch\u1ee7 y\u1ebfu li\u00ean quan \u0111\u1ebfn c\u00e1c s\u01a1 \u0111\u1ed3 m\u1eadt m\u00e3 b\u1ea5t \u0111\u1ed1i x\u1ee9ng kh\u00e1ng l\u01b0\u1ee3ng t\u1eed.<\/p>\n<\/li>\n<\/ol>\n<h2>C\u00e1c quan \u0111i\u1ec3m v\u00e0 c\u00f4ng ngh\u1ec7 c\u1ee7a t\u01b0\u01a1ng lai li\u00ean quan \u0111\u1ebfn m\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed<\/h2>\n<p>Khi c\u00f4ng ngh\u1ec7 \u0111i\u1ec7n to\u00e1n l\u01b0\u1ee3ng t\u1eed ti\u1ebfn b\u1ed9, vi\u1ec7c \u00e1p d\u1ee5ng m\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed d\u1ef1 ki\u1ebfn s\u1ebd t\u0103ng l\u00ean. Nghi\u00ean c\u1ee9u v\u00e0 ph\u00e1t tri\u1ec3n \u0111ang di\u1ec5n ra nh\u1eb1m m\u1ee5c \u0111\u00edch c\u1ea3i ti\u1ebfn c\u00e1c thu\u1eadt to\u00e1n hi\u1ec7n c\u00f3 v\u00e0 kh\u00e1m ph\u00e1 c\u00e1c ph\u01b0\u01a1ng ph\u00e1p ti\u1ebfp c\u1eadn m\u1edbi \u0111\u1ec3 \u0111\u1ea3m b\u1ea3o t\u00ednh b\u1ea3o m\u1eadt kh\u00e1ng l\u01b0\u1ee3ng t\u1eed m\u1ea1nh m\u1ebd. C\u00e1c c\u01a1 quan ti\u00eau chu\u1ea9n h\u00f3a, ch\u1eb3ng h\u1ea1n nh\u01b0 NIST, \u0111ang t\u00edch c\u1ef1c \u0111\u00e1nh gi\u00e1 v\u00e0 ch\u1ee9ng th\u1ef1c c\u00e1c thu\u1eadt to\u00e1n m\u00e3 h\u00f3a h\u1eadu l\u01b0\u1ee3ng t\u1eed, \u0111i\u1ec1u n\u00e0y s\u1ebd th\u00fac \u0111\u1ea9y s\u1ef1 t\u00edch h\u1ee3p c\u1ee7a ch\u00fang v\u00e0o c\u00e1c h\u1ec7 th\u1ed1ng kh\u00e1c nhau.<\/p>\n<h2>C\u00e1ch s\u1eed d\u1ee5ng ho\u1eb7c li\u00ean k\u1ebft m\u00e1y ch\u1ee7 proxy v\u1edbi m\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed<\/h2>\n<p>M\u00e1y ch\u1ee7 proxy \u0111\u00f3ng m\u1ed9t vai tr\u00f2 quan tr\u1ecdng trong vi\u1ec7c b\u1ea3o m\u1eadt v\u00e0 \u1ea9n danh l\u01b0u l\u01b0\u1ee3ng truy c\u1eadp internet. Khi \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng c\u00f9ng v\u1edbi m\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed, m\u00e1y ch\u1ee7 proxy c\u00f3 th\u1ec3 th\u00eam m\u1ed9t l\u1edbp b\u1ea3o m\u1eadt b\u1ed5 sung b\u1eb1ng c\u00e1ch m\u00e3 h\u00f3a v\u00e0 gi\u1ea3i m\u00e3 d\u1eef li\u1ec7u b\u1eb1ng thu\u1eadt to\u00e1n kh\u00e1ng l\u01b0\u1ee3ng t\u1eed. T\u00ednh n\u0103ng b\u1ea3o m\u1eadt n\u00e2ng cao n\u00e0y \u0111\u1ea3m b\u1ea3o r\u1eb1ng c\u00e1c k\u00eanh li\u00ean l\u1ea1c gi\u1eefa ng\u01b0\u1eddi d\u00f9ng v\u00e0 m\u00e1y ch\u1ee7 proxy v\u1eabn \u0111\u01b0\u1ee3c b\u1ea3o v\u1ec7 ngay c\u1ea3 khi c\u00f3 s\u1ef1 hi\u1ec7n di\u1ec7n c\u1ee7a c\u00e1c \u0111\u1ed1i th\u1ee7 l\u01b0\u1ee3ng t\u1eed ti\u1ec1m n\u0103ng.<\/p>\n<h2>Li\u00ean k\u1ebft li\u00ean quan<\/h2>\n<p>\u0110\u1ec3 bi\u1ebft th\u00eam th\u00f4ng tin v\u1ec1 m\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed, b\u1ea1n c\u00f3 th\u1ec3 tham kh\u1ea3o c\u00e1c t\u00e0i nguy\u00ean sau:<\/p>\n<ul>\n<li><a href=\"https:\/\/csrc.nist.gov\/Projects\/Post-Quantum-Cryptography\" target=\"_new\" rel=\"noopener nofollow\">Ti\u00eau chu\u1ea9n h\u00f3a m\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed c\u1ee7a NIST<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Post-quantum_cryptography\" target=\"_new\" rel=\"noopener nofollow\">M\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed tr\u00ean Wikipedia<\/a><\/li>\n<li><a href=\"https:\/\/pqcrypto.org\/\" target=\"_new\" rel=\"noopener nofollow\">H\u1ed9i ngh\u1ecb th\u1ebf gi\u1edbi h\u1eadu l\u01b0\u1ee3ng t\u1eed<\/a><\/li>\n<\/ul>\n<p>Khi l\u0129nh v\u1ef1c m\u1eadt m\u00e3 h\u1eadu l\u01b0\u1ee3ng t\u1eed ti\u1ebfp t\u1ee5c ph\u00e1t tri\u1ec3n, vi\u1ec7c c\u1eadp nh\u1eadt th\u00f4ng tin v\u1ec1 nh\u1eefng ph\u00e1t tri\u1ec3n m\u1edbi nh\u1ea5t v\u00e0 c\u00e1c ph\u01b0\u01a1ng ph\u00e1p hay nh\u1ea5t l\u00e0 \u0111i\u1ec1u c\u1ea7n thi\u1ebft \u0111\u1ec3 \u0111\u1ea3m b\u1ea3o an ninh d\u1eef li\u1ec7u trong m\u1ed9t t\u01b0\u01a1ng lai \u0111\u1ecbnh h\u01b0\u1edbng l\u01b0\u1ee3ng t\u1eed.<\/p>","protected":false},"featured_media":478483,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-478482","wiki","type-wiki","status-publish","has-post-thumbnail","hentry"],"acf":{"faq_title":"Frequently Asked Questions about <mark>Post-Quantum Cryptography: Safeguarding the Future of Data Security<\/mark>","faq_items":[{"question":"What is Post-quantum cryptography?","answer":"<p>Post-quantum cryptography is an advanced cryptographic approach designed to protect sensitive information and communication channels from attacks by quantum computers. Unlike traditional cryptographic schemes, post-quantum cryptography utilizes mathematical structures that remain secure even in the presence of powerful quantum algorithms.<\/p>"},{"question":"When did the concept of Post-quantum cryptography originate?","answer":"<p>The concept of post-quantum cryptography emerged in the early 1990s when researchers discovered quantum algorithms that could efficiently solve certain cryptographic problems. Mathematician Daniel Bernstein initiated the exploration of cryptographic algorithms that could resist quantum attacks, leading to the development of post-quantum cryptography.<\/p>"},{"question":"How does Post-quantum cryptography work?","answer":"<p>Post-quantum cryptographic algorithms leverage complex mathematical structures, such as lattice-based cryptography and code-based cryptography, to achieve data security. These algorithms transform plaintext into ciphertext in a way that is extremely difficult for attackers, both classical and quantum, to reverse without the proper decryption key.<\/p>"},{"question":"What are the key features of Post-quantum cryptography?","answer":"<p>Post-quantum cryptography offers several key features, including quantum resistance, compatibility with existing cryptographic systems, long-term security, enhanced public-key cryptography, and a diverse range of mathematical foundations for different security requirements.<\/p>"},{"question":"What types of Post-quantum cryptography exist?","answer":"<p>Post-quantum cryptography includes various types of algorithms, such as lattice-based (e.g., NTRU, Kyber), code-based (e.g., McEliece, RQC), hash-based (e.g., XMSS, SPHINCS), and multivariate polynomial (e.g., Rainbow, UOV) cryptographic schemes. Each type has distinct strengths and applications.<\/p>"},{"question":"How can Post-quantum cryptography be used?","answer":"<p>Post-quantum cryptography can be used to secure communication channels, provide digital signatures for document authentication, and facilitate secure key exchange between parties. It ensures data security in the face of quantum attacks.<\/p>"},{"question":"What challenges are associated with using Post-quantum cryptography?","answer":"<p>The adoption of post-quantum cryptography may present challenges such as potential performance issues, standardization, and key management during migration from classical to post-quantum cryptographic systems.<\/p>"},{"question":"How does Post-quantum cryptography compare to Quantum Cryptography?","answer":"<p>Quantum cryptography, also known as quantum key distribution (QKD), focuses on secure communication using quantum principles. While quantum cryptography provides unconditional security for key exchange, post-quantum cryptography is designed to resist quantum attacks.<\/p>"},{"question":"What is the future of Post-quantum cryptography?","answer":"<p>As quantum computing technology advances, the adoption of post-quantum cryptography is expected to grow. Ongoing research and development aim to refine existing algorithms and explore new approaches to ensure robust quantum-resistant security.<\/p>"},{"question":"How can proxy servers be associated with Post-quantum cryptography?","answer":"<p>Proxy servers can work alongside post-quantum cryptography to enhance online security. By encrypting and decrypting data using quantum-resistant algorithms, proxy servers add an extra layer of protection to communication channels, safeguarding sensitive information from potential quantum adversaries.<\/p>"}]},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki\/478482","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki"}],"about":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/types\/wiki"}],"version-history":[{"count":0,"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki\/478482\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/media\/478483"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/media?parent=478482"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}